Base field: \(\Q(\sqrt{-7}) \)
Generator \(a\), with minimal polynomial \(x^2 - x + 2\); class number \(1\).
Form
Weight: | 2 | |
Level: | 16128.5 = \( \left(-96 a + 48\right) \) | |
Level norm: | 16128 | |
Dimension: | 1 | |
CM: | no | |
Base change: | yes | 336.2.a.e , 2352.2.a.c |
Newspace: | 2.0.7.1-16128.5 (dimension 18) | |
Sign of functional equation: | $+1$ | |
Analytic rank: | \(0\) | |
L-ratio: | 3/2 |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
\( 2 \) | 2.1 = \( \left(a\right) \) | \( 1 \) |
\( 2 \) | 2.2 = \( \left(-a + 1\right) \) | \( 1 \) |
\( 7 \) | 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.
$N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
---|---|---|
\( 11 \) | 11.1 = \( \left(-2 a + 3\right) \) | \( 0 \) |
\( 11 \) | 11.2 = \( \left(2 a + 1\right) \) | \( 0 \) |
\( 23 \) | 23.1 = \( \left(-2 a + 5\right) \) | \( 4 \) |
\( 23 \) | 23.2 = \( \left(2 a + 3\right) \) | \( 4 \) |
\( 25 \) | 25.1 = \( \left(5\right) \) | \( -6 \) |
\( 29 \) | 29.1 = \( \left(-4 a + 1\right) \) | \( -10 \) |
\( 29 \) | 29.2 = \( \left(4 a - 3\right) \) | \( -10 \) |
\( 37 \) | 37.1 = \( \left(-4 a + 5\right) \) | \( 6 \) |
\( 37 \) | 37.2 = \( \left(4 a + 1\right) \) | \( 6 \) |
\( 43 \) | 43.1 = \( \left(-2 a + 7\right) \) | \( 4 \) |
\( 43 \) | 43.2 = \( \left(2 a + 5\right) \) | \( 4 \) |
\( 53 \) | 53.1 = \( \left(-4 a - 3\right) \) | \( -10 \) |
\( 53 \) | 53.2 = \( \left(4 a - 7\right) \) | \( -10 \) |
\( 67 \) | 67.1 = \( \left(-6 a + 1\right) \) | \( -12 \) |
\( 67 \) | 67.2 = \( \left(6 a - 5\right) \) | \( -12 \) |
\( 71 \) | 71.1 = \( \left(-2 a + 9\right) \) | \( 12 \) |
\( 71 \) | 71.2 = \( \left(2 a + 7\right) \) | \( 12 \) |
\( 79 \) | 79.1 = \( \left(-6 a + 7\right) \) | \( 8 \) |
\( 79 \) | 79.2 = \( \left(6 a + 1\right) \) | \( 8 \) |
\( 107 \) | 107.1 = \( \left(-2 a + 11\right) \) | \( 0 \) |