Base field: \(\Q(\sqrt{-17}) \)
Generator \(a\), with minimal polynomial \(x^2 + 17\); class number \(4\).
Form
| Weight: | 2 | |
| Level: | 159.2 = \( \left(159, a + 100\right) \) | |
| Level norm: | 159 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | no | |
| Newspace: | 2.0.68.1-159.2 (dimension 2) | |
| Sign of functional equation: | $+1$ | |
| Analytic rank: | \(\ge2\), even |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 3 \) | 3.1 = \( \left(3, a + 1\right) \) | \( 1 \) |
| \( 53 \) | 53.2 = \( \left(a - 6\right) \) | \( -1 \) |
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.
| $N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
|---|---|---|
| \( 2 \) | 2.1 = \( \left(2, a + 1\right) \) | \( -1 \) |
| \( 3 \) | 3.2 = \( \left(3, a + 2\right) \) | \( 2 \) |
| \( 7 \) | 7.1 = \( \left(7, a + 2\right) \) | \( 2 \) |
| \( 7 \) | 7.2 = \( \left(7, a + 5\right) \) | \( -2 \) |
| \( 11 \) | 11.1 = \( \left(11, a + 4\right) \) | \( -2 \) |
| \( 11 \) | 11.2 = \( \left(11, a + 7\right) \) | \( -6 \) |
| \( 13 \) | 13.1 = \( \left(13, a + 3\right) \) | \( -2 \) |
| \( 13 \) | 13.2 = \( \left(13, a + 10\right) \) | \( -2 \) |
| \( 17 \) | 17.1 = \( \left(a\right) \) | \( -6 \) |
| \( 23 \) | 23.1 = \( \left(23, a + 11\right) \) | \( 0 \) |
| \( 23 \) | 23.2 = \( \left(23, a + 12\right) \) | \( -6 \) |
| \( 25 \) | 25.1 = \( \left(5\right) \) | \( -6 \) |
| \( 31 \) | 31.1 = \( \left(31, a + 13\right) \) | \( 2 \) |
| \( 31 \) | 31.2 = \( \left(31, a + 18\right) \) | \( -4 \) |
| \( 53 \) | 53.1 = \( \left(a + 6\right) \) | \( -6 \) |
| \( 71 \) | 71.1 = \( \left(71, a + 14\right) \) | \( 6 \) |
| \( 71 \) | 71.2 = \( \left(71, a + 57\right) \) | \( 4 \) |
| \( 79 \) | 79.1 = \( \left(79, a + 33\right) \) | \( -8 \) |
| \( 79 \) | 79.2 = \( \left(79, a + 46\right) \) | \( -2 \) |
| \( 89 \) | 89.1 = \( \left(89, a + 28\right) \) | \( 10 \) |