Base field: \(\Q(\sqrt{-35}) \)
Generator \(a\), with minimal polynomial \(x^2 - x + 9\); class number \(2\).
Form
| Weight: | 2 | |
| Level: | 35.1 = \( \left(-2 a + 1\right) \) | |
| Level norm: | 35 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | yes | 175.2.a.b , 245.2.a.c |
| Newspace: | 2.0.35.1-35.1 (dimension 6) | |
| Sign of functional equation: | $+1$ | |
| Analytic rank: | \(0\) |
Associated elliptic curves
This Bianchi newform is associated to the isogeny class 2.0.35.1-35.1-a of elliptic curves.Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 5 \) | 5.1 = \( \left(5, a + 2\right) \) | \( -1 \) |
| \( 7 \) | 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 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.
| $N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
|---|---|---|
| \( 3 \) | 3.1 = \( \left(3, a\right) \) | \( -1 \) |
| \( 3 \) | 3.2 = \( \left(3, a + 2\right) \) | \( -1 \) |
| \( 4 \) | 4.1 = \( \left(2\right) \) | \( -4 \) |
| \( 11 \) | 11.1 = \( \left(a + 1\right) \) | \( -3 \) |
| \( 11 \) | 11.2 = \( \left(a - 2\right) \) | \( -3 \) |
| \( 13 \) | 13.1 = \( \left(13, a + 5\right) \) | \( -5 \) |
| \( 13 \) | 13.2 = \( \left(13, a + 7\right) \) | \( -5 \) |
| \( 17 \) | 17.1 = \( \left(17, a + 6\right) \) | \( -3 \) |
| \( 17 \) | 17.2 = \( \left(17, a + 10\right) \) | \( -3 \) |
| \( 29 \) | 29.1 = \( \left(a + 4\right) \) | \( 3 \) |
| \( 29 \) | 29.2 = \( \left(a - 5\right) \) | \( 3 \) |
| \( 47 \) | 47.1 = \( \left(47, a + 11\right) \) | \( -9 \) |
| \( 47 \) | 47.2 = \( \left(47, a + 35\right) \) | \( -9 \) |
| \( 71 \) | 71.1 = \( \left(-2 a + 7\right) \) | \( 0 \) |
| \( 71 \) | 71.2 = \( \left(2 a + 5\right) \) | \( 0 \) |
| \( 73 \) | 73.1 = \( \left(73, a + 14\right) \) | \( -2 \) |
| \( 73 \) | 73.2 = \( \left(73, a + 58\right) \) | \( -2 \) |
| \( 79 \) | 79.1 = \( \left(-3 a + 1\right) \) | \( -1 \) |
| \( 79 \) | 79.2 = \( \left(3 a - 2\right) \) | \( -1 \) |
| \( 83 \) | 83.1 = \( \left(83, a + 15\right) \) | \( -12 \) |