Base field: \(\Q(\sqrt{-14}) \)
Generator \(a\), with minimal polynomial \(x^2 + 14\); class number \(4\).
Form
| Weight: | 2 | |
| Level: | 90.2 = \( \left(90, a + 34\right) \) | |
| Level norm: | 90 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | no | |
| Newspace: | 2.0.56.1-90.2 (dimension 6) | |
| Sign of functional equation: | $+1$ | |
| Analytic rank: | \(0\) | |
| L-ratio: | 4 |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 2 \) | 2.1 = \( \left(2, a\right) \) | \( -1 \) |
| \( 3 \) | 3.1 = \( \left(3, a + 1\right) \) | \( 1 \) |
| \( 5 \) | 5.2 = \( \left(5, a + 4\right) \) | \( -1 \) |
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.
| $N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
|---|---|---|
| \( 3 \) | 3.2 = \( \left(3, a + 2\right) \) | \( -2 \) |
| \( 5 \) | 5.1 = \( \left(5, a + 1\right) \) | \( 0 \) |
| \( 7 \) | 7.1 = \( \left(7, a\right) \) | \( -4 \) |
| \( 13 \) | 13.1 = \( \left(13, a + 5\right) \) | \( -4 \) |
| \( 13 \) | 13.2 = \( \left(13, a + 8\right) \) | \( 2 \) |
| \( 19 \) | 19.1 = \( \left(19, a + 9\right) \) | \( 2 \) |
| \( 19 \) | 19.2 = \( \left(19, a + 10\right) \) | \( 8 \) |
| \( 23 \) | 23.1 = \( \left(a + 3\right) \) | \( 0 \) |
| \( 23 \) | 23.2 = \( \left(a - 3\right) \) | \( 0 \) |
| \( 59 \) | 59.1 = \( \left(59, a + 24\right) \) | \( 6 \) |
| \( 59 \) | 59.2 = \( \left(59, a + 35\right) \) | \( 0 \) |
| \( 61 \) | 61.1 = \( \left(61, a + 13\right) \) | \( -10 \) |
| \( 61 \) | 61.2 = \( \left(61, a + 48\right) \) | \( -4 \) |
| \( 71 \) | 71.1 = \( \left(71, a + 25\right) \) | \( -12 \) |
| \( 71 \) | 71.2 = \( \left(71, a + 46\right) \) | \( 0 \) |
| \( 79 \) | 79.1 = \( \left(79, a + 12\right) \) | \( -16 \) |
| \( 79 \) | 79.2 = \( \left(79, a + 67\right) \) | \( 8 \) |
| \( 83 \) | 83.1 = \( \left(83, a + 22\right) \) | \( 0 \) |
| \( 83 \) | 83.2 = \( \left(83, a + 61\right) \) | \( 6 \) |
| \( 101 \) | 101.1 = \( \left(101, a + 17\right) \) | \( 6 \) |