Base field: \(\Q(\sqrt{-43}) \)
Generator \(a\), with minimal polynomial \(x^2 - x + 11\); class number \(1\).
Form
Weight: | 2 | |
Level: | 387.1 = \( \left(-6 a + 3\right) \) | |
Level norm: | 387 | |
Dimension: | 1 | |
CM: | no | |
Base change: | yes | 5547.2.a.c , 129.2.a.a |
Newspace: | 2.0.43.1-387.1 (dimension 9) | |
Sign of functional equation: | $+1$ | |
Analytic rank: | \(\ge2\), even |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
\( 9 \) | 9.1 = \( \left(3\right) \) | \( -1 \) |
\( 43 \) | 43.1 = \( \left(-2 a + 1\right) \) | \( 1 \) |
Hecke eigenvalues
The Hecke eigenvalue field is $\Q$. The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 100 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.
$N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
---|---|---|
\( 4 \) | 4.1 = \( \left(2\right) \) | \( -4 \) |
\( 11 \) | 11.1 = \( \left(-a\right) \) | \( -5 \) |
\( 11 \) | 11.2 = \( \left(a - 1\right) \) | \( -5 \) |
\( 13 \) | 13.1 = \( \left(a + 1\right) \) | \( 3 \) |
\( 13 \) | 13.2 = \( \left(a - 2\right) \) | \( 3 \) |
\( 17 \) | 17.1 = \( \left(a + 2\right) \) | \( -3 \) |
\( 17 \) | 17.2 = \( \left(a - 3\right) \) | \( -3 \) |
\( 23 \) | 23.1 = \( \left(a + 3\right) \) | \( -1 \) |
\( 23 \) | 23.2 = \( \left(a - 4\right) \) | \( -1 \) |
\( 25 \) | 25.1 = \( \left(5\right) \) | \( -6 \) |
\( 31 \) | 31.1 = \( \left(a + 4\right) \) | \( -5 \) |
\( 31 \) | 31.2 = \( \left(a - 5\right) \) | \( -5 \) |
\( 41 \) | 41.1 = \( \left(a + 5\right) \) | \( -7 \) |
\( 41 \) | 41.2 = \( \left(a - 6\right) \) | \( -7 \) |
\( 47 \) | 47.1 = \( \left(-2 a + 3\right) \) | \( -8 \) |
\( 47 \) | 47.2 = \( \left(2 a + 1\right) \) | \( -8 \) |
\( 49 \) | 49.1 = \( \left(7\right) \) | \( -10 \) |
\( 53 \) | 53.1 = \( \left(a + 6\right) \) | \( 3 \) |
\( 53 \) | 53.2 = \( \left(a - 7\right) \) | \( 3 \) |
\( 59 \) | 59.1 = \( \left(-2 a + 5\right) \) | \( 12 \) |