Base Field: \(\Q(\sqrt{-7}) \)
Generator \(a\), with minimal polynomial \(x^2 - x + 2\); class number \(1\).
Form
| Weight | 2 | |
| Level | 242.4 = \( \left(a + 15\right) \) | |
| Label | 2.0.7.1-242.4-a | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | no | |
| Newspace: | 2.0.7.1-242.4 | (dimension 1) |
| Sign of functional equation: | +1 | |
| Analytic rank: | \(0\) | |
| L-ratio: | 1 |
Hecke eigenvalues
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 2 \) | 2.1 = (\( a \)) | \( 0 \) |
| \( 2 \) | 2.2 = (\( -a + 1 \)) | \( -1 \) |
| \( 7 \) | 7.1 = (\( -2 a + 1 \)) | \( 2 \) |
| \( 9 \) | 9.1 = (\( 3 \)) | \( -2 \) |
| \( 11 \) | 11.1 = (\( -2 a + 3 \)) | \( 0 \) |
| \( 11 \) | 11.2 = (\( 2 a + 1 \)) | \( 3 \) |
| \( 23 \) | 23.1 = (\( -2 a + 5 \)) | \( 3 \) |
| \( 23 \) | 23.2 = (\( 2 a + 3 \)) | \( 3 \) |
| \( 25 \) | 25.1 = (\( 5 \)) | \( 2 \) |
| \( 29 \) | 29.1 = (\( -4 a + 1 \)) | \( 0 \) |
| \( 29 \) | 29.2 = (\( 4 a - 3 \)) | \( 3 \) |
| \( 37 \) | 37.1 = (\( -4 a + 5 \)) | \( 5 \) |
| \( 37 \) | 37.2 = (\( 4 a + 1 \)) | \( 8 \) |
| \( 43 \) | 43.1 = (\( -2 a + 7 \)) | \( -1 \) |
| \( 43 \) | 43.2 = (\( 2 a + 5 \)) | \( -10 \) |
| \( 53 \) | 53.1 = (\( -4 a - 3 \)) | \( 9 \) |
| \( 53 \) | 53.2 = (\( 4 a - 7 \)) | \( -12 \) |
| \( 67 \) | 67.1 = (\( -6 a + 1 \)) | \( -4 \) |
| \( 67 \) | 67.2 = (\( 6 a - 5 \)) | \( -4 \) |
| \( 71 \) | 71.1 = (\( -2 a + 9 \)) | \( 12 \) |
| \( 71 \) | 71.2 = (\( 2 a + 7 \)) | \( 6 \) |
| \( 79 \) | 79.1 = (\( -6 a + 7 \)) | \( -10 \) |
| \( 79 \) | 79.2 = (\( 6 a + 1 \)) | \( 14 \) |
| \( 107 \) | 107.1 = (\( -2 a + 11 \)) | \( 6 \) |
| \( 107 \) | 107.2 = (\( 2 a + 9 \)) | \( 9 \) |
| \( 109 \) | 109.1 = (\( -4 a - 7 \)) | \( -4 \) |
| \( 109 \) | 109.2 = (\( 4 a - 11 \)) | \( -7 \) |
| \( 113 \) | 113.1 = (\( -8 a + 3 \)) | \( -12 \) |
| \( 113 \) | 113.2 = (\( -8 a + 5 \)) | \( -18 \) |
| \( 127 \) | 127.1 = (\( -6 a - 5 \)) | \( 11 \) |
| \( 127 \) | 127.2 = (\( 6 a - 11 \)) | \( -7 \) |
| \( 137 \) | 137.1 = (\( -8 a + 9 \)) | \( -3 \) |
| \( 137 \) | 137.2 = (\( 8 a + 1 \)) | \( 6 \) |
| \( 149 \) | 149.1 = (\( -4 a + 13 \)) | \( -6 \) |
| \( 149 \) | 149.2 = (\( 4 a + 9 \)) | \( -6 \) |
| \( 151 \) | 151.1 = (\( -2 a + 13 \)) | \( -13 \) |
| \( 151 \) | 151.2 = (\( 2 a + 11 \)) | \( -16 \) |
| \( 163 \) | 163.1 = (\( -6 a + 13 \)) | \( -16 \) |
| \( 163 \) | 163.2 = (\( 6 a + 7 \)) | \( -1 \) |
| \( 169 \) | 169.1 = (\( 13 \)) | \( 8 \) |
| \( 179 \) | 179.1 = (\( 10 a - 7 \)) | \( -9 \) |
| \( 179 \) | 179.2 = (\( 10 a - 3 \)) | \( -18 \) |
| \( 191 \) | 191.1 = (\( -10 a + 1 \)) | \( -6 \) |
| \( 191 \) | 191.2 = (\( 10 a - 9 \)) | \( 18 \) |
| \( 193 \) | 193.1 = (\( -8 a - 5 \)) | \( -16 \) |
| \( 193 \) | 193.2 = (\( -8 a + 13 \)) | \( -4 \) |
| \( 197 \) | 197.1 = (\( -4 a - 11 \)) | \( -18 \) |
| \( 197 \) | 197.2 = (\( 4 a - 15 \)) | \( 18 \) |
| \( 211 \) | 211.1 = (\( -10 a + 11 \)) | \( -22 \) |
| \( 211 \) | 211.2 = (\( 10 a + 1 \)) | \( 8 \) |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 2 \) | 2.2 = (\( -a + 1 \)) | \( 1 \) |
| \( 11 \) | 11.1 = (\( -2 a + 3 \)) | \( -1 \) |