Base field: \(\Q(\sqrt{-59}) \)
Generator \(a\), with minimal polynomial \(x^2 - x + 15\); class number \(3\).
Form
| Weight: | 2 | |
| Level: | 140.4 = \( \left(-2 a - 8\right) \) | |
| Level norm: | 140 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | no | |
| Newspace: | 2.0.59.1-140.4 (dimension 1) | |
| Sign of functional equation: | $-1$ | |
| Analytic rank: | odd |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 4 \) | 4.1 = \( \left(2\right) \) | \( -1 \) |
| \( 5 \) | 5.2 = \( \left(5, a + 4\right) \) | \( 1 \) |
| \( 7 \) | 7.2 = \( \left(7, a + 4\right) \) | \( -1 \) |
Hecke eigenvalues
The Hecke eigenvalue field is $\Q$. The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 100 eigenvalues, of which 20 are currently shown below. We only show the eigenvalues $a_{\mathfrak{p}}$ for primes $\mathfrak{p}$ which do not divide the level.
| $N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
|---|---|---|
| \( 3 \) | 3.1 = \( \left(3, a\right) \) | \( -2 \) |
| \( 3 \) | 3.2 = \( \left(3, a + 2\right) \) | \( 1 \) |
| \( 5 \) | 5.1 = \( \left(5, a\right) \) | \( 0 \) |
| \( 7 \) | 7.1 = \( \left(7, a + 2\right) \) | \( -1 \) |
| \( 17 \) | 17.1 = \( \left(a + 1\right) \) | \( 0 \) |
| \( 17 \) | 17.2 = \( \left(a - 2\right) \) | \( 0 \) |
| \( 19 \) | 19.1 = \( \left(19, a + 6\right) \) | \( 2 \) |
| \( 19 \) | 19.2 = \( \left(19, a + 12\right) \) | \( 2 \) |
| \( 29 \) | 29.1 = \( \left(29, a + 8\right) \) | \( 0 \) |
| \( 29 \) | 29.2 = \( \left(29, a + 20\right) \) | \( 6 \) |
| \( 41 \) | 41.1 = \( \left(41, a + 16\right) \) | \( 0 \) |
| \( 41 \) | 41.2 = \( \left(41, a + 24\right) \) | \( 3 \) |
| \( 53 \) | 53.1 = \( \left(53, a + 21\right) \) | \( -12 \) |
| \( 53 \) | 53.2 = \( \left(53, a + 31\right) \) | \( 3 \) |
| \( 59 \) | 59.1 = \( \left(-2 a + 1\right) \) | \( -12 \) |
| \( 71 \) | 71.1 = \( \left(a + 7\right) \) | \( 0 \) |
| \( 71 \) | 71.2 = \( \left(a - 8\right) \) | \( 9 \) |
| \( 79 \) | 79.1 = \( \left(79, a + 19\right) \) | \( -1 \) |
| \( 79 \) | 79.2 = \( \left(79, a + 59\right) \) | \( -10 \) |
| \( 107 \) | 107.1 = \( \left(107, a + 17\right) \) | \( -3 \) |