Base field: \(\Q(\sqrt{-19}) \)
Generator \(a\), with minimal polynomial \(x^2 - x + 5\); class number \(1\).
Form
Weight: | 2 | |
Level: | 275.2 = \( \left(7 a - 10\right) \) | |
Level norm: | 275 | |
Dimension: | 1 | |
CM: | no | |
Base change: | no | |
Newspace: | 2.0.19.1-275.2 (dimension 2) | |
Sign of functional equation: | $-1$ | |
Analytic rank: | odd |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
\( 5 \) | 5.1 = \( \left(-a\right) \) | \( 1 \) |
\( 11 \) | 11.2 = \( \left(a - 3\right) \) | \( 1 \) |
Hecke eigenvalues
The Hecke eigenvalue field is $\Q$. The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 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 = \( \left(2\right) \) | \( -1 \) |
\( 5 \) | 5.2 = \( \left(a - 1\right) \) | \( 2 \) |
\( 7 \) | 7.1 = \( \left(-a - 1\right) \) | \( -4 \) |
\( 7 \) | 7.2 = \( \left(a - 2\right) \) | \( 2 \) |
\( 9 \) | 9.1 = \( \left(3\right) \) | \( -4 \) |
\( 11 \) | 11.1 = \( \left(a + 2\right) \) | \( 6 \) |
\( 17 \) | 17.1 = \( \left(a + 3\right) \) | \( 2 \) |
\( 17 \) | 17.2 = \( \left(a - 4\right) \) | \( -1 \) |
\( 19 \) | 19.1 = \( \left(-2 a + 1\right) \) | \( -5 \) |
\( 23 \) | 23.1 = \( \left(-2 a + 3\right) \) | \( -6 \) |
\( 23 \) | 23.2 = \( \left(2 a + 1\right) \) | \( -1 \) |
\( 43 \) | 43.1 = \( \left(-3 a + 1\right) \) | \( -8 \) |
\( 43 \) | 43.2 = \( \left(3 a - 2\right) \) | \( 4 \) |
\( 47 \) | 47.1 = \( \left(a + 6\right) \) | \( 0 \) |
\( 47 \) | 47.2 = \( \left(a - 7\right) \) | \( 5 \) |
\( 61 \) | 61.1 = \( \left(a + 7\right) \) | \( -10 \) |
\( 61 \) | 61.2 = \( \left(a - 8\right) \) | \( 7 \) |
\( 73 \) | 73.1 = \( \left(-3 a + 7\right) \) | \( -2 \) |
\( 73 \) | 73.2 = \( \left(3 a + 4\right) \) | \( -10 \) |
\( 83 \) | 83.1 = \( \left(-2 a + 9\right) \) | \( -4 \) |