Base Field: \(\Q(\sqrt{-1}) \)
Generator \(i\), with minimal polynomial \(x^2 + 1\); class number \(1\).
Form
| Weight | 2 | |
| Level | 1458.1 = \( \left(27 i + 27\right) \) | |
| Label | 2.0.4.1-1458.1-d | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | yes | 432.2.a.b , 54.2.a.b |
| Newspace: | 2.0.4.1-1458.1 | (dimension 6) |
| Sign of functional equation: | -1 | |
| Analytic rank: | odd |
Hecke eigenvalues
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 2 \) | 2.1 = (\( i + 1 \)) | \( 1 \) |
| \( 5 \) | 5.1 = (\( -i - 2 \)) | \( -3 \) |
| \( 5 \) | 5.2 = (\( 2 i + 1 \)) | \( -3 \) |
| \( 9 \) | 9.1 = (\( 3 \)) | \( 0 \) |
| \( 13 \) | 13.1 = (\( -3 i - 2 \)) | \( -4 \) |
| \( 13 \) | 13.2 = (\( 2 i + 3 \)) | \( -4 \) |
| \( 17 \) | 17.1 = (\( i + 4 \)) | \( 0 \) |
| \( 17 \) | 17.2 = (\( i - 4 \)) | \( 0 \) |
| \( 29 \) | 29.1 = (\( -2 i + 5 \)) | \( -6 \) |
| \( 29 \) | 29.2 = (\( 2 i + 5 \)) | \( -6 \) |
| \( 37 \) | 37.1 = (\( i + 6 \)) | \( 2 \) |
| \( 37 \) | 37.2 = (\( i - 6 \)) | \( 2 \) |
| \( 41 \) | 41.1 = (\( -5 i - 4 \)) | \( 6 \) |
| \( 41 \) | 41.2 = (\( 4 i + 5 \)) | \( 6 \) |
| \( 49 \) | 49.1 = (\( 7 \)) | \( -13 \) |
| \( 53 \) | 53.1 = (\( -2 i + 7 \)) | \( -9 \) |
| \( 53 \) | 53.2 = (\( 2 i + 7 \)) | \( -9 \) |
| \( 61 \) | 61.1 = (\( -6 i - 5 \)) | \( 8 \) |
| \( 61 \) | 61.2 = (\( 5 i + 6 \)) | \( 8 \) |
| \( 73 \) | 73.1 = (\( -3 i - 8 \)) | \( -7 \) |
| \( 73 \) | 73.2 = (\( 3 i - 8 \)) | \( -7 \) |
| \( 89 \) | 89.1 = (\( -5 i + 8 \)) | \( 18 \) |
| \( 89 \) | 89.2 = (\( -8 i + 5 \)) | \( 18 \) |
| \( 97 \) | 97.1 = (\( -4 i + 9 \)) | \( -1 \) |
| \( 97 \) | 97.2 = (\( 4 i + 9 \)) | \( -1 \) |
| \( 101 \) | 101.1 = (\( i + 10 \)) | \( 3 \) |
| \( 101 \) | 101.2 = (\( i - 10 \)) | \( 3 \) |
| \( 109 \) | 109.1 = (\( -3 i + 10 \)) | \( 2 \) |
| \( 109 \) | 109.2 = (\( 3 i + 10 \)) | \( 2 \) |
| \( 113 \) | 113.1 = (\( -8 i - 7 \)) | \( 6 \) |
| \( 113 \) | 113.2 = (\( 7 i + 8 \)) | \( 6 \) |
| \( 121 \) | 121.1 = (\( 11 \)) | \( -13 \) |
| \( 137 \) | 137.1 = (\( -4 i - 11 \)) | \( -6 \) |
| \( 137 \) | 137.2 = (\( 4 i - 11 \)) | \( -6 \) |
| \( 149 \) | 149.1 = (\( 10 i - 7 \)) | \( -3 \) |
| \( 149 \) | 149.2 = (\( 7 i - 10 \)) | \( -3 \) |
| \( 157 \) | 157.1 = (\( -6 i - 11 \)) | \( -4 \) |
| \( 157 \) | 157.2 = (\( 6 i - 11 \)) | \( -4 \) |
| \( 173 \) | 173.1 = (\( -2 i + 13 \)) | \( -15 \) |
| \( 173 \) | 173.2 = (\( 2 i + 13 \)) | \( -15 \) |
| \( 181 \) | 181.1 = (\( -10 i - 9 \)) | \( -16 \) |
| \( 181 \) | 181.2 = (\( 9 i + 10 \)) | \( -16 \) |
| \( 193 \) | 193.1 = (\( 7 i - 12 \)) | \( 5 \) |
| \( 193 \) | 193.2 = (\( 7 i + 12 \)) | \( 5 \) |
| \( 197 \) | 197.1 = (\( i + 14 \)) | \( -9 \) |
| \( 197 \) | 197.2 = (\( i - 14 \)) | \( -9 \) |
| \( 229 \) | 229.1 = (\( -2 i + 15 \)) | \( 14 \) |
| \( 229 \) | 229.2 = (\( 2 i + 15 \)) | \( 14 \) |
| \( 233 \) | 233.1 = (\( -8 i - 13 \)) | \( -18 \) |
| \( 233 \) | 233.2 = (\( -8 i + 13 \)) | \( -18 \) |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 2 \) | 2.1 = (\( i + 1 \)) | \( -1 \) |
| \( 9 \) | 9.1 = (\( 3 \)) | \( -1 \) |