Base field: \(\Q(\sqrt{-51}) \)
Generator \(a\), with minimal polynomial \(x^2 - x + 13\); class number \(2\).
Form
| Weight: | 2 | |
| Level: | 17.1 = \( \left(17, a + 8\right) \) | |
| Level norm: | 17 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | yes | 17.2.a.a , 2601.2.a.g |
| Newspace: | 2.0.51.1-17.1 (dimension 2) | |
| Sign of functional equation: | $+1$ | |
| Analytic rank: | \(0\) | |
| L-ratio: | 1/2 |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 17 \) | 17.1 = \( \left(17, a + 8\right) \) | \( -1 \) |
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 = \( \left(3, a + 1\right) \) | \( 0 \) |
| \( 4 \) | 4.1 = \( \left(2\right) \) | \( -3 \) |
| \( 5 \) | 5.1 = \( \left(5, a + 1\right) \) | \( -2 \) |
| \( 5 \) | 5.2 = \( \left(5, a + 3\right) \) | \( -2 \) |
| \( 11 \) | 11.1 = \( \left(11, a + 4\right) \) | \( 0 \) |
| \( 11 \) | 11.2 = \( \left(11, a + 6\right) \) | \( 0 \) |
| \( 13 \) | 13.1 = \( \left(a\right) \) | \( -2 \) |
| \( 13 \) | 13.2 = \( \left(a - 1\right) \) | \( -2 \) |
| \( 19 \) | 19.1 = \( \left(a + 2\right) \) | \( -4 \) |
| \( 19 \) | 19.2 = \( \left(a - 3\right) \) | \( -4 \) |
| \( 23 \) | 23.1 = \( \left(23, a + 7\right) \) | \( 4 \) |
| \( 23 \) | 23.2 = \( \left(23, a + 15\right) \) | \( 4 \) |
| \( 29 \) | 29.1 = \( \left(29, a + 11\right) \) | \( 6 \) |
| \( 29 \) | 29.2 = \( \left(29, a + 17\right) \) | \( 6 \) |
| \( 41 \) | 41.1 = \( \left(41, a + 10\right) \) | \( -6 \) |
| \( 41 \) | 41.2 = \( \left(41, a + 30\right) \) | \( -6 \) |
| \( 43 \) | 43.1 = \( \left(a + 5\right) \) | \( 4 \) |
| \( 43 \) | 43.2 = \( \left(a - 6\right) \) | \( 4 \) |
| \( 49 \) | 49.1 = \( \left(7\right) \) | \( 2 \) |
| \( 67 \) | 67.1 = \( \left(-2 a + 5\right) \) | \( 4 \) |