Base field: \(\Q(\sqrt{-22}) \)
Generator \(a\), with minimal polynomial \(x^2 + 22\); class number \(2\).
Form
| Weight: | 2 | |
| Level: | 176.1 = \( \left(44, 4 a\right) \) | |
| Level norm: | 176 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | yes | 7744.2.a.bc , 176.2.a.a |
| Newspace: | 2.0.88.1-176.1 (dimension 10) | |
| Sign of functional equation: | $+1$ | |
| Analytic rank: | \(\ge2\), even |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 2 \) | 2.1 = \( \left(2, a\right) \) | \( -1 \) |
| \( 11 \) | 11.1 = \( \left(11, a\right) \) | \( -1 \) |
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.
| $N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
|---|---|---|
| \( 9 \) | 9.1 = \( \left(3\right) \) | \( -5 \) |
| \( 13 \) | 13.1 = \( \left(13, a + 2\right) \) | \( -4 \) |
| \( 13 \) | 13.2 = \( \left(13, a + 11\right) \) | \( -4 \) |
| \( 19 \) | 19.1 = \( \left(19, a + 4\right) \) | \( -8 \) |
| \( 19 \) | 19.2 = \( \left(19, a + 15\right) \) | \( -8 \) |
| \( 23 \) | 23.1 = \( \left(a + 1\right) \) | \( 3 \) |
| \( 23 \) | 23.2 = \( \left(a - 1\right) \) | \( 3 \) |
| \( 25 \) | 25.1 = \( \left(5\right) \) | \( -1 \) |
| \( 29 \) | 29.1 = \( \left(29, a + 6\right) \) | \( 0 \) |
| \( 29 \) | 29.2 = \( \left(29, a + 23\right) \) | \( 0 \) |
| \( 31 \) | 31.1 = \( \left(a + 3\right) \) | \( -5 \) |
| \( 31 \) | 31.2 = \( \left(a - 3\right) \) | \( -5 \) |
| \( 43 \) | 43.1 = \( \left(43, a + 8\right) \) | \( 10 \) |
| \( 43 \) | 43.2 = \( \left(43, a + 35\right) \) | \( 10 \) |
| \( 47 \) | 47.1 = \( \left(a + 5\right) \) | \( 0 \) |
| \( 47 \) | 47.2 = \( \left(a - 5\right) \) | \( 0 \) |
| \( 49 \) | 49.1 = \( \left(7\right) \) | \( -10 \) |
| \( 61 \) | 61.1 = \( \left(61, a + 10\right) \) | \( -4 \) |
| \( 61 \) | 61.2 = \( \left(61, a + 51\right) \) | \( -4 \) |
| \( 71 \) | 71.1 = \( \left(a + 7\right) \) | \( -15 \) |