Base field: \(\Q(\sqrt{-209}) \)
Generator \(a\), with minimal polynomial \(x^2 + 209\); class number \(20\).
Form
| Weight: | 2 | |
| Level: | 64.1 = \( \left(8\right) \) | |
| Level norm: | 64 | |
| Dimension: | 1 | |
| CM: | $-4$ | |
| Base change: | yes | 11552.2.a.h , 3872.2.a.f |
| Newspace: | 2.0.836.1-64.1 (dimension 82) | |
| Sign of functional equation: | $+1$ | |
| Analytic rank: | \(0\) |
Associated elliptic curves
This Bianchi newform is associated to the isogeny class 2.0.836.1-64.1-a of elliptic curves.Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 2 \) | 2.1 = \( \left(2, a + 1\right) \) | \( 1 \) |
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.
| $N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
|---|---|---|
| \( 3 \) | 3.1 = \( \left(3, a + 1\right) \) | \( 0 \) |
| \( 3 \) | 3.2 = \( \left(3, a + 2\right) \) | \( 0 \) |
| \( 5 \) | 5.1 = \( \left(5, a + 1\right) \) | \( -2 \) |
| \( 5 \) | 5.2 = \( \left(5, a + 4\right) \) | \( -2 \) |
| \( 7 \) | 7.1 = \( \left(7, a + 1\right) \) | \( 0 \) |
| \( 7 \) | 7.2 = \( \left(7, a + 6\right) \) | \( 0 \) |
| \( 11 \) | 11.1 = \( \left(11, a\right) \) | \( 0 \) |
| \( 13 \) | 13.1 = \( \left(13, a + 5\right) \) | \( -6 \) |
| \( 13 \) | 13.2 = \( \left(13, a + 8\right) \) | \( -6 \) |
| \( 19 \) | 19.1 = \( \left(19, a\right) \) | \( 0 \) |
| \( 29 \) | 29.1 = \( \left(29, a + 9\right) \) | \( 10 \) |
| \( 29 \) | 29.2 = \( \left(29, a + 20\right) \) | \( 10 \) |
| \( 31 \) | 31.1 = \( \left(31, a + 15\right) \) | \( 0 \) |
| \( 31 \) | 31.2 = \( \left(31, a + 16\right) \) | \( 0 \) |
| \( 41 \) | 41.1 = \( \left(41, a + 18\right) \) | \( -10 \) |
| \( 41 \) | 41.2 = \( \left(41, a + 23\right) \) | \( -10 \) |
| \( 43 \) | 43.1 = \( \left(43, a + 7\right) \) | \( 0 \) |
| \( 43 \) | 43.2 = \( \left(43, a + 36\right) \) | \( 0 \) |
| \( 59 \) | 59.1 = \( \left(59, a + 26\right) \) | \( 0 \) |
| \( 59 \) | 59.2 = \( \left(59, a + 33\right) \) | \( 0 \) |