Base field: \(\Q(\sqrt{-11}) \)
Generator \(a\), with minimal polynomial \(x^2 - x + 3\); class number \(1\).
Form
Weight: | 2 | |
Level: | 36864.2 = \( \left(192\right) \) | |
Level norm: | 36864 | |
Dimension: | 1 | |
CM: | no | |
Base change: | no, but is a twist of the base change of a form over \(\mathbb{Q}\) | |
Newspace: | 2.0.11.1-36864.2 (dimension 100) | |
Sign of functional equation: | $-1$ | |
Analytic rank: | odd |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
\( 3 \) | 3.1 = \( \left(-a\right) \) | \( -1 \) |
\( 3 \) | 3.2 = \( \left(a - 1\right) \) | \( 1 \) |
\( 4 \) | 4.1 = \( \left(2\right) \) | \( -1 \) |
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.
$N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
---|---|---|
\( 5 \) | 5.1 = \( \left(-a - 1\right) \) | \( 2 \) |
\( 5 \) | 5.2 = \( \left(a - 2\right) \) | \( 2 \) |
\( 11 \) | 11.1 = \( \left(-2 a + 1\right) \) | \( 0 \) |
\( 23 \) | 23.1 = \( \left(a + 4\right) \) | \( -4 \) |
\( 23 \) | 23.2 = \( \left(a - 5\right) \) | \( 4 \) |
\( 31 \) | 31.1 = \( \left(-3 a + 4\right) \) | \( -8 \) |
\( 31 \) | 31.2 = \( \left(3 a + 1\right) \) | \( 8 \) |
\( 37 \) | 37.1 = \( \left(-3 a - 2\right) \) | \( -2 \) |
\( 37 \) | 37.2 = \( \left(3 a - 5\right) \) | \( -2 \) |
\( 47 \) | 47.1 = \( \left(-2 a + 7\right) \) | \( 0 \) |
\( 47 \) | 47.2 = \( \left(2 a + 5\right) \) | \( 0 \) |
\( 49 \) | 49.1 = \( \left(7\right) \) | \( -10 \) |
\( 53 \) | 53.1 = \( \left(-4 a + 5\right) \) | \( -6 \) |
\( 53 \) | 53.2 = \( \left(4 a + 1\right) \) | \( -6 \) |
\( 59 \) | 59.1 = \( \left(a + 7\right) \) | \( 0 \) |
\( 59 \) | 59.2 = \( \left(a - 8\right) \) | \( 0 \) |
\( 67 \) | 67.1 = \( \left(-3 a - 5\right) \) | \( 4 \) |
\( 67 \) | 67.2 = \( \left(3 a - 8\right) \) | \( -4 \) |
\( 71 \) | 71.1 = \( \left(-5 a + 1\right) \) | \( 0 \) |
\( 71 \) | 71.2 = \( \left(5 a - 4\right) \) | \( 0 \) |