Base Field: \(\Q(\sqrt{-1}) \)
Generator \(i\), with minimal polynomial \(x^2 + 1\); class number \(1\).
Form
| Weight | 2 | |
| Level | 16384.1 = \( \left(128\right) \) | |
| Label | 2.0.4.1-16384.1-d | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | yes, of a form over \(\mathbb{Q}\) with coefficients in \(\mathbb{Q}(\sqrt{2})\) | |
| Newspace: | 2.0.4.1-16384.1 | (dimension 14) |
| 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 = (\( i + 1 \)) | \( 0 \) |
| \( 5 \) | 5.1 = (\( -i - 2 \)) | \( 2 \) |
| \( 5 \) | 5.2 = (\( 2 i + 1 \)) | \( 2 \) |
| \( 9 \) | 9.1 = (\( 3 \)) | \( -4 \) |
| \( 13 \) | 13.1 = (\( -3 i - 2 \)) | \( 6 \) |
| \( 13 \) | 13.2 = (\( 2 i + 3 \)) | \( 6 \) |
| \( 17 \) | 17.1 = (\( i + 4 \)) | \( 0 \) |
| \( 17 \) | 17.2 = (\( i - 4 \)) | \( 0 \) |
| \( 29 \) | 29.1 = (\( -2 i + 5 \)) | \( 2 \) |
| \( 29 \) | 29.2 = (\( 2 i + 5 \)) | \( 2 \) |
| \( 37 \) | 37.1 = (\( i + 6 \)) | \( 6 \) |
| \( 37 \) | 37.2 = (\( i - 6 \)) | \( 6 \) |
| \( 41 \) | 41.1 = (\( -5 i - 4 \)) | \( 6 \) |
| \( 41 \) | 41.2 = (\( 4 i + 5 \)) | \( 6 \) |
| \( 49 \) | 49.1 = (\( 7 \)) | \( -6 \) |
| \( 53 \) | 53.1 = (\( -2 i + 7 \)) | \( -2 \) |
| \( 53 \) | 53.2 = (\( 2 i + 7 \)) | \( -2 \) |
| \( 61 \) | 61.1 = (\( -6 i - 5 \)) | \( 6 \) |
| \( 61 \) | 61.2 = (\( 5 i + 6 \)) | \( 6 \) |
| \( 73 \) | 73.1 = (\( -3 i - 8 \)) | \( -12 \) |
| \( 73 \) | 73.2 = (\( 3 i - 8 \)) | \( -12 \) |
| \( 89 \) | 89.1 = (\( -5 i + 8 \)) | \( -12 \) |
| \( 89 \) | 89.2 = (\( -8 i + 5 \)) | \( -12 \) |
| \( 97 \) | 97.1 = (\( -4 i + 9 \)) | \( -8 \) |
| \( 97 \) | 97.2 = (\( 4 i + 9 \)) | \( -8 \) |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 2 \) | 2.1 = (\( i + 1 \)) | \( -1 \) |