Base field: \(\Q(\sqrt{-39}) \)
Generator \(a\), with minimal polynomial \(x^2 - x + 10\); class number \(4\).
Form
| Weight: | 2 | |
| Level: | 192.4 = \( \left(24, 8 a + 8\right) \) | |
| Level norm: | 192 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | no, but is a twist of the base change of a form over \(\mathbb{Q}\) | |
| Newspace: | 2.0.39.1-192.4 (dimension 8) | |
| 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 = \( \left(3, a + 1\right) \) | \( 1 \) |
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 = \( \left(5, a\right) \) | \( -4 \) |
| \( 5 \) | 5.2 = \( \left(5, a + 4\right) \) | \( 4 \) |
| \( 11 \) | 11.1 = \( \left(11, a + 3\right) \) | \( 2 \) |
| \( 11 \) | 11.2 = \( \left(11, a + 7\right) \) | \( -2 \) |
| \( 13 \) | 13.1 = \( \left(13, a + 6\right) \) | \( -6 \) |
| \( 41 \) | 41.1 = \( \left(41, a + 8\right) \) | \( 0 \) |
| \( 41 \) | 41.2 = \( \left(41, a + 32\right) \) | \( 0 \) |
| \( 43 \) | 43.1 = \( \left(-2 a + 3\right) \) | \( -4 \) |
| \( 43 \) | 43.2 = \( \left(2 a + 1\right) \) | \( -4 \) |
| \( 47 \) | 47.1 = \( \left(47, a + 16\right) \) | \( -2 \) |
| \( 47 \) | 47.2 = \( \left(47, a + 30\right) \) | \( 2 \) |
| \( 49 \) | 49.1 = \( \left(7\right) \) | \( 10 \) |
| \( 59 \) | 59.1 = \( \left(59, a + 21\right) \) | \( 14 \) |
| \( 59 \) | 59.2 = \( \left(59, a + 37\right) \) | \( -14 \) |
| \( 61 \) | 61.1 = \( \left(61, a + 24\right) \) | \( 2 \) |
| \( 61 \) | 61.2 = \( \left(61, a + 36\right) \) | \( 2 \) |
| \( 71 \) | 71.1 = \( \left(71, a + 11\right) \) | \( 6 \) |
| \( 71 \) | 71.2 = \( \left(71, a + 59\right) \) | \( -6 \) |
| \( 79 \) | 79.1 = \( \left(79, a + 17\right) \) | \( 0 \) |
| \( 79 \) | 79.2 = \( \left(79, a + 61\right) \) | \( 0 \) |