Base field: \(\Q(\sqrt{-2491}) \)
Generator \(a\), with minimal polynomial \(x^2 - x + 623\); class number \(12\).
Form
| Weight: | 2 | |
| Level: | 4.1 = \( \left(2\right) \) | |
| Level norm: | 4 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | no, but is a twist of the base change of a form over \(\mathbb{Q}\) | |
| Newspace: | 2.0.2491.1-4.1 (dimension 8) | |
| Sign of functional equation: | $-1$ | |
| Analytic rank: | odd |
Associated elliptic curves
This Bianchi newform is associated to the isogeny class 2.0.2491.1-4.1-d of elliptic curves.Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 4 \) | 4.1 = \( \left(2\right) \) | \( 1 \) |
Hecke eigenvalues
The Hecke eigenvalue field is $\Q$. The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 26 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 = \( \left(5, a + 1\right) \) | \( 2 \) |
| \( 5 \) | 5.2 = \( \left(5, a + 3\right) \) | \( -2 \) |
| \( 7 \) | 7.1 = \( \left(7, a\right) \) | \( 2 \) |
| \( 7 \) | 7.2 = \( \left(7, a + 6\right) \) | \( 2 \) |
| \( 9 \) | 9.1 = \( \left(3\right) \) | \( 5 \) |
| \( 17 \) | 17.1 = \( \left(17, a + 2\right) \) | \( 3 \) |
| \( 17 \) | 17.2 = \( \left(17, a + 14\right) \) | \( 3 \) |
| \( 19 \) | 19.1 = \( \left(19, a + 6\right) \) | \( -1 \) |
| \( 19 \) | 19.2 = \( \left(19, a + 12\right) \) | \( 1 \) |
| \( 23 \) | 23.1 = \( \left(23, a + 9\right) \) | \( -9 \) |
| \( 23 \) | 23.2 = \( \left(23, a + 13\right) \) | \( 9 \) |
| \( 31 \) | 31.1 = \( \left(31, a + 9\right) \) | \( 0 \) |
| \( 31 \) | 31.2 = \( \left(31, a + 21\right) \) | \( 0 \) |
| \( 37 \) | 37.1 = \( \left(37, a + 2\right) \) | \( -7 \) |
| \( 37 \) | 37.2 = \( \left(37, a + 34\right) \) | \( -7 \) |
| \( 41 \) | 41.1 = \( \left(41, a + 12\right) \) | \( 0 \) |
| \( 41 \) | 41.2 = \( \left(41, a + 28\right) \) | \( 0 \) |
| \( 47 \) | 47.1 = \( \left(47, a + 23\right) \) | \( 12 \) |
| \( 53 \) | 53.1 = \( \left(53, a + 26\right) \) | \( -14 \) |
| \( 59 \) | 59.1 = \( \left(59, a + 19\right) \) | \( 0 \) |