Base field: \(\Q(\sqrt{-15}) \)
Generator \(a\), with minimal polynomial \(x^2 - x + 4\); class number \(2\).
Form
| Weight: | 2 | |
| Level: | 80.3 = \( \left(20, 4 a + 8\right) \) | |
| Level norm: | 80 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | yes | 20.2.a.a , 900.2.a.b |
| Newspace: | 2.0.15.1-80.3 (dimension 2) | |
| Sign of functional equation: | $-1$ | |
| Analytic rank: | \(0\) | |
| L-ratio: | 1/2 |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 2 \) | 2.1 = \( \left(2, a\right) \) | \( 1 \) |
| \( 2 \) | 2.2 = \( \left(2, a + 1\right) \) | \( 1 \) |
| \( 5 \) | 5.1 = \( \left(5, a + 2\right) \) | \( 1 \) |
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.
| $N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
|---|---|---|
| \( 3 \) | 3.1 = \( \left(3, a + 1\right) \) | \( -2 \) |
| \( 17 \) | 17.1 = \( \left(17, a + 5\right) \) | \( -6 \) |
| \( 17 \) | 17.2 = \( \left(17, a + 11\right) \) | \( -6 \) |
| \( 19 \) | 19.1 = \( \left(-2 a + 3\right) \) | \( -4 \) |
| \( 19 \) | 19.2 = \( \left(2 a + 1\right) \) | \( -4 \) |
| \( 23 \) | 23.1 = \( \left(23, a + 6\right) \) | \( 6 \) |
| \( 23 \) | 23.2 = \( \left(23, a + 16\right) \) | \( 6 \) |
| \( 31 \) | 31.1 = \( \left(-2 a + 5\right) \) | \( -4 \) |
| \( 31 \) | 31.2 = \( \left(2 a + 3\right) \) | \( -4 \) |
| \( 47 \) | 47.1 = \( \left(47, a + 9\right) \) | \( -6 \) |
| \( 47 \) | 47.2 = \( \left(47, a + 37\right) \) | \( -6 \) |
| \( 49 \) | 49.1 = \( \left(7\right) \) | \( -10 \) |
| \( 53 \) | 53.1 = \( \left(53, a + 20\right) \) | \( -6 \) |
| \( 53 \) | 53.2 = \( \left(53, a + 32\right) \) | \( -6 \) |
| \( 61 \) | 61.1 = \( \left(-4 a + 1\right) \) | \( 2 \) |
| \( 61 \) | 61.2 = \( \left(4 a - 3\right) \) | \( 2 \) |
| \( 79 \) | 79.1 = \( \left(-2 a + 9\right) \) | \( 8 \) |
| \( 79 \) | 79.2 = \( \left(2 a + 7\right) \) | \( 8 \) |
| \( 83 \) | 83.1 = \( \left(83, a + 31\right) \) | \( 6 \) |
| \( 83 \) | 83.2 = \( \left(83, a + 51\right) \) | \( 6 \) |