Base field: \(\Q(\sqrt{-5}) \)
Generator \(a\), with minimal polynomial \(x^2 + 5\); class number \(2\).
Form
| Weight: | 2 | |
| Level: | 90.2 = \( \left(30, 3 a + 15\right) \) | |
| Level norm: | 90 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | yes | 150.2.a.b , 240.2.a.b |
| Newspace: | 2.0.20.1-90.2 (dimension 2) | |
| Sign of functional equation: | $+1$ | |
| Analytic rank: | \(0\) | |
| L-ratio: | 1/2 |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 2 \) | 2.1 = \( \left(2, a + 1\right) \) | \( -1 \) |
| \( 3 \) | 3.1 = \( \left(3, a + 1\right) \) | \( 1 \) |
| \( 3 \) | 3.2 = \( \left(3, a + 2\right) \) | \( 1 \) |
| \( 5 \) | 5.1 = \( \left(-a\right) \) | \( 1 \) |
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.
| $N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
|---|---|---|
| \( 7 \) | 7.1 = \( \left(7, a + 3\right) \) | \( 4 \) |
| \( 7 \) | 7.2 = \( \left(7, a + 4\right) \) | \( 4 \) |
| \( 23 \) | 23.1 = \( \left(23, a + 8\right) \) | \( 0 \) |
| \( 23 \) | 23.2 = \( \left(23, a + 15\right) \) | \( 0 \) |
| \( 29 \) | 29.1 = \( \left(-2 a + 3\right) \) | \( -6 \) |
| \( 29 \) | 29.2 = \( \left(2 a + 3\right) \) | \( -6 \) |
| \( 41 \) | 41.1 = \( \left(a + 6\right) \) | \( -6 \) |
| \( 41 \) | 41.2 = \( \left(a - 6\right) \) | \( -6 \) |
| \( 43 \) | 43.1 = \( \left(43, a + 9\right) \) | \( 4 \) |
| \( 43 \) | 43.2 = \( \left(43, a + 34\right) \) | \( 4 \) |
| \( 47 \) | 47.1 = \( \left(47, a + 18\right) \) | \( 0 \) |
| \( 47 \) | 47.2 = \( \left(47, a + 29\right) \) | \( 0 \) |
| \( 61 \) | 61.1 = \( \left(-3 a + 4\right) \) | \( -10 \) |
| \( 61 \) | 61.2 = \( \left(3 a + 4\right) \) | \( -10 \) |
| \( 67 \) | 67.1 = \( \left(67, a + 14\right) \) | \( 4 \) |
| \( 67 \) | 67.2 = \( \left(67, a + 53\right) \) | \( 4 \) |
| \( 83 \) | 83.1 = \( \left(83, a + 24\right) \) | \( -12 \) |
| \( 83 \) | 83.2 = \( \left(83, a + 59\right) \) | \( -12 \) |
| \( 89 \) | 89.1 = \( \left(-4 a - 3\right) \) | \( 18 \) |
| \( 89 \) | 89.2 = \( \left(4 a - 3\right) \) | \( 18 \) |