Base field: \(\Q(\sqrt{-182}) \)
Generator \(a\), with minimal polynomial \(x^2 + 182\); class number \(12\).
Form
| Weight: | 2 | |
| Level: | 26.1 = \( \left(26, a\right) \) | |
| Level norm: | 26 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | yes | 26.2.a.a |
| Newspace: | 2.0.728.1-26.1 (dimension 8) | |
| Sign of functional equation: | $+1$ | |
| Analytic rank: | \(0\) |
Associated elliptic curves
This Bianchi newform is associated to the isogeny class 2.0.728.1-26.1-c of elliptic curves.Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 2 \) | 2.1 = \( \left(2, a\right) \) | \( 1 \) |
| \( 13 \) | 13.1 = \( \left(13, a\right) \) | \( -1 \) |
Hecke eigenvalues
The Hecke eigenvalue field is $\Q$. The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 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.
| $N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
|---|---|---|
| \( 3 \) | 3.1 = \( \left(3, a + 1\right) \) | \( 1 \) |
| \( 3 \) | 3.2 = \( \left(3, a + 2\right) \) | \( 1 \) |
| \( 7 \) | 7.1 = \( \left(7, a\right) \) | \( -1 \) |
| \( 11 \) | 11.1 = \( \left(11, a + 4\right) \) | \( 6 \) |
| \( 11 \) | 11.2 = \( \left(11, a + 7\right) \) | \( 6 \) |
| \( 23 \) | 23.1 = \( \left(23, a + 5\right) \) | \( 0 \) |
| \( 23 \) | 23.2 = \( \left(23, a + 18\right) \) | \( 0 \) |
| \( 25 \) | 25.1 = \( \left(5\right) \) | \( -1 \) |
| \( 31 \) | 31.1 = \( \left(31, a + 2\right) \) | \( -4 \) |
| \( 31 \) | 31.2 = \( \left(31, a + 29\right) \) | \( -4 \) |
| \( 37 \) | 37.1 = \( \left(37, a + 15\right) \) | \( -7 \) |
| \( 37 \) | 37.2 = \( \left(37, a + 22\right) \) | \( -7 \) |
| \( 41 \) | 41.1 = \( \left(41, a + 8\right) \) | \( 0 \) |
| \( 41 \) | 41.2 = \( \left(41, a + 33\right) \) | \( 0 \) |
| \( 47 \) | 47.1 = \( \left(47, a + 10\right) \) | \( 3 \) |
| \( 47 \) | 47.2 = \( \left(47, a + 37\right) \) | \( 3 \) |
| \( 61 \) | 61.1 = \( \left(61, a + 1\right) \) | \( 8 \) |
| \( 61 \) | 61.2 = \( \left(61, a + 60\right) \) | \( 8 \) |
| \( 67 \) | 67.1 = \( \left(67, a + 32\right) \) | \( 14 \) |
| \( 67 \) | 67.2 = \( \left(67, a + 35\right) \) | \( 14 \) |