Base field: \(\Q(\sqrt{-79}) \)
Generator \(a\), with minimal polynomial \(x^2 - x + 20\); class number \(5\).
Form
| Weight: | 2 | |
| Level: | 38.2 = \( \left(38, a + 30\right) \) | |
| Level norm: | 38 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | no | |
| Newspace: | 2.0.79.1-38.2 (dimension 5) | |
| Sign of functional equation: | $+1$ | |
| Analytic rank: | \(0\) | |
| L-ratio: | 5/2 |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 2 \) | 2.1 = \( \left(2, a\right) \) | \( 1 \) |
| \( 19 \) | 19.2 = \( \left(19, a + 11\right) \) | \( -1 \) |
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.
| $N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
|---|---|---|
| \( 2 \) | 2.2 = \( \left(2, a + 1\right) \) | \( 1 \) |
| \( 5 \) | 5.1 = \( \left(5, a\right) \) | \( -2 \) |
| \( 5 \) | 5.2 = \( \left(5, a + 4\right) \) | \( 0 \) |
| \( 9 \) | 9.1 = \( \left(3\right) \) | \( 2 \) |
| \( 11 \) | 11.1 = \( \left(11, a + 1\right) \) | \( 4 \) |
| \( 11 \) | 11.2 = \( \left(11, a + 9\right) \) | \( 0 \) |
| \( 13 \) | 13.1 = \( \left(13, a + 2\right) \) | \( -2 \) |
| \( 13 \) | 13.2 = \( \left(13, a + 10\right) \) | \( -6 \) |
| \( 19 \) | 19.1 = \( \left(19, a + 7\right) \) | \( -6 \) |
| \( 23 \) | 23.1 = \( \left(23, a + 8\right) \) | \( -4 \) |
| \( 23 \) | 23.2 = \( \left(23, a + 14\right) \) | \( 2 \) |
| \( 31 \) | 31.1 = \( \left(31, a + 6\right) \) | \( 4 \) |
| \( 31 \) | 31.2 = \( \left(31, a + 24\right) \) | \( -8 \) |
| \( 49 \) | 49.1 = \( \left(7\right) \) | \( 10 \) |
| \( 67 \) | 67.1 = \( \left(67, a + 25\right) \) | \( 8 \) |
| \( 67 \) | 67.2 = \( \left(67, a + 41\right) \) | \( -4 \) |
| \( 73 \) | 73.1 = \( \left(73, a + 16\right) \) | \( 10 \) |
| \( 73 \) | 73.2 = \( \left(73, a + 56\right) \) | \( 14 \) |
| \( 79 \) | 79.1 = \( \left(-2 a + 1\right) \) | \( 16 \) |
| \( 83 \) | 83.1 = \( \left(-2 a + 3\right) \) | \( -4 \) |