Base field: \(\Q(\sqrt{-31}) \)
Generator \(a\), with minimal polynomial \(x^2 - x + 8\); class number \(3\).
Form
| Weight: | 2 | |
| Level: | 196.4 = \( \left(98, 2 a + 18\right) \) | |
| Level norm: | 196 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | no | |
| Newspace: | 2.0.31.1-196.4 (dimension 2) | |
| Sign of functional equation: | $+1$ | |
| Analytic rank: | \(0\) | |
| L-ratio: | 2 |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 2 \) | 2.1 = \( \left(2, a\right) \) | \( -1 \) |
| \( 2 \) | 2.2 = \( \left(2, a + 1\right) \) | \( 1 \) |
| \( 7 \) | 7.1 = \( \left(7, a + 2\right) \) | \( 1 \) |
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.
| $N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
|---|---|---|
| \( 5 \) | 5.1 = \( \left(5, a + 1\right) \) | \( 0 \) |
| \( 5 \) | 5.2 = \( \left(5, a + 3\right) \) | \( 3 \) |
| \( 7 \) | 7.2 = \( \left(7, a + 4\right) \) | \( -1 \) |
| \( 9 \) | 9.1 = \( \left(3\right) \) | \( 4 \) |
| \( 19 \) | 19.1 = \( \left(19, a + 5\right) \) | \( 8 \) |
| \( 19 \) | 19.2 = \( \left(19, a + 13\right) \) | \( -7 \) |
| \( 31 \) | 31.1 = \( \left(-2 a + 1\right) \) | \( 2 \) |
| \( 41 \) | 41.1 = \( \left(41, a + 12\right) \) | \( 6 \) |
| \( 41 \) | 41.2 = \( \left(41, a + 28\right) \) | \( 6 \) |
| \( 47 \) | 47.1 = \( \left(-2 a + 5\right) \) | \( 0 \) |
| \( 47 \) | 47.2 = \( \left(2 a + 3\right) \) | \( 3 \) |
| \( 59 \) | 59.1 = \( \left(59, a + 10\right) \) | \( 0 \) |
| \( 59 \) | 59.2 = \( \left(59, a + 48\right) \) | \( 6 \) |
| \( 67 \) | 67.1 = \( \left(-2 a + 7\right) \) | \( -7 \) |
| \( 67 \) | 67.2 = \( \left(2 a + 5\right) \) | \( -10 \) |
| \( 71 \) | 71.1 = \( \left(71, a + 26\right) \) | \( 6 \) |
| \( 71 \) | 71.2 = \( \left(71, a + 44\right) \) | \( 0 \) |
| \( 97 \) | 97.1 = \( \left(97, a + 19\right) \) | \( -16 \) |
| \( 97 \) | 97.2 = \( \left(97, a + 77\right) \) | \( -10 \) |
| \( 101 \) | 101.1 = \( \left(101, a + 37\right) \) | \( -6 \) |