Base field: \(\Q(\sqrt{-37}) \)
Generator \(a\), with minimal polynomial \(x^2 + 37\); class number \(2\).
Form
| Weight: | 2 | |
| Level: | 98.1 = \( \left(14, 7 a + 7\right) \) | |
| Level norm: | 98 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | yes | 19166.2.a.a , 112.2.a.c |
| Newspace: | 2.0.148.1-98.1 (dimension 2) | |
| Sign of functional equation: | $-1$ | |
| Analytic rank: | \(0\) |
Associated elliptic curves
This Bianchi newform is associated to the isogeny class 2.0.148.1-98.1-b of elliptic curves.Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 2 \) | 2.1 = \( \left(2, a + 1\right) \) | \( -1 \) |
| \( 49 \) | 49.1 = \( \left(7\right) \) | \( -1 \) |
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.
| $N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
|---|---|---|
| \( 9 \) | 9.1 = \( \left(3\right) \) | \( -2 \) |
| \( 19 \) | 19.1 = \( \left(19, a + 1\right) \) | \( -2 \) |
| \( 19 \) | 19.2 = \( \left(19, a + 18\right) \) | \( -2 \) |
| \( 23 \) | 23.1 = \( \left(23, a + 3\right) \) | \( 0 \) |
| \( 23 \) | 23.2 = \( \left(23, a + 20\right) \) | \( 0 \) |
| \( 25 \) | 25.1 = \( \left(5\right) \) | \( -10 \) |
| \( 31 \) | 31.1 = \( \left(31, a + 5\right) \) | \( 4 \) |
| \( 31 \) | 31.2 = \( \left(31, a + 26\right) \) | \( 4 \) |
| \( 37 \) | 37.1 = \( \left(a\right) \) | \( 2 \) |
| \( 41 \) | 41.1 = \( \left(a + 2\right) \) | \( 6 \) |
| \( 41 \) | 41.2 = \( \left(a - 2\right) \) | \( 6 \) |
| \( 43 \) | 43.1 = \( \left(43, a + 7\right) \) | \( -8 \) |
| \( 43 \) | 43.2 = \( \left(43, a + 36\right) \) | \( -8 \) |
| \( 53 \) | 53.1 = \( \left(a + 4\right) \) | \( 6 \) |
| \( 53 \) | 53.2 = \( \left(a - 4\right) \) | \( 6 \) |
| \( 59 \) | 59.1 = \( \left(59, a + 9\right) \) | \( 6 \) |
| \( 59 \) | 59.2 = \( \left(59, a + 50\right) \) | \( 6 \) |
| \( 73 \) | 73.1 = \( \left(a + 6\right) \) | \( 2 \) |
| \( 73 \) | 73.2 = \( \left(a - 6\right) \) | \( 2 \) |
| \( 79 \) | 79.1 = \( \left(79, a + 11\right) \) | \( -8 \) |