Base field: \(\Q(\sqrt{-57}) \)
Generator \(a\), with minimal polynomial \(x^2 + 57\); class number \(4\).
Form
| Weight: | 2 | |
| Level: | 81.1 = \( \left(9\right) \) | |
| Level norm: | 81 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | no, but is a twist of the base change of a form over \(\mathbb{Q}\) with coefficients in \(\mathbb{Q}(\sqrt{10})\) | 432.2.a.e , 9747.2.a.f |
| Newspace: | 2.0.228.1-81.1 (dimension 46) | |
| Sign of functional equation: | $+1$ | |
| Analytic rank: | \(0\) |
Associated elliptic curves
This Bianchi newform is associated to the isogeny class 2.0.228.1-81.1-a of elliptic curves.Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 3 \) | 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 101 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 = \( \left(2, a + 1\right) \) | \( 0 \) |
| \( 11 \) | 11.1 = \( \left(11, a + 3\right) \) | \( -1 \) |
| \( 11 \) | 11.2 = \( \left(11, a + 8\right) \) | \( 1 \) |
| \( 19 \) | 19.1 = \( \left(19, a\right) \) | \( -6 \) |
| \( 23 \) | 23.1 = \( \left(23, a + 9\right) \) | \( 2 \) |
| \( 23 \) | 23.2 = \( \left(23, a + 14\right) \) | \( -2 \) |
| \( 25 \) | 25.1 = \( \left(5\right) \) | \( 0 \) |
| \( 29 \) | 29.1 = \( \left(29, a + 1\right) \) | \( -9 \) |
| \( 29 \) | 29.2 = \( \left(29, a + 28\right) \) | \( 9 \) |
| \( 31 \) | 31.1 = \( \left(31, a + 6\right) \) | \( -3 \) |
| \( 31 \) | 31.2 = \( \left(31, a + 25\right) \) | \( -3 \) |
| \( 41 \) | 41.1 = \( \left(41, a + 5\right) \) | \( -9 \) |
| \( 41 \) | 41.2 = \( \left(41, a + 36\right) \) | \( 9 \) |
| \( 47 \) | 47.1 = \( \left(47, a + 15\right) \) | \( -1 \) |
| \( 47 \) | 47.2 = \( \left(47, a + 32\right) \) | \( 1 \) |
| \( 49 \) | 49.1 = \( \left(7\right) \) | \( 4 \) |
| \( 53 \) | 53.1 = \( \left(53, a + 7\right) \) | \( 3 \) |
| \( 53 \) | 53.2 = \( \left(53, a + 46\right) \) | \( -3 \) |
| \( 61 \) | 61.1 = \( \left(a + 2\right) \) | \( 3 \) |
| \( 61 \) | 61.2 = \( \left(a - 2\right) \) | \( 3 \) |