"""
  This code can be loaded, or copied and paste using cpaste, into Sage.
  It will load the data associated to the BMF, including
  the field, level, and Hecke and Atkin-Lehner eigenvalue data (if known).
"""

P = PolynomialRing(QQ, "x")
x = P.gen()
g = P([15, -1, 1])
F = NumberField(g, "a")
a = F.gen()
ZF = F.ring_of_integers()

NN = ZF.ideal((15, 5*a))

primes_array = [
(3,a),(3,a+2),(2,),(5,a),(5,a+4),(7,a+2),(7,a+4),(a+1,),(a-2,),(19,a+6),(19,a+12),(29,a+8),(29,a+20),(41,a+16),(41,a+24),(53,a+21),(53,a+31),(-2*a+1,),(a+7,),(a-8,),(79,a+19),(79,a+59),(107,a+17),(107,a+89),(11,),(127,a+51),(127,a+75),(137,a+53),(137,a+83),(-3*a+4,),(3*a+1,),(-3*a+7,),(3*a+4,),(167,a+64),(167,a+102),(13,),(181,a+79),(181,a+101),(193,a+41),(193,a+151),(a+13,),(a-14,),(199,a+54),(199,a+144),(-3*a-8,),(3*a-11,),(239,a+26),(239,a+212),(241,a+34),(241,a+206),(251,a+72),(251,a+178),(257,a+27),(257,a+229),(263,a+48),(263,a+214),(271,a+117),(271,a+153),(277,a+106),(277,a+170),(281,a+126),(281,a+154),(293,a+85),(293,a+207),(307,a+127),(307,a+179),(311,a+46),(311,a+264),(-4*a-7,),(4*a-11,),(331,a+40),(331,a+290),(359,a+82),(359,a+276),(-3*a-14,),(3*a-17,),(379,a+33),(379,a+345),(-2*a+19,),(2*a+17,),(5*a+2,),(5*a-7,),(433,a+80),(433,a+352),(-3*a+19,),(3*a+16,),(449,a+36),(449,a+412),(-4*a+17,),(4*a+13,),(-5*a+13,),(-5*a-8,),(487,a+130),(487,a+356),(491,a+58),(491,a+432),(499,a+38),(499,a+460),(a+22,),(a-23,)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [1, 0, -1, 1, 1, 0, 4, -6, 2, 4, 4, -6, 2, 6, -2, 6, 14, 12, 0, -8, 0, 8, 4, 16, 10, 12, -16, -22, -6, 4, -4, -20, 24, 12, 24, -2, 2, 2, -6, -14, -2, 22, -8, 24, -24, -20, 0, -16, 2, 2, 12, -28, -30, 18, -16, 20, -8, 0, -18, 14, -22, 10, -26, 14, -12, 16, 24, 0, 6, 22, 28, -20, -24, -8, -34, 14, -12, -20, 4, -16, -6, -14, -30, -6, -24, -16, -10, -2, 10, 2, 0, 32, 12, 8, -12, 12, -36, -20, -18, -10]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal((3, a))] = -1
AL_eigenvalues[ZF.ideal((5, a))] = -1
AL_eigenvalues[ZF.ideal((5, a + 4))] = -1

# EXAMPLE:
# pp = ZF.ideal(2).factor()[0][0]
# hecke_eigenvalues[pp]