-
hmf_forms • Show schema
{'deg': 3, 'dimension': 1, 'disc': 961, 'field_bad_primes': [31], 'field_label': '3.3.961.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.961.1-8.1-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [2], 'level_ideal': '[8, 2, 2]', 'level_label': '8.1', 'level_norm': 8, 'parallel_weight': 2, 'short_label': '8.1-b', 'weight': '[2, 2, 2]'} -
hmf_hecke • Show schema
{'AL_eigenvalues': [['[2, 2, 1/2*w^2 - 1/2*w - 4]', 1], ['[2, 2, 1/2*w^2 + 1/2*w - 3]', -1], ['[2, 2, -w + 1]', 1]], 'hecke_eigenvalues': [-1, 1, -1, 0, 0, 0, 4, -6, -6, 6, 8, 0, 0, 0, 2, 2, 14, -6, 6, -18, -10, 14, 2, -6, 6, -6, 2, 2, 14, 6, -4, -4, 20, 8, 8, 8, 2, 14, 2, -4, -4, 20, -18, 6, -6, -24, -24, 24, -16, -16, 32, -22, 26, -10, -6, -6, -30, 20, -28, -4, 24, -24, 24, 2, 2, -22, -16, 26, -10, -22, -34, 14, 14, 18, 30, 6, -12, 12, -36, 26, 14, -34, -6, -30, -30, -22, -10, -10, 18, -30, -18, -16, 32, 32, 12, -12, 36, -28, -28, -4, -30, 30, 18, -36, -12, -12, 18, -6, 18, 44, 20, -28, -4, 44, -28, 0, 48, -48, 18, -18, 18, 36, 36, -12, -12, 12, 12, -10, -10, 38, 24, 24, -24, 6, -42, 6, -42, -6, -6, 50, 2, 14, 24, -24, -24, -10, 26, -22, 20, -52, -4, -4, -4, -52, 30, -30, 30, 6, 54, -30, -42, -30, -18, -16, -16, 32], 'hecke_polynomial': 'x', 'label': '3.3.961.1-8.1-b'} -
hmf_fields • Show schema
{'degree': 3, 'discriminant': 961, 'ideals': ['[1, 1, 1]', '[2, 2, 1/2*w^2 - 1/2*w - 4]', '[2, 2, 1/2*w^2 + 1/2*w - 3]', '[2, 2, -w + 1]', '[4, 2, -w^2 + 10]', '[4, 2, 1/2*w^2 - 3/2*w]', '[4, 2, -1/2*w^2 - 3/2*w + 1]', '[4, 4, -1/2*w^2 + 1/2*w + 6]', '[4, 4, w - 3]', '[4, 4, 1/2*w^2 + 1/2*w - 1]', '[8, 2, 2]', '[8, 4, w]', '[8, 4, -1/2*w^2 + 1/2*w + 3]', '[8, 4, -1/2*w^2 - 1/2*w + 2]', '[8, 4, -1/2*w^2 - 1/2*w + 4]', '[8, 4, -1/2*w^2 + 1/2*w + 5]', '[8, 4, -w + 2]', '[8, 8, -w^2 + 9]', '[8, 8, -1/2*w^2 + 3/2*w + 1]', '[8, 8, -1/2*w^2 - 3/2*w + 2]', '[16, 4, w^2 - w - 8]', '[16, 4, w^2 + 2*w - 4]', '[16, 4, -1/2*w^2 + 5/2*w - 1]', '[16, 4, w^2 + w - 6]', '[16, 4, 3/2*w^2 - 1/2*w - 14]', '[16, 4, -2*w + 2]', '[16, 8, 1/2*w^2 + 1/2*w - 6]', '[16, 8, 1/2*w^2 + 1/2*w]', '[16, 8, -1/2*w^2 + 1/2*w + 1]', '[16, 8, -w - 2]', '[16, 8, w - 4]', '[16, 8, 1/2*w^2 - 1/2*w - 7]', '[16, 16, w + 1]', '[16, 16, 1/2*w^2 - 1/2*w - 2]', '[16, 16, 1/2*w^2 + 1/2*w - 5]', '[23, 23, -w^2 + w + 7]', '[23, 23, w^2 + w - 7]', '[23, 23, -2*w + 1]', '[27, 3, 3]', '[29, 29, -w^2 - 3*w + 1]', '[29, 29, w^2 - 3*w + 1]', '[29, 29, -2*w^2 + 21]', '[31, 31, -3*w^2 + w + 31]', '[32, 4, -2*w^2 + 20]', '[32, 4, w^2 - 3*w]', '[32, 4, -w^2 - 3*w + 2]', '[32, 8, -w^2 + 8]', '[32, 8, -1/2*w^2 + 3/2*w - 2]', '[32, 8, -w^2 + w + 12]', '[32, 8, 1/2*w^2 + 3/2*w - 3]', '[32, 8, 2*w - 6]', '[32, 8, -w^2 + 12]', '[32, 8, -1/2*w^2 - 3/2*w - 1]', '[32, 8, 1/2*w^2 - 3/2*w - 2]', '[32, 8, w^2 + w - 2]', '[32, 16, 1/2*w^2 + 1/2*w - 8]', '[32, 16, 3/2*w^2 + 5/2*w - 7]', '[32, 16, w + 4]', '[32, 16, -1/2*w^2 + 1/2*w - 1]', '[32, 16, 1/2*w^2 - 7/2*w + 2]', '[32, 16, -2*w^2 + w + 18]', '[32, 32, 2*w^2 - w - 19]', '[32, 32, -3/2*w^2 - 5/2*w + 6]', '[32, 32, -1/2*w^2 + 7/2*w - 3]', '[46, 46, -w^2 + 4*w - 1]', '[46, 46, -5/2*w^2 + 1/2*w + 24]', '[46, 46, 1/2*w^2 + 5/2*w - 3]', '[46, 46, -w^2 + 2*w + 5]', '[46, 46, 3/2*w^2 - 1/2*w - 17]', '[46, 46, 3/2*w^2 + 1/2*w - 12]', '[46, 46, -w^2 - 2*w + 1]', '[46, 46, 1/2*w^2 - 5/2*w + 4]', '[46, 46, -3/2*w^2 - 7/2*w + 5]', '[47, 47, 2*w - 3]', '[47, 47, w^2 + w - 5]', '[47, 47, w^2 - w - 9]', '[54, 6, 3/2*w^2 - 3/2*w - 12]', '[54, 6, 3/2*w^2 + 3/2*w - 9]', '[54, 6, -3*w + 3]', '[58, 58, -2*w^2 + w + 21]', '[58, 58, 1/2*w^2 + 1/2*w + 1]', '[58, 58, -3/2*w^2 - 5/2*w + 4]', '[58, 58, -1/2*w^2 + 5/2*w]', '[58, 58, 1/2*w^2 - 7/2*w + 5]', '[58, 58, -3/2*w^2 + 1/2*w + 13]', '[58, 58, -1/2*w^2 + 1/2*w + 8]', '[58, 58, -w^2 - 2*w + 5]', '[58, 58, -w + 5]', '[61, 61, w^2 - w - 11]', '[61, 61, -w^2 - w + 3]', '[61, 61, -2*w + 5]', '[62, 62, -1/2*w^2 + 3/2*w + 3]', '[62, 62, -1/2*w^2 - 3/2*w + 4]', '[62, 62, -w^2 + 7]', '[64, 4, 4]', '[64, 8, 2*w]', '[64, 8, -w^2 + 2*w]', '[64, 8, -w^2 + w + 6]', '[64, 8, 1/2*w^2 + 5/2*w + 2]', '[64, 8, -w^2 - w + 4]', '[64, 8, -3/2*w^2 - 1/2*w + 17]', '[64, 8, -w^2 - w + 8]', '[64, 8, -w^2 + w + 10]', '[64, 8, -2*w + 4]', '[64, 16, 3/2*w^2 + 7/2*w - 2]', '[64, 16, -2*w^2 + 18]', '[64, 16, w^2 - 4*w + 4]', '[64, 16, -w^2 + 3*w + 2]', '[64, 16, -5/2*w^2 + 1/2*w + 27]', '[64, 16, -1/2*w^2 + 3/2*w + 10]', '[64, 16, -w^2 - 3*w + 4]', '[64, 16, -1/2*w^2 - 3/2*w + 11]', '[64, 16, w^2]', '[64, 32, -1/2*w^2 + 7/2*w - 4]', '[64, 32, 3/2*w^2 - 11/2*w + 1]', '[64, 32, 7/2*w^2 - 1/2*w - 34]', '[64, 32, 2*w^2 - w - 20]', '[64, 32, -3/2*w^2 - 5/2*w + 5]', '[64, 32, -2*w^2 - 5*w + 6]', '[64, 64, 3/2*w^2 + 1/2*w - 14]', '[64, 64, w^2 - 2*w - 3]', '[64, 64, 1/2*w^2 + 5/2*w - 1]', '[89, 89, w^2 - w - 1]', '[89, 89, w^2 + w - 13]', '[89, 89, -2*w - 5]', '[92, 46, -w^2 + 2*w + 2]', '[92, 46, -1/2*w^2 - 5/2*w]', '[92, 46, 1/2*w^2 + 3/2*w - 5]', '[92, 46, -1/2*w^2 + 3/2*w + 4]', '[92, 46, -1/2*w^2 - 3/2*w + 9]', '[92, 46, 1/2*w^2 - 3/2*w - 8]', '[92, 46, 3/2*w^2 + 1/2*w - 15]', '[92, 46, w^2 - 2]', '[92, 46, w^2 - 6]', '[92, 92, -w - 5]', '[92, 92, 1/2*w^2 - 7/2*w + 7]', '[92, 92, -3/2*w^2 - 5/2*w + 2]', '[92, 92, -w^2 + 13]', '[92, 92, 1/2*w^2 + 1/2*w - 9]', '[92, 92, 1/2*w^2 - 1/2*w + 2]', '[92, 92, 2*w^2 - w - 23]', '[92, 92, -1/2*w^2 + 3/2*w - 3]', '[92, 92, -1/2*w^2 - 3/2*w - 2]', '[94, 94, -3/2*w^2 + 7/2*w + 4]', '[94, 94, 1/2*w^2 + 5/2*w + 1]', '[94, 94, 3/2*w^2 + 11/2*w + 3]', '[94, 94, -3/2*w^2 - 1/2*w + 16]', '[94, 94, w^2 - 2*w - 1]', '[94, 94, -2*w^2 + 5*w - 3]', '[94, 94, -w^2 - 4*w + 3]', '[94, 94, -5/2*w^2 - 1/2*w + 23]', '[94, 94, -7/2*w^2 - 1/2*w + 40]', '[97, 97, 2*w + 7]', '[97, 97, -w^2 + w - 1]', '[97, 97, -w^2 - w + 15]', '[101, 101, -2*w - 1]', '[101, 101, w^2 - w - 5]', '[101, 101, w^2 + w - 9]', '[108, 6, -3*w^2 + 30]', '[108, 6, 3/2*w^2 - 9/2*w]', '[108, 6, -3/2*w^2 - 9/2*w + 3]', '[108, 12, -3/2*w^2 + 3/2*w + 18]', '[108, 12, 3*w - 9]', '[108, 12, 3/2*w^2 + 3/2*w - 3]', '[109, 109, w^2 + 3*w + 1]', '[109, 109, -2*w^2 + 23]', '[109, 109, -w^2 + 3*w - 3]', '[116, 58, w^2 - 2*w - 6]', '[116, 58, -1/2*w^2 - 5/2*w + 4]', '[116, 58, -1/2*w^2 + 5/2*w + 1]', '[116, 58, w^2 + 2*w - 6]', '[116, 58, w^2 - 2*w + 2]', '[116, 58, 3/2*w^2 + 1/2*w - 19]', '[116, 58, 3/2*w^2 - 1/2*w - 12]', '[116, 58, 3/2*w^2 + 1/2*w - 11]', '[116, 58, -1/2*w^2 - 5/2*w - 4]', '[116, 116, 1/2*w^2 + 5/2*w - 13]', '[116, 116, -3/2*w^2 - 9/2*w + 2]', '[116, 116, -3/2*w^2 - 1/2*w + 2]', '[116, 116, w^2 - 2*w - 15]', '[116, 116, -w^2 + 5]', '[116, 116, 1/2*w^2 + 3/2*w - 6]', '[116, 116, 1/2*w^2 - 3/2*w - 5]', '[116, 116, -3/2*w^2 + 9/2*w - 1]', '[116, 116, 3*w^2 - 31]', '[122, 122, -7/2*w^2 - 3/2*w + 29]', '[122, 122, -9/2*w^2 + 1/2*w + 48]', '[122, 122, 3/2*w^2 - 5/2*w - 9]', '[122, 122, 1/2*w^2 + 3/2*w - 8]', '[122, 122, 1/2*w^2 - 3/2*w - 7]', '[122, 122, 5/2*w^2 - 9/2*w - 12]', '[122, 122, w^2 - 3]', '[122, 122, 2*w^2 - w - 17]', '[122, 122, 2*w^2 - 7*w + 5]', '[124, 62, -w^2 - 4*w - 2]', '[124, 62, -3/2*w^2 + 7/2*w - 1]', '[124, 62, 5/2*w^2 + 1/2*w - 28]', '[124, 124, 3/2*w^2 + 3/2*w - 11]', '[124, 124, 3*w - 1]', '[124, 124, 3/2*w^2 - 3/2*w - 10]', '[125, 5, -5]', '[128, 8, 2*w^2 - 2*w - 16]', '[128, 8, 2*w^2 + 4*w - 8]', '[128, 8, -w^2 + 5*w - 2]', '[128, 8, 2*w^2 + 2*w - 12]', '[128, 8, 3*w^2 - w - 28]', '[128, 8, -4*w + 4]', '[128, 16, w^2 + w - 12]', '[128, 16, -w^2 + 6*w - 8]', '[128, 16, 3/2*w^2 - 1/2*w - 18]', '[128, 16, 7/2*w^2 - 3/2*w - 37]', '[128, 16, w^2 + w]', '[128, 16, -w^2 + w + 2]', '[128, 16, -2*w - 4]', '[128, 16, -w^2 - 2*w]', '[128, 16, 2*w - 8]', '[128, 16, w^2 - w - 14]', '[128, 16, -5/2*w^2 - 9/2*w + 6]', '[128, 16, 1/2*w^2 - 5/2*w + 5]', '[128, 32, 2*w + 2]', '[128, 32, -3/2*w^2 - 7/2*w + 6]', '[128, 32, -1/2*w^2 - 3/2*w + 7]', '[128, 32, w^2 - w - 4]', '[128, 32, 5/2*w^2 - 1/2*w - 23]', '[128, 32, w^2 - 4*w]', '[128, 32, 1/2*w^2 - 3/2*w - 6]', '[128, 32, w^2 - 4]', '[128, 32, w^2 + w - 10]', '[128, 64, 3*w - 4]', '[128, 64, -1/2*w^2 + 1/2*w + 9]', '[128, 64, -3/2*w^2 - 3/2*w + 8]', '[128, 64, -1/2*w^2 - 1/2*w - 2]', '[128, 64, 3/2*w^2 - 3/2*w - 13]', '[128, 64, w - 6]', '[128, 128, -1/2*w^2 - 7/2*w + 2]', '[128, 128, -2*w^2 - w + 17]', '[128, 128, 3/2*w^2 - 5/2*w - 7]', '[139, 139, -2*w - 3]', '[139, 139, w^2 + w - 11]', '[139, 139, w^2 - w - 3]', '[151, 151, w^2 + 3*w - 5]', '[151, 151, 2*w^2 - 17]', '[151, 151, w^2 - 3*w - 3]', '[157, 157, 4*w^2 - 39]', '[157, 157, 5*w^2 - w - 49]', '[157, 157, -2*w^2 + 6*w + 1]', '[163, 163, 3*w^2 - w - 33]', '[163, 163, w^2 - 5*w + 7]', '[163, 163, 2*w^2 + 4*w - 3]', '[178, 178, -2*w^2 + 3*w + 11]', '[178, 178, -11/2*w^2 + 7/2*w + 48]', '[178, 178, -5/2*w^2 + 3/2*w + 27]', '[178, 178, 2*w^2 + 3*w - 5]', '[178, 178, 3/2*w^2 + 7/2*w - 1]', '[178, 178, 1/2*w^2 - 9/2*w + 8]', '[178, 178, -w^2 + 4*w - 5]', '[178, 178, -5/2*w^2 + 1/2*w + 28]', '[178, 178, -1/2*w^2 - 9/2*w + 3]', '[184, 46, -2*w^2 + 2*w + 14]', '[184, 46, 2*w^2 + 2*w - 14]', '[184, 46, -4*w + 2]', '[184, 92, -w - 6]', '[184, 92, -5/2*w^2 + 3/2*w + 24]', '[184, 92, -3/2*w^2 + 3/2*w - 1]', '[184, 92, 3/2*w^2 - 3/2*w - 17]', '[184, 92, 3/2*w^2 + 3/2*w - 22]', '[184, 92, -1/2*w^2 + 1/2*w - 3]', '[184, 92, 3/2*w^2 + 3/2*w - 4]', '[184, 92, -3*w + 8]', '[184, 92, 3*w + 10]', '[184, 92, 2*w^2 + 3*w - 8]', '[184, 92, 1/2*w^2 + 7/2*w + 5]', '[184, 92, -1/2*w^2 - 1/2*w + 10]', '[184, 92, -3/2*w^2 + 5/2*w]', '[184, 92, 3/2*w^2 - 11/2*w + 5]', '[184, 92, -7/2*w^2 + 1/2*w + 38]', '[184, 92, -1/2*w^2 + 9/2*w - 5]', '[184, 92, 2*w^2 + 5*w - 2]', '[184, 92, -2*w^2 - w + 24]', '[184, 184, -1/2*w^2 + 5/2*w + 2]', '[184, 184, -5/2*w^2 - 1/2*w + 21]', '[184, 184, 3/2*w^2 - 7/2*w - 6]', '[184, 184, w^2 + 2*w - 7]', '[184, 184, -3/2*w^2 - 3/2*w + 7]', '[184, 184, w^2 + 4*w - 5]', '[184, 184, 3/2*w^2 - 1/2*w - 11]', '[184, 184, -3*w + 5]', '[184, 184, -3/2*w^2 + 3/2*w + 14]', '[188, 94, w^2 - 14]', '[188, 94, 3*w^2 - 2*w - 34]', '[188, 94, -7/2*w^2 + 29/2*w - 8]', '[188, 94, -5/2*w^2 - 7/2*w + 5]', '[188, 94, -11/2*w^2 - 25/2*w + 15]', '[188, 94, 1/2*w^2 - 3/2*w + 4]', '[188, 94, 1/2*w^2 + 3/2*w + 3]', '[188, 94, 1/2*w^2 - 11/2*w + 12]', '[188, 94, 9*w^2 - 2*w - 90]', '[188, 188, 1/2*w^2 + 13/2*w - 5]', '[188, 188, 7/2*w^2 + 5/2*w - 26]', '[188, 188, 2*w^2 - 9*w + 9]', '[188, 188, -1/2*w^2 - 5/2*w + 5]', '[188, 188, 3/2*w^2 + 1/2*w - 10]', '[188, 188, 7/2*w^2 + 15/2*w - 7]', '[188, 188, -3*w^2 + 4*w + 19]', '[188, 188, -w^2 + 2*w + 7]', '[188, 188, 11/2*w^2 - 3/2*w - 58]', '[194, 194, 7/2*w^2 - 3/2*w - 36]', '[194, 194, 3/2*w^2 + 3/2*w - 1]', '[194, 194, -3*w + 11]', '[194, 194, 7/2*w^2 - 1/2*w - 33]', '[194, 194, 3/2*w^2 - 3/2*w - 20]', '[194, 194, -2*w^2 - 5*w + 7]', '[194, 194, -5/2*w^2 - 9/2*w + 7]', '[194, 194, -3/2*w^2 + 11/2*w]', '[194, 194, w^2 - 6*w + 7]', '[202, 202, 2*w^2 - w - 1]', '[202, 202, w^2 - 6*w + 3]', '[202, 202, -w^2 - 1]', '[202, 202, -1/2*w^2 - 3/2*w + 12]', '[202, 202, -5/2*w^2 - 9/2*w + 11]', '[202, 202, -3/2*w^2 - 5/2*w + 24]', '[202, 202, -1/2*w^2 + 3/2*w + 11]', '[202, 202, -7/2*w^2 + 3/2*w + 32]', '[202, 202, -1/2*w^2 + 7/2*w + 15]', '[216, 6, 6]', '[216, 12, 3*w]', '[216, 12, -3/2*w^2 + 3/2*w + 9]', '[216, 12, -3/2*w^2 - 3/2*w + 6]', '[216, 12, -3/2*w^2 - 3/2*w + 12]', '[216, 12, -3/2*w^2 + 3/2*w + 15]', '[216, 12, -3*w + 6]', '[216, 24, -3*w^2 + 27]', '[216, 24, -3/2*w^2 + 9/2*w + 3]', '[216, 24, -3/2*w^2 - 9/2*w + 6]', '[218, 218, 5/2*w^2 + 1/2*w - 27]', '[218, 218, 3/2*w^2 - 3/2*w - 16]', '[218, 218, 3/2*w^2 - 13/2*w + 7]', '[218, 218, -3/2*w^2 + 7/2*w]', '[218, 218, -3/2*w^2 - 3/2*w + 5]', '[218, 218, 5/2*w^2 + 11/2*w - 4]', '[218, 218, 4*w^2 - w - 43]', '[218, 218, -3*w + 7]', '[218, 218, w^2 + 4*w + 1]', '[232, 58, -2*w^2 - 6*w + 2]', '[232, 58, 2*w^2 - 6*w + 2]', '[232, 58, -4*w^2 + 42]', '[232, 116, -2*w^2 - w + 18]', '[232, 116, 3/2*w^2 + 3/2*w - 20]', '[232, 116, -1/2*w^2 - 7/2*w - 7]', '[232, 116, -2*w^2 + w + 16]', '[232, 116, 2*w^2 - 7*w]', '[232, 116, -3/2*w^2 + 5/2*w - 2]', '[232, 116, -9/2*w^2 + 1/2*w + 43]', '[232, 116, 3/2*w^2 - 3/2*w - 1]', '[232, 116, -5/2*w^2 + 3/2*w + 26]', '[232, 116, 3*w + 8]', '[232, 116, 3/2*w^2 - 5/2*w - 6]', '[232, 116, 3/2*w^2 + 5/2*w - 9]', '[232, 116, -2*w^2 - w + 26]', '[232, 116, 2*w^2 + 3*w - 6]', '[232, 116, -1/2*w^2 + 9/2*w - 7]', '[232, 116, 1/2*w^2 - 7/2*w]', '[232, 116, -1/2*w^2 - 7/2*w + 1]', '[232, 116, 5/2*w^2 + 13/2*w - 8]', '[232, 232, -5/2*w^2 - 5/2*w + 17]', '[232, 232, -1/2*w^2 - 1/2*w - 3]', '[232, 232, -5/2*w^2 + 3/2*w + 25]', '[232, 232, -1/2*w^2 + 1/2*w + 10]', '[232, 232, -1/2*w^2 + 9/2*w - 6]', '[232, 232, 2*w^2 + 3*w - 7]', '[232, 232, 5*w - 3]', '[232, 232, -5/2*w^2 + 5/2*w + 18]', '[232, 232, w - 7]', '[233, 233, -5*w^2 + w + 53]', '[233, 233, -2*w^2 + 8*w - 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11/2*w + 17]', '[9952, 4976, -5/2*w^2 + 13/2*w + 35]', '[9952, 4976, 15/2*w^2 + 23/2*w - 20]', '[9952, 4976, -5/2*w^2 - 3/2*w - 7]', '[9952, 4976, -2*w^2 + 17*w - 28]', '[9952, 4976, -11*w + 20]', '[9952, 4976, -2*w^2 + 3*w + 38]', '[9952, 4976, -7/2*w^2 + 1/2*w + 50]', '[9952, 4976, 1/2*w^2 + 9/2*w - 30]', '[9952, 4976, -2*w^2 - 7*w + 36]', '[9952, 4976, 1/2*w^2 + 1/2*w + 18]', '[9952, 4976, -19/2*w^2 + 11/2*w + 101]', '[9952, 4976, 11/2*w^2 - 11/2*w - 53]', '[9952, 4976, w - 22]', '[9952, 9952, 5/2*w^2 - 25/2*w - 2]', '[9952, 9952, 1/2*w^2 + 23/2*w - 2]', '[9952, 9952, -15/2*w^2 + 5/2*w + 63]', '[9952, 9952, 6*w^2 + 5*w - 49]', '[9952, 9952, 11/2*w^2 - 13/2*w - 31]', '[9952, 9952, -3*w^2 - 6*w + 29]', '[9952, 9952, -9/2*w^2 + 3/2*w + 25]', '[9952, 9952, 5*w^2 + 10*w - 27]', '[9952, 9952, -3/2*w^2 + 15/2*w + 14]', '[9959, 9959, 20*w^2 - 2*w - 203]', '[9959, 9959, 19*w^2 - 5*w - 185]', '[9959, 9959, -11*w^2 - 3*w + 99]', '[9959, 9959, 12*w^2 + 26*w - 39]', '[9959, 9959, -10*w^2 + 89]', '[9959, 9959, -5*w^2 - 15*w + 21]', '[9959, 9959, 5*w^2 - 15*w - 11]', '[9959, 9959, -13*w^2 + 5*w + 143]', '[9959, 9959, -4*w^2 + 22*w - 33]', '[9967, 9967, 8*w^2 + 4*w - 69]', '[9967, 9967, 27*w^2 - 7*w - 267]', '[9967, 9967, -17*w^2 - 37*w + 51]', '[9974, 9974, w^2 - 8*w - 27]', '[9974, 9974, 2*w^2 + 7*w - 25]', '[9974, 9974, 6*w^2 - w - 73]', '[9974, 9974, -7/2*w^2 - 17/2*w - 4]', '[9974, 9974, 9/2*w^2 + 1/2*w - 23]', '[9974, 9974, 9/2*w^2 - 5/2*w - 8]', '[9974, 9974, -5/2*w^2 + 19/2*w - 17]', '[9974, 9974, 5/2*w^2 - 13/2*w - 24]', '[9974, 9974, 7/2*w^2 + 11/2*w - 49]', '[9986, 9986, 13/2*w^2 + 7/2*w - 44]', '[9986, 9986, 9/2*w^2 - 3/2*w - 59]', '[9986, 9986, 13/2*w^2 - 31/2*w - 15]', '[9986, 9986, -3/2*w^2 + 15/2*w - 20]', '[9986, 9986, -3*w^2 - 6*w - 5]', '[9986, 9986, 11*w^2 + 2*w - 103]', '[9986, 9986, 5*w^2 - 8*w - 35]', '[9986, 9986, 3/2*w^2 + 23/2*w - 17]', '[9986, 9986, -9/2*w^2 - 35/2*w + 12]', '[9998, 9998, -23/2*w^2 - 35/2*w + 53]', '[9998, 9998, -13/2*w^2 + 13/2*w + 56]', '[9998, 9998, 13*w - 17]', '[9998, 9998, -15/2*w^2 + 27/2*w + 40]', '[9998, 9998, -13/2*w^2 - 13/2*w + 35]', '[9998, 9998, 3*w^2 + 18*w - 19]', '[9998, 9998, -21/2*w^2 - 9/2*w + 83]', '[9998, 9998, -29/2*w^2 + 17/2*w + 132]', '[9998, 9998, -3*w^2 + 26*w - 21]'], 'label': '3.3.961.1', 'narrow_class_no': 1, 'primes': ['[2, 2, 1/2*w^2 - 1/2*w - 4]', '[2, 2, 1/2*w^2 + 1/2*w - 3]', '[2, 2, -w + 1]', '[23, 23, -w^2 + w + 7]', '[23, 23, w^2 + w - 7]', '[23, 23, -2*w + 1]', '[27, 3, 3]', '[29, 29, -w^2 - 3*w + 1]', '[29, 29, w^2 - 3*w + 1]', '[29, 29, -2*w^2 + 21]', '[31, 31, -3*w^2 + w + 31]', '[47, 47, 2*w - 3]', '[47, 47, w^2 + w - 5]', '[47, 47, w^2 - w - 9]', '[61, 61, w^2 - w - 11]', '[61, 61, -w^2 - w + 3]', '[61, 61, -2*w + 5]', '[89, 89, w^2 - w - 1]', '[89, 89, w^2 + w - 13]', '[89, 89, -2*w - 5]', '[97, 97, 2*w + 7]', '[97, 97, -w^2 + w - 1]', '[97, 97, -w^2 - w + 15]', '[101, 101, -2*w - 1]', '[101, 101, w^2 - w - 5]', '[101, 101, w^2 + w - 9]', '[109, 109, w^2 + 3*w + 1]', '[109, 109, -2*w^2 + 23]', '[109, 109, -w^2 + 3*w - 3]', '[125, 5, -5]', '[139, 139, -2*w - 3]', '[139, 139, w^2 + w - 11]', '[139, 139, w^2 - w - 3]', '[151, 151, w^2 + 3*w - 5]', '[151, 151, 2*w^2 - 17]', '[151, 151, w^2 - 3*w - 3]', '[157, 157, 4*w^2 - 39]', '[157, 157, 5*w^2 - w - 49]', '[157, 157, -2*w^2 + 6*w + 1]', '[163, 163, 3*w^2 - w - 33]', '[163, 163, w^2 - 5*w + 7]', '[163, 163, 2*w^2 + 4*w - 3]', '[233, 233, -5*w^2 + w + 53]', '[233, 233, -2*w^2 + 8*w - 7]', '[233, 233, -2*w^2 + 6*w + 3]', '[263, 263, 2*w^2 + 2*w - 11]', '[263, 263, 2*w^2 - 2*w - 17]', '[263, 263, 4*w - 5]', '[271, 271, w^2 + w + 1]', '[271, 271, w^2 - w - 15]', '[271, 271, -2*w + 9]', '[277, 277, w^2 - 5*w + 1]', '[277, 277, -3*w^2 + w + 27]', '[277, 277, 2*w^2 + 4*w - 9]', '[281, 281, 2*w^2 - 2*w + 1]', '[281, 281, -w^2 - 5*w - 5]', '[281, 281, 4*w + 13]', '[283, 283, -2*w^2 - 6*w + 3]', '[283, 283, 2*w^2 - 6*w + 1]', '[283, 283, -4*w^2 + 41]', '[311, 311, 4*w^2 - 2*w - 43]', '[311, 311, w^2 - 7*w + 11]', '[311, 311, 3*w^2 + 5*w - 7]', '[337, 337, 3*w^2 + w - 27]', '[337, 337, -w^2 - 5*w + 3]', '[337, 337, -2*w^2 + 4*w + 7]', '[343, 7, -7]', '[349, 349, 2*w^2 + 2*w - 15]', '[349, 349, -4*w + 1]', '[349, 349, 2*w^2 - 2*w - 13]', '[373, 373, w^2 - 3*w - 5]', '[373, 373, 2*w^2 - 15]', '[373, 373, w^2 + 3*w - 7]', '[401, 401, 2*w^2 - 2*w - 23]', '[401, 401, -4*w + 11]', '[401, 401, -2*w^2 - 2*w + 5]', '[419, 419, -w^2 + 7*w - 7]', '[419, 419, -4*w^2 + 2*w + 39]', '[419, 419, -3*w^2 - 5*w + 11]', '[433, 433, -4*w^2 + 4*w + 31]', '[433, 433, -4*w^2 - 4*w + 25]', '[433, 433, -3*w^2 - w + 37]', '[449, 449, -4*w^2 + 45]', '[449, 449, 2*w^2 + 6*w + 1]', '[449, 449, -2*w^2 + 6*w - 5]', '[457, 457, 4*w + 11]', '[457, 457, 2*w^2 - 2*w - 1]', '[457, 457, -2*w^2 - 2*w + 27]', '[461, 461, 2*w^2 + 2*w - 9]', '[461, 461, 4*w - 7]', '[461, 461, 2*w^2 - 2*w - 19]', '[463, 463, -w^2 + 3*w - 5]', '[463, 463, -2*w^2 + 25]', '[463, 463, -w^2 - 3*w - 3]', '[467, 467, w^2 + w - 17]', '[467, 467, -w^2 + w - 3]', '[467, 467, -2*w - 9]', '[523, 523, 2*w^2 - 2*w - 21]', '[523, 523, -2*w^2 - 2*w + 7]', '[523, 523, 4*w - 9]', '[557, 557, -4*w^2 - 8*w + 15]', '[557, 557, 2*w^2 - 10*w + 5]', '[557, 557, -6*w^2 + 2*w + 57]', '[587, 587, 5*w^2 + 13*w - 9]', '[587, 587, -4*w^2 + 14*w - 7]', '[587, 587, 9*w^2 - w - 93]', '[593, 593, 4*w^2 - 2*w - 35]', '[593, 593, w^2 - 7*w + 3]', '[593, 593, -3*w^2 - 5*w + 15]', '[619, 619, 2*w^2 - 13]', '[619, 619, w^2 + 3*w - 9]', '[619, 619, w^2 - 3*w - 7]', '[643, 643, 3*w^2 + w - 23]', '[643, 643, w^2 + 5*w - 7]', '[643, 643, 2*w^2 - 4*w - 11]', '[647, 647, w^2 + 5*w - 1]', '[647, 647, 2*w^2 - 4*w - 5]', '[647, 647, 3*w^2 + w - 29]', '[653, 653, 2*w^2 + 4*w - 1]', '[653, 653, 3*w^2 - w - 35]', '[653, 653, w^2 - 5*w + 9]', '[659, 659, -2*w^2 + 8*w - 1]', '[659, 659, -3*w^2 - 7*w + 11]', '[659, 659, 5*w^2 - w - 47]', '[683, 683, 2*w^2 + 4*w - 11]', '[683, 683, 3*w^2 - w - 25]', '[683, 683, w^2 - 5*w - 1]', '[709, 709, 7*w^2 + 17*w - 19]', '[709, 709, -2*w^2 + 10*w - 13]', '[709, 709, 9*w^2 - w - 91]', '[743, 743, 3*w^2 + 3*w - 17]', '[743, 743, 3*w^2 - 3*w - 25]', '[743, 743, 6*w - 7]', '[773, 773, -2*w^2 + 4*w + 3]', '[773, 773, 3*w^2 + w - 31]', '[773, 773, w^2 + 5*w + 1]', '[821, 821, -8*w + 5]', '[821, 821, -4*w^2 + 4*w + 29]', '[821, 821, -4*w^2 - 4*w + 27]', '[829, 829, -6*w^2 + 4*w + 53]', '[829, 829, -4*w^2 - 2*w + 51]', '[829, 829, 4*w^2 + 2*w - 49]', '[839, 839, -2*w^2 - 6*w + 9]', '[839, 839, -2*w^2 + 6*w + 5]', '[839, 839, 4*w^2 - 35]', '[853, 853, -5*w^2 + 5*w + 37]', '[853, 853, -5*w^2 - 5*w + 33]', '[853, 853, -5*w^2 + 3*w + 43]', '[883, 883, 2*w^2 - 5]', '[883, 883, w^2 - 3*w - 15]', '[883, 883, w^2 + 3*w - 17]', '[907, 907, -5*w^2 + w + 55]', '[907, 907, -3*w^2 - 7*w + 3]', '[907, 907, -2*w^2 + 8*w - 9]', '[929, 929, 2*w^2 - 2*w - 9]', '[929, 929, -4*w - 3]', '[929, 929, 2*w^2 + 2*w - 19]', '[953, 953, -2*w^2 + 12*w - 19]', '[953, 953, 7*w^2 - 3*w - 77]', '[953, 953, 5*w^2 + 9*w - 9]', '[977, 977, -3*w^2 + 11*w - 1]', '[977, 977, -4*w^2 - 10*w + 13]', '[977, 977, 7*w^2 - w - 67]', '[991, 991, w^2 - 3*w - 11]', '[991, 991, 2*w^2 - 9]', '[991, 991, w^2 + 3*w - 13]']} -
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [8, -10, -1, 1], 'conductor': 31, 'degree': 3, 'dirichlet_group': [1, 5, 25], 'disc_abs': 961, 'disc_rad': 31, 'disc_sign': 1, 'frobs': [[2, [[1, 3]]], [3, [[3, 1]]], [5, [[3, 1]]], [7, [[3, 1]]], [11, [[3, 1]]], [13, [[3, 1]]], [17, [[3, 1]]], [19, [[3, 1]]], [23, [[1, 3]]], [29, [[1, 3]]], [31, [0]], [37, [[3, 1]]], [41, [[3, 1]]], [43, [[3, 1]]], [47, [[1, 3]]], [53, [[3, 1]]], [59, [[3, 1]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [2], 'galois_label': '3T1', 'galt': 1, 'grd': 9.868272403218974, 'index': 2, 'inessentialp': [2], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.961.1', 'local_algs': ['31.3.2.1'], 'monogenic': -1, 'num_ram': 1, 'r2': 0, 'ramps': [31], 'rd': 9.86827240322, 'regulator': {'__RealLiteral__': 0, 'data': '12.1957819126', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{2} - 3 a - 1 \\)', '\\( a^{2} + 3 a - 3 \\)'], 'used_grh': False, 'zk': ['1', 'a', '1/2*a^2 - 1/2*a']}
Hilbert modular form data - 3.3.961.1-8.1-b