Base field: \(\Q(\sqrt{-91}) \)
Generator \(a\), with minimal polynomial \(x^2 - x + 23\); class number \(2\).
Form
| Weight: | 2 | |
| Level: | 121.1 = \( \left(11\right) \) | |
| Level norm: | 121 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | yes | 11.2.a.a |
| Newspace: | 2.0.91.1-121.1 (dimension 2) | |
| Sign of functional equation: | $+1$ | |
| Analytic rank: | \(0\) |
Associated elliptic curves
This Bianchi newform is associated to the isogeny class 2.0.91.1-121.1-b of elliptic curves.Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 121 \) | 121.1 = \( \left(11\right) \) | \( -1 \) |
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 = \( \left(2\right) \) | \( 0 \) |
| \( 5 \) | 5.1 = \( \left(5, a + 1\right) \) | \( 1 \) |
| \( 5 \) | 5.2 = \( \left(5, a + 3\right) \) | \( 1 \) |
| \( 7 \) | 7.1 = \( \left(7, a + 3\right) \) | \( -2 \) |
| \( 9 \) | 9.1 = \( \left(3\right) \) | \( -5 \) |
| \( 13 \) | 13.1 = \( \left(13, a + 6\right) \) | \( 4 \) |
| \( 19 \) | 19.1 = \( \left(19, a + 8\right) \) | \( 0 \) |
| \( 19 \) | 19.2 = \( \left(19, a + 10\right) \) | \( 0 \) |
| \( 23 \) | 23.1 = \( \left(a\right) \) | \( -1 \) |
| \( 23 \) | 23.2 = \( \left(a - 1\right) \) | \( -1 \) |
| \( 29 \) | 29.1 = \( \left(a + 2\right) \) | \( 0 \) |
| \( 29 \) | 29.2 = \( \left(a - 3\right) \) | \( 0 \) |
| \( 31 \) | 31.1 = \( \left(31, a + 11\right) \) | \( 7 \) |
| \( 31 \) | 31.2 = \( \left(31, a + 19\right) \) | \( 7 \) |
| \( 41 \) | 41.1 = \( \left(41, a + 13\right) \) | \( -8 \) |
| \( 41 \) | 41.2 = \( \left(41, a + 27\right) \) | \( -8 \) |
| \( 43 \) | 43.1 = \( \left(a + 4\right) \) | \( -6 \) |
| \( 43 \) | 43.2 = \( \left(a - 5\right) \) | \( -6 \) |
| \( 47 \) | 47.1 = \( \left(47, a + 17\right) \) | \( 8 \) |
| \( 47 \) | 47.2 = \( \left(47, a + 29\right) \) | \( 8 \) |
| \( 53 \) | 53.1 = \( \left(a + 5\right) \) | \( -6 \) |