Base field: \(\Q(\sqrt{-165}) \)
Generator \(a\), with minimal polynomial \(x^2 + 165\); class number \(8\).
Form
| Weight: | 2 | |
| Level: | 44.1 = \( \left(22, 2 a\right) \) | |
| Level norm: | 44 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | yes | 4356.2.a.j , 4400.2.a.v |
| Newspace: | 2.0.660.1-44.1 (dimension 104) | |
| Sign of functional equation: | $-1$ | |
| Analytic rank: | \(0\) |
Associated elliptic curves
This Bianchi newform is associated to the isogeny class 2.0.660.1-44.1-h of elliptic curves.Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 2 \) | 2.1 = \( \left(2, a + 1\right) \) | \( -1 \) |
| \( 11 \) | 11.1 = \( \left(11, a\right) \) | \( -1 \) |
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.
| $N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
|---|---|---|
| \( 3 \) | 3.1 = \( \left(3, a\right) \) | \( 1 \) |
| \( 5 \) | 5.1 = \( \left(5, a\right) \) | \( 3 \) |
| \( 13 \) | 13.1 = \( \left(13, a + 2\right) \) | \( 4 \) |
| \( 13 \) | 13.2 = \( \left(13, a + 11\right) \) | \( 4 \) |
| \( 19 \) | 19.1 = \( \left(19, a + 5\right) \) | \( -8 \) |
| \( 19 \) | 19.2 = \( \left(19, a + 14\right) \) | \( -8 \) |
| \( 29 \) | 29.1 = \( \left(29, a + 3\right) \) | \( 0 \) |
| \( 29 \) | 29.2 = \( \left(29, a + 26\right) \) | \( 0 \) |
| \( 41 \) | 41.1 = \( \left(41, a + 9\right) \) | \( 0 \) |
| \( 41 \) | 41.2 = \( \left(41, a + 32\right) \) | \( 0 \) |
| \( 49 \) | 49.1 = \( \left(7\right) \) | \( -10 \) |
| \( 53 \) | 53.1 = \( \left(53, a + 10\right) \) | \( 6 \) |
| \( 53 \) | 53.2 = \( \left(53, a + 43\right) \) | \( 6 \) |
| \( 59 \) | 59.1 = \( \left(59, a + 22\right) \) | \( -3 \) |
| \( 59 \) | 59.2 = \( \left(59, a + 37\right) \) | \( -3 \) |
| \( 67 \) | 67.1 = \( \left(67, a + 6\right) \) | \( -1 \) |
| \( 67 \) | 67.2 = \( \left(67, a + 61\right) \) | \( -1 \) |
| \( 71 \) | 71.1 = \( \left(71, a + 30\right) \) | \( -15 \) |
| \( 71 \) | 71.2 = \( \left(71, a + 41\right) \) | \( -15 \) |
| \( 73 \) | 73.1 = \( \left(73, a + 28\right) \) | \( 4 \) |