Base Field: \(\Q(\sqrt{-2}) \)
Generator \(a\), with minimal polynomial \(x^2 + 2\); class number \(1\).
Form
Weight | 2 | |
Level | 114.4 = \( \left(-7 a + 4\right) \) | |
Label | 2.0.8.1-114.4-a | |
Dimension: | 1 | |
CM: | no | |
Base change: | no | |
Newspace: | 2.0.8.1-114.4 | (dimension 1) |
Sign of functional equation: | +1 | |
Analytic rank: | \(0\) | |
L-ratio: | 1/2 |
Hecke eigenvalues
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
\( 2 \) | 2.1 = (\( a \)) | \( 1 \) |
\( 3 \) | 3.1 = (\( -a - 1 \)) | \( 0 \) |
\( 3 \) | 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 = (\( 2 a + 3 \)) | \( -6 \) |
\( 19 \) | 19.1 = (\( -3 a + 1 \)) | \( 0 \) |
\( 19 \) | 19.2 = (\( 3 a + 1 \)) | \( -1 \) |
\( 25 \) | 25.1 = (\( 5 \)) | \( -2 \) |
\( 41 \) | 41.1 = (\( -4 a - 3 \)) | \( 6 \) |
\( 41 \) | 41.2 = (\( 4 a - 3 \)) | \( -10 \) |
\( 43 \) | 43.1 = (\( -3 a - 5 \)) | \( 0 \) |
\( 43 \) | 43.2 = (\( 3 a - 5 \)) | \( -4 \) |
\( 49 \) | 49.1 = (\( 7 \)) | \( 2 \) |
\( 59 \) | 59.1 = (\( -5 a + 3 \)) | \( -4 \) |
\( 59 \) | 59.2 = (\( -5 a - 3 \)) | \( 4 \) |
\( 67 \) | 67.1 = (\( -3 a + 7 \)) | \( 4 \) |
\( 67 \) | 67.2 = (\( 3 a + 7 \)) | \( -12 \) |
\( 73 \) | 73.1 = (\( -6 a + 1 \)) | \( -14 \) |
\( 73 \) | 73.2 = (\( 6 a + 1 \)) | \( -14 \) |
\( 83 \) | 83.1 = (\( a + 9 \)) | \( -16 \) |
\( 83 \) | 83.2 = (\( a - 9 \)) | \( 12 \) |
\( 89 \) | 89.1 = (\( -2 a + 9 \)) | \( -6 \) |
\( 89 \) | 89.2 = (\( 2 a + 9 \)) | \( 10 \) |
\( 97 \) | 97.1 = (\( -6 a - 5 \)) | \( 10 \) |
\( 97 \) | 97.2 = (\( 6 a - 5 \)) | \( 14 \) |
\( 107 \) | 107.1 = (\( 7 a + 3 \)) | \( 20 \) |
\( 107 \) | 107.2 = (\( 7 a - 3 \)) | \( 12 \) |
\( 113 \) | 113.1 = (\( -4 a + 9 \)) | \( -6 \) |
\( 113 \) | 113.2 = (\( 4 a + 9 \)) | \( -6 \) |
\( 131 \) | 131.1 = (\( -5 a - 9 \)) | \( -8 \) |
\( 131 \) | 131.2 = (\( 5 a - 9 \)) | \( 12 \) |
\( 137 \) | 137.1 = (\( -8 a + 3 \)) | \( 22 \) |
\( 137 \) | 137.2 = (\( -8 a - 3 \)) | \( 18 \) |
\( 139 \) | 139.1 = (\( -3 a - 11 \)) | \( -4 \) |
\( 139 \) | 139.2 = (\( 3 a - 11 \)) | \( 12 \) |
\( 163 \) | 163.1 = (\( -9 a + 1 \)) | \( 4 \) |
\( 163 \) | 163.2 = (\( 9 a + 1 \)) | \( -4 \) |
\( 169 \) | 169.1 = (\( 13 \)) | \( 6 \) |
\( 179 \) | 179.1 = (\( 7 a + 9 \)) | \( -20 \) |
\( 179 \) | 179.2 = (\( 7 a - 9 \)) | \( 16 \) |
\( 193 \) | 193.1 = (\( -6 a - 11 \)) | \( -2 \) |
\( 193 \) | 193.2 = (\( 6 a - 11 \)) | \( -14 \) |
\( 211 \) | 211.1 = (\( 9 a - 7 \)) | \( 8 \) |
\( 211 \) | 211.2 = (\( 9 a + 7 \)) | \( -12 \) |
\( 227 \) | 227.1 = (\( a + 15 \)) | \( 12 \) |
\( 227 \) | 227.2 = (\( a - 15 \)) | \( 0 \) |
\( 233 \) | 233.1 = (\( -2 a + 15 \)) | \( -14 \) |
\( 233 \) | 233.2 = (\( 2 a + 15 \)) | \( 10 \) |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
\( 2 \) | 2.1 = (\( a \)) | \( -1 \) |
\( 3 \) | 3.2 = (\( a - 1 \)) | \( 1 \) |
\( 19 \) | 19.2 = (\( 3 a + 1 \)) | \( 1 \) |