Base field: \(\Q(\sqrt{-219}) \)
Generator \(a\), with minimal polynomial \(x^2 - x + 55\); class number \(4\).
Form
| Weight: | 2 | |
| Level: | 3.1 = \( \left(3, a + 1\right) \) | |
| Level norm: | 3 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | no, but is a twist of the base change of a form over \(\mathbb{Q}\) | |
| Newspace: | 2.0.219.1-3.1 (dimension 14) | |
| Sign of functional equation: | $+1$ | |
| Analytic rank: | \(0\) |
Associated elliptic curves
This Bianchi newform is associated to the isogeny class 2.0.219.1-3.1-b of elliptic curves.Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 3 \) | 3.1 = \( \left(3, a + 1\right) \) | \( -1 \) |
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.
| $N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
|---|---|---|
| \( 4 \) | 4.1 = \( \left(2\right) \) | \( -3 \) |
| \( 5 \) | 5.1 = \( \left(5, a\right) \) | \( 0 \) |
| \( 5 \) | 5.2 = \( \left(5, a + 4\right) \) | \( 0 \) |
| \( 11 \) | 11.1 = \( \left(11, a\right) \) | \( 6 \) |
| \( 11 \) | 11.2 = \( \left(11, a + 10\right) \) | \( -6 \) |
| \( 17 \) | 17.1 = \( \left(17, a + 5\right) \) | \( 4 \) |
| \( 17 \) | 17.2 = \( \left(17, a + 11\right) \) | \( -4 \) |
| \( 19 \) | 19.1 = \( \left(19, a + 1\right) \) | \( 4 \) |
| \( 19 \) | 19.2 = \( \left(19, a + 17\right) \) | \( 4 \) |
| \( 29 \) | 29.1 = \( \left(29, a + 9\right) \) | \( -8 \) |
| \( 29 \) | 29.2 = \( \left(29, a + 19\right) \) | \( 8 \) |
| \( 37 \) | 37.1 = \( \left(37, a + 7\right) \) | \( 2 \) |
| \( 37 \) | 37.2 = \( \left(37, a + 29\right) \) | \( 2 \) |
| \( 47 \) | 47.1 = \( \left(47, a + 21\right) \) | \( 2 \) |
| \( 47 \) | 47.2 = \( \left(47, a + 25\right) \) | \( -2 \) |
| \( 49 \) | 49.1 = \( \left(7\right) \) | \( 10 \) |
| \( 53 \) | 53.1 = \( \left(53, a + 14\right) \) | \( 0 \) |
| \( 53 \) | 53.2 = \( \left(53, a + 38\right) \) | \( 0 \) |
| \( 59 \) | 59.1 = \( \left(59, a + 15\right) \) | \( -10 \) |
| \( 59 \) | 59.2 = \( \left(59, a + 43\right) \) | \( 10 \) |