Base field: \(\Q(\sqrt{-7}) \)
Generator \(a\), with minimal polynomial \(x^2 - x + 2\); class number \(1\).
Form
| Weight: | 2 | |
| Level: | 35721.1 = \( \left(189\right) \) | |
| Level norm: | 35721 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | yes | 1323.2.a.e , 1323.2.a.f |
| Newspace: | 2.0.7.1-35721.1 (dimension 57) | |
| Sign of functional equation: | $-1$ | |
| Analytic rank: | odd |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 7 \) | 7.1 = \( \left(-2 a + 1\right) \) | \( -1 \) |
| \( 9 \) | 9.1 = \( \left(3\right) \) | \( -1 \) |
Hecke eigenvalues
The Hecke eigenvalue field is $\Q$. The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 200 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 = \( \left(a\right) \) | \( -1 \) |
| \( 2 \) | 2.2 = \( \left(-a + 1\right) \) | \( -1 \) |
| \( 11 \) | 11.1 = \( \left(-2 a + 3\right) \) | \( 5 \) |
| \( 11 \) | 11.2 = \( \left(2 a + 1\right) \) | \( 5 \) |
| \( 23 \) | 23.1 = \( \left(-2 a + 5\right) \) | \( 1 \) |
| \( 23 \) | 23.2 = \( \left(2 a + 3\right) \) | \( 1 \) |
| \( 25 \) | 25.1 = \( \left(5\right) \) | \( -1 \) |
| \( 29 \) | 29.1 = \( \left(-4 a + 1\right) \) | \( -2 \) |
| \( 29 \) | 29.2 = \( \left(4 a - 3\right) \) | \( -2 \) |
| \( 37 \) | 37.1 = \( \left(-4 a + 5\right) \) | \( 3 \) |
| \( 37 \) | 37.2 = \( \left(4 a + 1\right) \) | \( 3 \) |
| \( 43 \) | 43.1 = \( \left(-2 a + 7\right) \) | \( 6 \) |
| \( 43 \) | 43.2 = \( \left(2 a + 5\right) \) | \( 6 \) |
| \( 53 \) | 53.1 = \( \left(-4 a - 3\right) \) | \( -8 \) |
| \( 53 \) | 53.2 = \( \left(4 a - 7\right) \) | \( -8 \) |
| \( 67 \) | 67.1 = \( \left(-6 a + 1\right) \) | \( -14 \) |
| \( 67 \) | 67.2 = \( \left(6 a - 5\right) \) | \( -14 \) |
| \( 71 \) | 71.1 = \( \left(-2 a + 9\right) \) | \( -7 \) |
| \( 71 \) | 71.2 = \( \left(2 a + 7\right) \) | \( -7 \) |
| \( 79 \) | 79.1 = \( \left(-6 a + 7\right) \) | \( -10 \) |