Base field: \(\Q(\sqrt{-129}) \)
Generator \(a\), with minimal polynomial \(x^2 + 129\); class number \(12\).
Form
| Weight: | 2 | |
| Level: | 24.1 = \( \left(12, 2 a + 6\right) \) | |
| Level norm: | 24 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | yes | 44376.2.a.i , 144.2.a.b |
| Newspace: | 2.0.516.1-24.1 (dimension 4) | |
| Sign of functional equation: | $-1$ | |
| Analytic rank: | \(0\) |
Associated elliptic curves
This Bianchi newform is associated to the isogeny class 2.0.516.1-24.1-d of elliptic curves.Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 2 \) | 2.1 = \( \left(2, a + 1\right) \) | \( -1 \) |
| \( 3 \) | 3.1 = \( \left(3, a\right) \) | \( -1 \) |
Hecke eigenvalues
The Hecke eigenvalue field is $\Q$. The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 25 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 = \( \left(5, a + 4\right) \) | \( 2 \) |
| \( 7 \) | 7.1 = \( \left(7, a + 2\right) \) | \( 0 \) |
| \( 7 \) | 7.2 = \( \left(7, a + 5\right) \) | \( 0 \) |
| \( 11 \) | 11.1 = \( \left(11, a + 5\right) \) | \( 4 \) |
| \( 11 \) | 11.2 = \( \left(11, a + 6\right) \) | \( 4 \) |
| \( 13 \) | 13.1 = \( \left(13, a + 1\right) \) | \( -2 \) |
| \( 13 \) | 13.2 = \( \left(13, a + 12\right) \) | \( -2 \) |
| \( 19 \) | 19.1 = \( \left(19, a + 2\right) \) | \( 4 \) |
| \( 19 \) | 19.2 = \( \left(19, a + 17\right) \) | \( 4 \) |
| \( 23 \) | 23.1 = \( \left(23, a + 3\right) \) | \( -8 \) |
| \( 23 \) | 23.2 = \( \left(23, a + 20\right) \) | \( -8 \) |
| \( 29 \) | 29.1 = \( \left(29, a + 4\right) \) | \( -6 \) |
| \( 29 \) | 29.2 = \( \left(29, a + 25\right) \) | \( -6 \) |
| \( 43 \) | 43.1 = \( \left(43, a\right) \) | \( -4 \) |
| \( 47 \) | 47.1 = \( \left(47, a + 23\right) \) | \( 0 \) |
| \( 47 \) | 47.2 = \( \left(47, a + 24\right) \) | \( 0 \) |
| \( 59 \) | 59.1 = \( \left(59, a + 15\right) \) | \( 4 \) |
| \( 59 \) | 59.2 = \( \left(59, a + 44\right) \) | \( 4 \) |
| \( 83 \) | 83.1 = \( \left(83, a + 28\right) \) | \( -4 \) |