Base field: \(\Q(\sqrt{-21}) \)
Generator \(a\), with minimal polynomial \(x^2 + 21\); class number \(4\).
Form
| Weight: | 2 | |
| Level: | 21.1 = \( \left(-a\right) \) | |
| Level norm: | 21 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | yes | 21.2.a.a , 7056.2.a.p |
| Newspace: | 2.0.84.1-21.1 (dimension 4) | |
| Sign of functional equation: | $+1$ | |
| Analytic rank: | \(0\) | |
| L-ratio: | 7/2 |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 3 \) | 3.1 = \( \left(3, a\right) \) | \( -1 \) |
| \( 7 \) | 7.1 = \( \left(7, a\right) \) | \( 1 \) |
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.
| $N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
|---|---|---|
| \( 2 \) | 2.1 = \( \left(2, a + 1\right) \) | \( -1 \) |
| \( 5 \) | 5.1 = \( \left(5, a + 2\right) \) | \( -2 \) |
| \( 5 \) | 5.2 = \( \left(5, a + 3\right) \) | \( -2 \) |
| \( 11 \) | 11.1 = \( \left(11, a + 1\right) \) | \( 4 \) |
| \( 11 \) | 11.2 = \( \left(11, a + 10\right) \) | \( 4 \) |
| \( 17 \) | 17.1 = \( \left(17, a + 8\right) \) | \( -6 \) |
| \( 17 \) | 17.2 = \( \left(17, a + 9\right) \) | \( -6 \) |
| \( 19 \) | 19.1 = \( \left(19, a + 6\right) \) | \( 4 \) |
| \( 19 \) | 19.2 = \( \left(19, a + 13\right) \) | \( 4 \) |
| \( 23 \) | 23.1 = \( \left(23, a + 5\right) \) | \( 0 \) |
| \( 23 \) | 23.2 = \( \left(23, a + 18\right) \) | \( 0 \) |
| \( 31 \) | 31.1 = \( \left(31, a + 14\right) \) | \( 0 \) |
| \( 31 \) | 31.2 = \( \left(31, a + 17\right) \) | \( 0 \) |
| \( 37 \) | 37.1 = \( \left(a + 4\right) \) | \( 6 \) |
| \( 37 \) | 37.2 = \( \left(a - 4\right) \) | \( 6 \) |
| \( 41 \) | 41.1 = \( \left(41, a + 15\right) \) | \( 2 \) |
| \( 41 \) | 41.2 = \( \left(41, a + 26\right) \) | \( 2 \) |
| \( 71 \) | 71.1 = \( \left(71, a + 11\right) \) | \( 0 \) |
| \( 71 \) | 71.2 = \( \left(71, a + 60\right) \) | \( 0 \) |
| \( 89 \) | 89.1 = \( \left(89, a + 35\right) \) | \( -14 \) |