Base field: \(\Q(\sqrt{-67}) \)
Generator \(a\), with minimal polynomial \(x^2 - x + 17\); class number \(1\).
Form
Weight: | 2 | |
Level: | 67.1 = \( \left(-2 a + 1\right) \) | |
Level norm: | 67 | |
Dimension: | 1 | |
CM: | no | |
Base change: | yes | 67.2.a.a , 4489.2.a.a |
Newspace: | 2.0.67.1-67.1 (dimension 5) | |
Sign of functional equation: | $+1$ | |
Analytic rank: | \(0\) | |
L-ratio: | 1520 |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
\( 67 \) | 67.1 = \( \left(-2 a + 1\right) \) | \( -1 \) |
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 = \( \left(2\right) \) | \( 0 \) |
\( 9 \) | 9.1 = \( \left(3\right) \) | \( -2 \) |
\( 17 \) | 17.1 = \( \left(-a\right) \) | \( 3 \) |
\( 17 \) | 17.2 = \( \left(a - 1\right) \) | \( 3 \) |
\( 19 \) | 19.1 = \( \left(a + 1\right) \) | \( 7 \) |
\( 19 \) | 19.2 = \( \left(a - 2\right) \) | \( 7 \) |
\( 23 \) | 23.1 = \( \left(a + 2\right) \) | \( 9 \) |
\( 23 \) | 23.2 = \( \left(a - 3\right) \) | \( 9 \) |
\( 25 \) | 25.1 = \( \left(5\right) \) | \( -6 \) |
\( 29 \) | 29.1 = \( \left(a + 3\right) \) | \( -5 \) |
\( 29 \) | 29.2 = \( \left(a - 4\right) \) | \( -5 \) |
\( 37 \) | 37.1 = \( \left(a + 4\right) \) | \( -1 \) |
\( 37 \) | 37.2 = \( \left(a - 5\right) \) | \( -1 \) |
\( 47 \) | 47.1 = \( \left(a + 5\right) \) | \( -1 \) |
\( 47 \) | 47.2 = \( \left(a - 6\right) \) | \( -1 \) |
\( 49 \) | 49.1 = \( \left(7\right) \) | \( -10 \) |
\( 59 \) | 59.1 = \( \left(a + 6\right) \) | \( 9 \) |
\( 59 \) | 59.2 = \( \left(a - 7\right) \) | \( 9 \) |
\( 71 \) | 71.1 = \( \left(-2 a + 3\right) \) | \( 0 \) |
\( 71 \) | 71.2 = \( \left(2 a + 1\right) \) | \( 0 \) |