Base Field: \(\Q(\sqrt{-2}) \)
Generator \(a\), with minimal polynomial \(x^2 + 2\); class number \(1\).
Form
| Weight | 2 | |
| Level | 144.2 = \( \left(12\right) \) | |
| Label | 2.0.8.1-144.2-a | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | yes | 192.2.a.d , 48.2.a.a |
| Newspace: | 2.0.8.1-144.2 | (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 = (\( a \)) | \( 0 \) |
| \( 3 \) | 3.1 = (\( -a - 1 \)) | \( 1 \) |
| \( 3 \) | 3.2 = (\( a - 1 \)) | \( 1 \) |
| \( 11 \) | 11.1 = (\( a + 3 \)) | \( -4 \) |
| \( 11 \) | 11.2 = (\( a - 3 \)) | \( -4 \) |
| \( 17 \) | 17.1 = (\( -2 a + 3 \)) | \( 2 \) |
| \( 17 \) | 17.2 = (\( 2 a + 3 \)) | \( 2 \) |
| \( 19 \) | 19.1 = (\( -3 a + 1 \)) | \( 4 \) |
| \( 19 \) | 19.2 = (\( 3 a + 1 \)) | \( 4 \) |
| \( 25 \) | 25.1 = (\( 5 \)) | \( -6 \) |
| \( 41 \) | 41.1 = (\( -4 a - 3 \)) | \( -6 \) |
| \( 41 \) | 41.2 = (\( 4 a - 3 \)) | \( -6 \) |
| \( 43 \) | 43.1 = (\( -3 a - 5 \)) | \( -4 \) |
| \( 43 \) | 43.2 = (\( 3 a - 5 \)) | \( -4 \) |
| \( 49 \) | 49.1 = (\( 7 \)) | \( -14 \) |
| \( 59 \) | 59.1 = (\( -5 a + 3 \)) | \( -4 \) |
| \( 59 \) | 59.2 = (\( -5 a - 3 \)) | \( -4 \) |
| \( 67 \) | 67.1 = (\( -3 a + 7 \)) | \( 4 \) |
| \( 67 \) | 67.2 = (\( 3 a + 7 \)) | \( 4 \) |
| \( 73 \) | 73.1 = (\( -6 a + 1 \)) | \( 10 \) |
| \( 73 \) | 73.2 = (\( 6 a + 1 \)) | \( 10 \) |
| \( 83 \) | 83.1 = (\( a + 9 \)) | \( 4 \) |
| \( 83 \) | 83.2 = (\( a - 9 \)) | \( 4 \) |
| \( 89 \) | 89.1 = (\( -2 a + 9 \)) | \( -6 \) |
| \( 89 \) | 89.2 = (\( 2 a + 9 \)) | \( -6 \) |
| \( 97 \) | 97.1 = (\( -6 a - 5 \)) | \( 2 \) |
| \( 97 \) | 97.2 = (\( 6 a - 5 \)) | \( 2 \) |
| \( 107 \) | 107.1 = (\( 7 a + 3 \)) | \( 12 \) |
| \( 107 \) | 107.2 = (\( 7 a - 3 \)) | \( 12 \) |
| \( 113 \) | 113.1 = (\( -4 a + 9 \)) | \( 18 \) |
| \( 113 \) | 113.2 = (\( 4 a + 9 \)) | \( 18 \) |
| \( 131 \) | 131.1 = (\( -5 a - 9 \)) | \( 4 \) |
| \( 131 \) | 131.2 = (\( 5 a - 9 \)) | \( 4 \) |
| \( 137 \) | 137.1 = (\( -8 a + 3 \)) | \( -6 \) |
| \( 137 \) | 137.2 = (\( -8 a - 3 \)) | \( -6 \) |
| \( 139 \) | 139.1 = (\( -3 a - 11 \)) | \( 12 \) |
| \( 139 \) | 139.2 = (\( 3 a - 11 \)) | \( 12 \) |
| \( 163 \) | 163.1 = (\( -9 a + 1 \)) | \( -12 \) |
| \( 163 \) | 163.2 = (\( 9 a + 1 \)) | \( -12 \) |
| \( 169 \) | 169.1 = (\( 13 \)) | \( -22 \) |
| \( 179 \) | 179.1 = (\( 7 a + 9 \)) | \( -12 \) |
| \( 179 \) | 179.2 = (\( 7 a - 9 \)) | \( -12 \) |
| \( 193 \) | 193.1 = (\( -6 a - 11 \)) | \( 2 \) |
| \( 193 \) | 193.2 = (\( 6 a - 11 \)) | \( 2 \) |
| \( 211 \) | 211.1 = (\( 9 a - 7 \)) | \( 20 \) |
| \( 211 \) | 211.2 = (\( 9 a + 7 \)) | \( 20 \) |
| \( 227 \) | 227.1 = (\( a + 15 \)) | \( -12 \) |
| \( 227 \) | 227.2 = (\( a - 15 \)) | \( -12 \) |
| \( 233 \) | 233.1 = (\( -2 a + 15 \)) | \( 10 \) |
| \( 233 \) | 233.2 = (\( 2 a + 15 \)) | \( 10 \) |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 2 \) | 2.1 = (\( a \)) | \( -1 \) |
| \( 3 \) | 3.1 = (\( -a - 1 \)) | \( -1 \) |
| \( 3 \) | 3.2 = (\( a - 1 \)) | \( -1 \) |