Base field: \(\Q(\sqrt{-71}) \)
Generator \(a\), with minimal polynomial \(x^2 - x + 18\); class number \(7\).
Form
| Weight: | 2 | |
| Level: | 36.4 = \( \left(18, 2 a\right) \) | |
| Level norm: | 36 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | no, but is a twist of the base change of a form over \(\mathbb{Q}\) | |
| Newspace: | 2.0.71.1-36.4 (dimension 3) | |
| Sign of functional equation: | $-1$ | |
| Analytic rank: | \(0\) |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 2 \) | 2.1 = \( \left(2, a\right) \) | \( 1 \) |
| \( 2 \) | 2.2 = \( \left(2, a + 1\right) \) | \( -1 \) |
| \( 3 \) | 3.1 = \( \left(3, a\right) \) | \( -1 \) |
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.
| $N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
|---|---|---|
| \( 3 \) | 3.2 = \( \left(3, a + 2\right) \) | \( -1 \) |
| \( 5 \) | 5.1 = \( \left(5, a + 1\right) \) | \( -2 \) |
| \( 5 \) | 5.2 = \( \left(5, a + 3\right) \) | \( 2 \) |
| \( 19 \) | 19.1 = \( \left(19, a + 4\right) \) | \( -1 \) |
| \( 19 \) | 19.2 = \( \left(19, a + 14\right) \) | \( -1 \) |
| \( 29 \) | 29.1 = \( \left(29, a + 12\right) \) | \( -4 \) |
| \( 29 \) | 29.2 = \( \left(29, a + 16\right) \) | \( 4 \) |
| \( 37 \) | 37.1 = \( \left(37, a + 7\right) \) | \( -8 \) |
| \( 37 \) | 37.2 = \( \left(37, a + 29\right) \) | \( -8 \) |
| \( 43 \) | 43.1 = \( \left(43, a + 15\right) \) | \( 9 \) |
| \( 43 \) | 43.2 = \( \left(43, a + 27\right) \) | \( 9 \) |
| \( 49 \) | 49.1 = \( \left(7\right) \) | \( -11 \) |
| \( 71 \) | 71.1 = \( \left(-2 a + 1\right) \) | \( 0 \) |
| \( 73 \) | 73.1 = \( \left(73, a + 20\right) \) | \( 1 \) |
| \( 73 \) | 73.2 = \( \left(73, a + 52\right) \) | \( 1 \) |
| \( 79 \) | 79.1 = \( \left(79, a + 30\right) \) | \( -4 \) |
| \( 79 \) | 79.2 = \( \left(79, a + 48\right) \) | \( -4 \) |
| \( 83 \) | 83.1 = \( \left(83, a + 28\right) \) | \( -4 \) |
| \( 83 \) | 83.2 = \( \left(83, a + 54\right) \) | \( 4 \) |
| \( 89 \) | 89.1 = \( \left(89, a + 37\right) \) | \( -15 \) |