Base Field: \(\Q(\sqrt{-7}) \)
Generator \(a\), with minimal polynomial \(x^2 - x + 2\); class number \(1\).
Form
| Weight | 2 | |
| Level | 13266.3 = \( \left(-27 a - 96\right) \) | |
| Label | 2.0.7.1-13266.3-a | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | no | |
| Newspace: | 2.0.7.1-13266.3 | (dimension 3) |
| Sign of functional equation: | -1 | |
| Analytic rank: | odd |
Hecke eigenvalues
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 2 \) | 2.1 = (\( a \)) | \( -1 \) |
| \( 2 \) | 2.2 = (\( -a + 1 \)) | \( 0 \) |
| \( 7 \) | 7.1 = (\( -2 a + 1 \)) | \( -1 \) |
| \( 9 \) | 9.1 = (\( 3 \)) | \( 1 \) |
| \( 11 \) | 11.1 = (\( -2 a + 3 \)) | \( 3 \) |
| \( 11 \) | 11.2 = (\( 2 a + 1 \)) | \( -1 \) |
| \( 23 \) | 23.1 = (\( -2 a + 5 \)) | \( 3 \) |
| \( 23 \) | 23.2 = (\( 2 a + 3 \)) | \( 0 \) |
| \( 25 \) | 25.1 = (\( 5 \)) | \( -4 \) |
| \( 29 \) | 29.1 = (\( -4 a + 1 \)) | \( 9 \) |
| \( 29 \) | 29.2 = (\( 4 a - 3 \)) | \( 9 \) |
| \( 37 \) | 37.1 = (\( -4 a + 5 \)) | \( -7 \) |
| \( 37 \) | 37.2 = (\( 4 a + 1 \)) | \( -7 \) |
| \( 43 \) | 43.1 = (\( -2 a + 7 \)) | \( -4 \) |
| \( 43 \) | 43.2 = (\( 2 a + 5 \)) | \( -4 \) |
| \( 53 \) | 53.1 = (\( -4 a - 3 \)) | \( -3 \) |
| \( 53 \) | 53.2 = (\( 4 a - 7 \)) | \( 6 \) |
| \( 67 \) | 67.1 = (\( -6 a + 1 \)) | \( 1 \) |
| \( 67 \) | 67.2 = (\( 6 a - 5 \)) | \( -7 \) |
| \( 71 \) | 71.1 = (\( -2 a + 9 \)) | \( 3 \) |
| \( 71 \) | 71.2 = (\( 2 a + 7 \)) | \( -12 \) |
| \( 79 \) | 79.1 = (\( -6 a + 7 \)) | \( -10 \) |
| \( 79 \) | 79.2 = (\( 6 a + 1 \)) | \( 2 \) |
| \( 107 \) | 107.1 = (\( -2 a + 11 \)) | \( 3 \) |
| \( 107 \) | 107.2 = (\( 2 a + 9 \)) | \( -6 \) |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 2 \) | 2.1 = (\( a \)) | \( 1 \) |
| \( 9 \) | 9.1 = (\( 3 \)) | \( -1 \) |
| \( 11 \) | 11.2 = (\( 2 a + 1 \)) | \( 1 \) |
| \( 67 \) | 67.1 = (\( -6 a + 1 \)) | \( -1 \) |