Base field: \(\Q(\sqrt{-23}) \)
Generator \(a\), with minimal polynomial \(x^2 - x + 6\); class number \(3\).
Form
| Weight: | 2 | |
| Level: | 27.2 = \( \left(9, 3 a\right) \) | |
| Level norm: | 27 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | no, but is a twist of the base change of a form over \(\mathbb{Q}\) | |
| Newspace: | 2.0.23.1-27.2 (dimension 1) | |
| Sign of functional equation: | $+1$ | |
| Analytic rank: | \(0\) | |
| L-ratio: | 1 |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 3 \) | 3.1 = \( \left(3, a\right) \) | \( -1 \) |
| \( 3 \) | 3.2 = \( \left(3, a + 2\right) \) | \( 1 \) |
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.
| $N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
|---|---|---|
| \( 2 \) | 2.1 = \( \left(2, a\right) \) | \( -1 \) |
| \( 2 \) | 2.2 = \( \left(2, a + 1\right) \) | \( 1 \) |
| \( 13 \) | 13.1 = \( \left(13, a + 4\right) \) | \( 2 \) |
| \( 13 \) | 13.2 = \( \left(13, a + 8\right) \) | \( 2 \) |
| \( 23 \) | 23.1 = \( \left(-2 a + 1\right) \) | \( 0 \) |
| \( 25 \) | 25.1 = \( \left(5\right) \) | \( 6 \) |
| \( 29 \) | 29.1 = \( \left(29, a + 10\right) \) | \( -2 \) |
| \( 29 \) | 29.2 = \( \left(29, a + 18\right) \) | \( 2 \) |
| \( 31 \) | 31.1 = \( \left(31, a + 7\right) \) | \( 8 \) |
| \( 31 \) | 31.2 = \( \left(31, a + 23\right) \) | \( 8 \) |
| \( 41 \) | 41.1 = \( \left(41, a + 15\right) \) | \( -6 \) |
| \( 41 \) | 41.2 = \( \left(41, a + 25\right) \) | \( 6 \) |
| \( 47 \) | 47.1 = \( \left(47, a + 13\right) \) | \( 0 \) |
| \( 47 \) | 47.2 = \( \left(47, a + 33\right) \) | \( 0 \) |
| \( 49 \) | 49.1 = \( \left(7\right) \) | \( -2 \) |
| \( 59 \) | 59.1 = \( \left(-2 a + 7\right) \) | \( -4 \) |
| \( 59 \) | 59.2 = \( \left(2 a + 5\right) \) | \( 4 \) |
| \( 71 \) | 71.1 = \( \left(71, a + 20\right) \) | \( 8 \) |
| \( 71 \) | 71.2 = \( \left(71, a + 50\right) \) | \( -8 \) |
| \( 73 \) | 73.1 = \( \left(73, a + 29\right) \) | \( -6 \) |