Base field: \(\Q(\sqrt{-6}) \)
Generator \(a\), with minimal polynomial \(x^2 + 6\); class number \(2\).
Form
| Weight: | 2 | |
| Level: | 36.1 = \( \left(6\right) \) | |
| Level norm: | 36 | |
| Dimension: | 1 | |
| CM: | $-3$ | |
| Base change: | yes | 576.2.a.e , 36.2.a.a |
| Newspace: | 2.0.24.1-36.1 (dimension 3) | |
| Sign of functional equation: | $-1$ | |
| Analytic rank: | odd |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 2 \) | 2.1 = \( \left(2, a\right) \) | \( -1 \) |
| \( 3 \) | 3.1 = \( \left(3, a\right) \) | \( -1 \) |
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.
| $N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
|---|---|---|
| \( 5 \) | 5.1 = \( \left(5, a + 2\right) \) | \( 0 \) |
| \( 5 \) | 5.2 = \( \left(5, a + 3\right) \) | \( 0 \) |
| \( 7 \) | 7.1 = \( \left(a + 1\right) \) | \( -4 \) |
| \( 7 \) | 7.2 = \( \left(a - 1\right) \) | \( -4 \) |
| \( 11 \) | 11.1 = \( \left(11, a + 4\right) \) | \( 0 \) |
| \( 11 \) | 11.2 = \( \left(11, a + 7\right) \) | \( 0 \) |
| \( 29 \) | 29.1 = \( \left(29, a + 9\right) \) | \( 0 \) |
| \( 29 \) | 29.2 = \( \left(29, a + 20\right) \) | \( 0 \) |
| \( 31 \) | 31.1 = \( \left(a + 5\right) \) | \( -4 \) |
| \( 31 \) | 31.2 = \( \left(a - 5\right) \) | \( -4 \) |
| \( 53 \) | 53.1 = \( \left(53, a + 10\right) \) | \( 0 \) |
| \( 53 \) | 53.2 = \( \left(53, a + 43\right) \) | \( 0 \) |
| \( 59 \) | 59.1 = \( \left(59, a + 17\right) \) | \( 0 \) |
| \( 59 \) | 59.2 = \( \left(59, a + 42\right) \) | \( 0 \) |
| \( 73 \) | 73.1 = \( \left(-2 a + 7\right) \) | \( -10 \) |
| \( 73 \) | 73.2 = \( \left(2 a + 7\right) \) | \( -10 \) |
| \( 79 \) | 79.1 = \( \left(-3 a - 5\right) \) | \( -4 \) |
| \( 79 \) | 79.2 = \( \left(3 a - 5\right) \) | \( -4 \) |
| \( 83 \) | 83.1 = \( \left(83, a + 34\right) \) | \( 0 \) |
| \( 83 \) | 83.2 = \( \left(83, a + 49\right) \) | \( 0 \) |