Base field: \(\Q(\sqrt{-103}) \)
Generator \(a\), with minimal polynomial \(x^2 - x + 26\); class number \(5\).
Form
| Weight: | 2 | |
| Level: | 576.4 = \( \left(24\right) \) | |
| Level norm: | 576 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | yes | , 24.2.a.a |
| Newspace: | 2.0.103.1-576.4 (dimension 3) | |
| Sign of functional equation: | $+1$ | |
| Analytic rank: | \(0\) |
Associated elliptic curves
This Bianchi newform is associated to the isogeny class 2.0.103.1-576.4-a of elliptic curves.Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 2 \) | 2.1 = \( \left(2, a\right) \) | \( -1 \) |
| \( 2 \) | 2.2 = \( \left(2, a + 1\right) \) | \( -1 \) |
| \( 9 \) | 9.1 = \( \left(3\right) \) | \( -1 \) |
Hecke eigenvalues
The Hecke eigenvalue field is $\Q$. The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 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.
| $N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
|---|---|---|
| \( 7 \) | 7.1 = \( \left(7, a + 1\right) \) | \( 0 \) |
| \( 7 \) | 7.2 = \( \left(7, a + 5\right) \) | \( 0 \) |
| \( 13 \) | 13.1 = \( \left(13, a\right) \) | \( -2 \) |
| \( 13 \) | 13.2 = \( \left(13, a + 12\right) \) | \( -2 \) |
| \( 17 \) | 17.1 = \( \left(17, a + 6\right) \) | \( 2 \) |
| \( 17 \) | 17.2 = \( \left(17, a + 10\right) \) | \( 2 \) |
| \( 19 \) | 19.1 = \( \left(19, a + 3\right) \) | \( -4 \) |
| \( 19 \) | 19.2 = \( \left(19, a + 15\right) \) | \( -4 \) |
| \( 23 \) | 23.1 = \( \left(23, a + 4\right) \) | \( -8 \) |
| \( 23 \) | 23.2 = \( \left(23, a + 18\right) \) | \( -8 \) |
| \( 25 \) | 25.1 = \( \left(5\right) \) | \( -6 \) |
| \( 29 \) | 29.1 = \( \left(29, a + 9\right) \) | \( 6 \) |
| \( 29 \) | 29.2 = \( \left(29, a + 19\right) \) | \( 6 \) |
| \( 41 \) | 41.1 = \( \left(41, a + 7\right) \) | \( -6 \) |
| \( 41 \) | 41.2 = \( \left(41, a + 33\right) \) | \( -6 \) |
| \( 59 \) | 59.1 = \( \left(59, a + 14\right) \) | \( 4 \) |
| \( 59 \) | 59.2 = \( \left(59, a + 44\right) \) | \( 4 \) |
| \( 61 \) | 61.1 = \( \left(61, a + 21\right) \) | \( -2 \) |
| \( 61 \) | 61.2 = \( \left(61, a + 39\right) \) | \( -2 \) |
| \( 79 \) | 79.1 = \( \left(79, a + 11\right) \) | \( -8 \) |