Base field: \(\Q(\sqrt{-10}) \)
Generator \(a\), with minimal polynomial \(x^2 + 10\); class number \(2\).
Form
| Weight: | 2 | |
| Level: | 44.1 = \( \left(2 a + 2\right) \) | |
| Level norm: | 44 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | no | |
| Newspace: | 2.0.40.1-44.1 (dimension 2) | |
| Sign of functional equation: | $+1$ | |
| Analytic rank: | \(0\) |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 2 \) | 2.1 = \( \left(2, a\right) \) | \( -1 \) |
| \( 11 \) | 11.1 = \( \left(a + 1\right) \) | \( 1 \) |
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 = \( \left(5, a\right) \) | \( 3 \) |
| \( 7 \) | 7.1 = \( \left(7, a + 2\right) \) | \( 4 \) |
| \( 7 \) | 7.2 = \( \left(7, a + 5\right) \) | \( 1 \) |
| \( 9 \) | 9.1 = \( \left(3\right) \) | \( 4 \) |
| \( 11 \) | 11.2 = \( \left(a - 1\right) \) | \( -3 \) |
| \( 13 \) | 13.1 = \( \left(13, a + 4\right) \) | \( 1 \) |
| \( 13 \) | 13.2 = \( \left(13, a + 9\right) \) | \( -2 \) |
| \( 19 \) | 19.1 = \( \left(a + 3\right) \) | \( -4 \) |
| \( 19 \) | 19.2 = \( \left(a - 3\right) \) | \( 2 \) |
| \( 23 \) | 23.1 = \( \left(23, a + 6\right) \) | \( -6 \) |
| \( 23 \) | 23.2 = \( \left(23, a + 17\right) \) | \( 3 \) |
| \( 37 \) | 37.1 = \( \left(37, a + 8\right) \) | \( -2 \) |
| \( 37 \) | 37.2 = \( \left(37, a + 29\right) \) | \( -5 \) |
| \( 41 \) | 41.1 = \( \left(-2 a + 1\right) \) | \( 12 \) |
| \( 41 \) | 41.2 = \( \left(2 a + 1\right) \) | \( -3 \) |
| \( 47 \) | 47.1 = \( \left(47, a + 15\right) \) | \( -3 \) |
| \( 47 \) | 47.2 = \( \left(47, a + 32\right) \) | \( -6 \) |
| \( 53 \) | 53.1 = \( \left(53, a + 19\right) \) | \( -12 \) |
| \( 53 \) | 53.2 = \( \left(53, a + 34\right) \) | \( 6 \) |
| \( 59 \) | 59.1 = \( \left(a + 7\right) \) | \( 6 \) |