Base field: \(\Q(\sqrt{-11}) \)
Generator \(a\), with minimal polynomial \(x^2 - x + 3\); class number \(1\).
Form
| Weight: | 2 | |
| Level: | 45056.1 = \( \left(-128 a + 64\right) \) | |
| Level norm: | 45056 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | yes | 7744.2.a.a , 704.2.a.a |
| Newspace: | 2.0.11.1-45056.1 (dimension 36) | |
| Sign of functional equation: | $+1$ | |
| Analytic rank: | \(\ge2\), even |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 4 \) | 4.1 = \( \left(2\right) \) | \( 1 \) |
| \( 11 \) | 11.1 = \( \left(-2 a + 1\right) \) | \( -1 \) |
Hecke eigenvalues
The Hecke eigenvalue field is $\Q$. The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 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.
| $N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
|---|---|---|
| \( 3 \) | 3.1 = \( \left(-a\right) \) | \( -3 \) |
| \( 3 \) | 3.2 = \( \left(a - 1\right) \) | \( -3 \) |
| \( 5 \) | 5.1 = \( \left(-a - 1\right) \) | \( -1 \) |
| \( 5 \) | 5.2 = \( \left(a - 2\right) \) | \( -1 \) |
| \( 23 \) | 23.1 = \( \left(a + 4\right) \) | \( 3 \) |
| \( 23 \) | 23.2 = \( \left(a - 5\right) \) | \( 3 \) |
| \( 31 \) | 31.1 = \( \left(-3 a + 4\right) \) | \( -9 \) |
| \( 31 \) | 31.2 = \( \left(3 a + 1\right) \) | \( -9 \) |
| \( 37 \) | 37.1 = \( \left(-3 a - 2\right) \) | \( -7 \) |
| \( 37 \) | 37.2 = \( \left(3 a - 5\right) \) | \( -7 \) |
| \( 47 \) | 47.1 = \( \left(-2 a + 7\right) \) | \( 12 \) |
| \( 47 \) | 47.2 = \( \left(2 a + 5\right) \) | \( 12 \) |
| \( 49 \) | 49.1 = \( \left(7\right) \) | \( -14 \) |
| \( 53 \) | 53.1 = \( \left(-4 a + 5\right) \) | \( -2 \) |
| \( 53 \) | 53.2 = \( \left(4 a + 1\right) \) | \( -2 \) |
| \( 59 \) | 59.1 = \( \left(a + 7\right) \) | \( -9 \) |
| \( 59 \) | 59.2 = \( \left(a - 8\right) \) | \( -9 \) |
| \( 67 \) | 67.1 = \( \left(-3 a - 5\right) \) | \( 15 \) |
| \( 67 \) | 67.2 = \( \left(3 a - 8\right) \) | \( 15 \) |
| \( 71 \) | 71.1 = \( \left(-5 a + 1\right) \) | \( -3 \) |