Base field: \(\Q(\sqrt{-87}) \)
Generator \(a\), with minimal polynomial \(x^2 - x + 22\); class number \(6\).
Form
| Weight: | 2 | |
| Level: | 588.5 = \( \left(42, 14 a + 14\right) \) | |
| Level norm: | 588 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | yes | 126.2.a.a , 35322.2.a.n |
| Newspace: | 2.0.87.1-588.5 (dimension 26) | |
| Sign of functional equation: | $+1$ | |
| Analytic rank: | \(0\) |
Associated elliptic curves
This Bianchi newform is associated to the isogeny class 2.0.87.1-588.5-a of elliptic curves.Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 2 \) | 2.1 = \( \left(2, a\right) \) | \( 1 \) |
| \( 2 \) | 2.2 = \( \left(2, a + 1\right) \) | \( 1 \) |
| \( 3 \) | 3.1 = \( \left(3, a + 1\right) \) | \( -1 \) |
| \( 7 \) | 7.1 = \( \left(7, a + 2\right) \) | \( 1 \) |
| \( 7 \) | 7.2 = \( \left(7, a + 4\right) \) | \( 1 \) |
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.
| $N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
|---|---|---|
| \( 11 \) | 11.1 = \( \left(11, a\right) \) | \( 4 \) |
| \( 11 \) | 11.2 = \( \left(11, a + 10\right) \) | \( 4 \) |
| \( 13 \) | 13.1 = \( \left(13, a + 5\right) \) | \( 6 \) |
| \( 13 \) | 13.2 = \( \left(13, a + 7\right) \) | \( 6 \) |
| \( 17 \) | 17.1 = \( \left(17, a + 3\right) \) | \( -2 \) |
| \( 17 \) | 17.2 = \( \left(17, a + 13\right) \) | \( -2 \) |
| \( 25 \) | 25.1 = \( \left(5\right) \) | \( -6 \) |
| \( 29 \) | 29.1 = \( \left(29, a + 14\right) \) | \( 2 \) |
| \( 41 \) | 41.1 = \( \left(41, a + 17\right) \) | \( 6 \) |
| \( 41 \) | 41.2 = \( \left(41, a + 23\right) \) | \( 6 \) |
| \( 47 \) | 47.1 = \( \left(47, a + 8\right) \) | \( 0 \) |
| \( 47 \) | 47.2 = \( \left(47, a + 38\right) \) | \( 0 \) |
| \( 67 \) | 67.1 = \( \left(67, a + 19\right) \) | \( 4 \) |
| \( 67 \) | 67.2 = \( \left(67, a + 47\right) \) | \( 4 \) |
| \( 89 \) | 89.1 = \( \left(89, a + 12\right) \) | \( 6 \) |
| \( 89 \) | 89.2 = \( \left(89, a + 76\right) \) | \( 6 \) |
| \( 101 \) | 101.1 = \( \left(101, a + 34\right) \) | \( 2 \) |
| \( 101 \) | 101.2 = \( \left(101, a + 66\right) \) | \( 2 \) |
| \( 103 \) | 103.1 = \( \left(-2 a + 5\right) \) | \( 8 \) |
| \( 103 \) | 103.2 = \( \left(2 a + 3\right) \) | \( 8 \) |