Base field: \(\Q(\sqrt{-30}) \)
Generator \(a\), with minimal polynomial \(x^2 + 30\); class number \(4\).
Form
| Weight: | 2 | |
| Level: | 300.1 = \( \left(30, 10 a\right) \) | |
| Level norm: | 300 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | yes | 300.2.a.c , 14400.2.a.dn |
| Newspace: | 2.0.120.1-300.1 (dimension 36) | |
| Sign of functional equation: | $+1$ | |
| Analytic rank: | \(0\) |
Associated elliptic curves
This Bianchi newform is associated to the isogeny class 2.0.120.1-300.1-h of elliptic curves.Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 2 \) | 2.1 = \( \left(2, a\right) \) | \( -1 \) |
| \( 3 \) | 3.1 = \( \left(3, a\right) \) | \( -1 \) |
| \( 5 \) | 5.1 = \( \left(5, a\right) \) | \( -1 \) |
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.
| $N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
|---|---|---|
| \( 11 \) | 11.1 = \( \left(11, a + 5\right) \) | \( 6 \) |
| \( 11 \) | 11.2 = \( \left(11, a + 6\right) \) | \( 6 \) |
| \( 13 \) | 13.1 = \( \left(13, a + 3\right) \) | \( 5 \) |
| \( 13 \) | 13.2 = \( \left(13, a + 10\right) \) | \( 5 \) |
| \( 17 \) | 17.1 = \( \left(17, a + 2\right) \) | \( -6 \) |
| \( 17 \) | 17.2 = \( \left(17, a + 15\right) \) | \( -6 \) |
| \( 23 \) | 23.1 = \( \left(23, a + 4\right) \) | \( -6 \) |
| \( 23 \) | 23.2 = \( \left(23, a + 19\right) \) | \( -6 \) |
| \( 29 \) | 29.1 = \( \left(29, a + 12\right) \) | \( -6 \) |
| \( 29 \) | 29.2 = \( \left(29, a + 17\right) \) | \( -6 \) |
| \( 31 \) | 31.1 = \( \left(a + 1\right) \) | \( -1 \) |
| \( 31 \) | 31.2 = \( \left(a - 1\right) \) | \( -1 \) |
| \( 37 \) | 37.1 = \( \left(37, a + 9\right) \) | \( 2 \) |
| \( 37 \) | 37.2 = \( \left(37, a + 28\right) \) | \( 2 \) |
| \( 43 \) | 43.1 = \( \left(43, a + 20\right) \) | \( -1 \) |
| \( 43 \) | 43.2 = \( \left(43, a + 23\right) \) | \( -1 \) |
| \( 47 \) | 47.1 = \( \left(47, a + 8\right) \) | \( 6 \) |
| \( 47 \) | 47.2 = \( \left(47, a + 39\right) \) | \( 6 \) |
| \( 49 \) | 49.1 = \( \left(7\right) \) | \( -13 \) |
| \( 59 \) | 59.1 = \( \left(59, a + 18\right) \) | \( -6 \) |