Base field: \(\Q(\sqrt{-1}) \)
Generator \(i\), with minimal polynomial \(x^2 + 1\); class number \(1\).
Form
Weight: | 2 | |
Level: | 13122.1 = \( \left(81 i + 81\right) \) | |
Level norm: | 13122 | |
Dimension: | 1 | |
CM: | no | |
Base change: | yes | 1296.2.a.c , 162.2.a.a |
Newspace: | 2.0.4.1-13122.1 (dimension 4) | |
Sign of functional equation: | $-1$ | |
Analytic rank: | odd |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
\( 2 \) | 2.1 = \( \left(i + 1\right) \) | \( 1 \) |
\( 9 \) | 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.
$N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
---|---|---|
\( 5 \) | 5.1 = \( \left(-i - 2\right) \) | \( -3 \) |
\( 5 \) | 5.2 = \( \left(2 i + 1\right) \) | \( -3 \) |
\( 13 \) | 13.1 = \( \left(-2 i + 3\right) \) | \( -1 \) |
\( 13 \) | 13.2 = \( \left(2 i + 3\right) \) | \( -1 \) |
\( 17 \) | 17.1 = \( \left(i + 4\right) \) | \( -3 \) |
\( 17 \) | 17.2 = \( \left(i - 4\right) \) | \( -3 \) |
\( 29 \) | 29.1 = \( \left(-2 i + 5\right) \) | \( 9 \) |
\( 29 \) | 29.2 = \( \left(2 i + 5\right) \) | \( 9 \) |
\( 37 \) | 37.1 = \( \left(i + 6\right) \) | \( -1 \) |
\( 37 \) | 37.2 = \( \left(i - 6\right) \) | \( -1 \) |
\( 41 \) | 41.1 = \( \left(-4 i + 5\right) \) | \( 6 \) |
\( 41 \) | 41.2 = \( \left(4 i + 5\right) \) | \( 6 \) |
\( 49 \) | 49.1 = \( \left(7\right) \) | \( 2 \) |
\( 53 \) | 53.1 = \( \left(-2 i + 7\right) \) | \( -6 \) |
\( 53 \) | 53.2 = \( \left(2 i + 7\right) \) | \( -6 \) |
\( 61 \) | 61.1 = \( \left(-6 i - 5\right) \) | \( -1 \) |
\( 61 \) | 61.2 = \( \left(6 i - 5\right) \) | \( -1 \) |
\( 73 \) | 73.1 = \( \left(-3 i - 8\right) \) | \( 11 \) |
\( 73 \) | 73.2 = \( \left(3 i - 8\right) \) | \( 11 \) |
\( 89 \) | 89.1 = \( \left(-5 i + 8\right) \) | \( -3 \) |