Base field: \(\Q(\sqrt{-166}) \)
Generator \(a\), with minimal polynomial \(x^2 + 166\); class number \(10\).
Form
| Weight: | 2 | |
| Level: | 70.3 = \( \left(70, a + 38\right) \) | |
| Level norm: | 70 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | no | |
| Newspace: | 2.0.664.1-70.3 (dimension 2) | |
| Sign of functional equation: | $-1$ | |
| Analytic rank: | \(0\) |
Associated elliptic curves
This Bianchi newform is associated to the isogeny class 2.0.664.1-70.3-a of elliptic curves.Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 2 \) | 2.1 = \( \left(2, a\right) \) | \( 1 \) |
| \( 5 \) | 5.2 = \( \left(5, a + 3\right) \) | \( 1 \) |
| \( 7 \) | 7.1 = \( \left(7, a + 3\right) \) | \( 1 \) |
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.
| $N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
|---|---|---|
| \( 5 \) | 5.1 = \( \left(5, a + 2\right) \) | \( -1 \) |
| \( 7 \) | 7.2 = \( \left(7, a + 4\right) \) | \( -2 \) |
| \( 9 \) | 9.1 = \( \left(3\right) \) | \( -1 \) |
| \( 13 \) | 13.1 = \( \left(13, a + 4\right) \) | \( 1 \) |
| \( 13 \) | 13.2 = \( \left(13, a + 9\right) \) | \( 0 \) |
| \( 17 \) | 17.1 = \( \left(17, a + 2\right) \) | \( -7 \) |
| \( 17 \) | 17.2 = \( \left(17, a + 15\right) \) | \( 6 \) |
| \( 19 \) | 19.1 = \( \left(19, a + 9\right) \) | \( 5 \) |
| \( 19 \) | 19.2 = \( \left(19, a + 10\right) \) | \( -2 \) |
| \( 23 \) | 23.1 = \( \left(23, a + 8\right) \) | \( -8 \) |
| \( 23 \) | 23.2 = \( \left(23, a + 15\right) \) | \( 3 \) |
| \( 31 \) | 31.1 = \( \left(31, a + 12\right) \) | \( -2 \) |
| \( 31 \) | 31.2 = \( \left(31, a + 19\right) \) | \( 10 \) |
| \( 41 \) | 41.1 = \( \left(41, a + 11\right) \) | \( 6 \) |
| \( 41 \) | 41.2 = \( \left(41, a + 30\right) \) | \( 2 \) |
| \( 43 \) | 43.1 = \( \left(43, a + 7\right) \) | \( 4 \) |
| \( 43 \) | 43.2 = \( \left(43, a + 36\right) \) | \( -4 \) |
| \( 53 \) | 53.1 = \( \left(53, a + 24\right) \) | \( -6 \) |
| \( 53 \) | 53.2 = \( \left(53, a + 29\right) \) | \( 2 \) |
| \( 67 \) | 67.1 = \( \left(67, a + 13\right) \) | \( 8 \) |