Base field: \(\Q(\sqrt{-70}) \)
Generator \(a\), with minimal polynomial \(x^2 + 70\); class number \(4\).
Form
| Weight: | 2 | |
| Level: | 32.1 = \( \left(8, 4 a\right) \) | |
| Level norm: | 32 | |
| Dimension: | 1 | |
| CM: | $-4$ | |
| Base change: | yes | 800.2.a.d , 3136.2.a.m |
| Newspace: | 2.0.280.1-32.1 (dimension 52) | |
| Sign of functional equation: | $+1$ | |
| Analytic rank: | \(0\) |
Associated elliptic curves
This Bianchi newform is associated to the isogeny class 2.0.280.1-32.1-d of elliptic curves.Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 2 \) | 2.1 = \( \left(2, a\right) \) | \( -1 \) |
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.
| $N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
|---|---|---|
| \( 5 \) | 5.1 = \( \left(5, a\right) \) | \( 2 \) |
| \( 7 \) | 7.1 = \( \left(7, a\right) \) | \( 0 \) |
| \( 9 \) | 9.1 = \( \left(3\right) \) | \( -6 \) |
| \( 17 \) | 17.1 = \( \left(17, a + 7\right) \) | \( 2 \) |
| \( 17 \) | 17.2 = \( \left(17, a + 10\right) \) | \( 2 \) |
| \( 19 \) | 19.1 = \( \left(19, a + 5\right) \) | \( 0 \) |
| \( 19 \) | 19.2 = \( \left(19, a + 14\right) \) | \( 0 \) |
| \( 37 \) | 37.1 = \( \left(37, a + 2\right) \) | \( 2 \) |
| \( 37 \) | 37.2 = \( \left(37, a + 35\right) \) | \( 2 \) |
| \( 43 \) | 43.1 = \( \left(43, a + 4\right) \) | \( 0 \) |
| \( 43 \) | 43.2 = \( \left(43, a + 39\right) \) | \( 0 \) |
| \( 47 \) | 47.1 = \( \left(47, a + 20\right) \) | \( 0 \) |
| \( 47 \) | 47.2 = \( \left(47, a + 27\right) \) | \( 0 \) |
| \( 53 \) | 53.1 = \( \left(53, a + 6\right) \) | \( -14 \) |
| \( 53 \) | 53.2 = \( \left(53, a + 47\right) \) | \( -14 \) |
| \( 59 \) | 59.1 = \( \left(59, a + 15\right) \) | \( 0 \) |
| \( 59 \) | 59.2 = \( \left(59, a + 44\right) \) | \( 0 \) |
| \( 61 \) | 61.1 = \( \left(61, a + 28\right) \) | \( 10 \) |
| \( 61 \) | 61.2 = \( \left(61, a + 33\right) \) | \( 10 \) |
| \( 67 \) | 67.1 = \( \left(67, a + 8\right) \) | \( 0 \) |