Base field: \(\Q(\sqrt{-1}) \)
Generator \(i\), with minimal polynomial \(x^2 + 1\); class number \(1\).
Form
| Weight: | 2 | |
| Level: | 484.1 = \( \left(22\right) \) | |
| Level norm: | 484 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | yes | 44.2.a.a , 176.2.a.a |
| Newspace: | 2.0.4.1-484.1 (dimension 1) | |
| Sign of functional equation: | $-1$ | |
| Analytic rank: | odd |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 2 \) | 2.1 = (\( i + 1 \)) | \( -1 \) |
| \( 121 \) | 121.1 = (\( 11 \)) | \( -1 \) |
Hecke eigenvalues
The Hecke eigenvalue field is $\Q$. The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 1000 eigenvalues, of which 20 are currently shown below. We only show the eigenvalues $a_{\mathfrak{p}}$ for primes $\mathfrak{p}$ which do not divide the level.
| $N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
|---|---|---|
| \( 5 \) | 5.1 = (\( -i - 2 \)) | \( -3 \) |
| \( 5 \) | 5.2 = (\( 2 i + 1 \)) | \( -3 \) |
| \( 9 \) | 9.1 = (\( 3 \)) | \( -5 \) |
| \( 13 \) | 13.1 = (\( -3 i - 2 \)) | \( -4 \) |
| \( 13 \) | 13.2 = (\( 2 i + 3 \)) | \( -4 \) |
| \( 17 \) | 17.1 = (\( i + 4 \)) | \( 6 \) |
| \( 17 \) | 17.2 = (\( i - 4 \)) | \( 6 \) |
| \( 29 \) | 29.1 = (\( -2 i + 5 \)) | \( 0 \) |
| \( 29 \) | 29.2 = (\( 2 i + 5 \)) | \( 0 \) |
| \( 37 \) | 37.1 = (\( i + 6 \)) | \( -1 \) |
| \( 37 \) | 37.2 = (\( i - 6 \)) | \( -1 \) |
| \( 41 \) | 41.1 = (\( -5 i - 4 \)) | \( 0 \) |
| \( 41 \) | 41.2 = (\( 4 i + 5 \)) | \( 0 \) |
| \( 49 \) | 49.1 = (\( 7 \)) | \( -10 \) |
| \( 53 \) | 53.1 = (\( -2 i + 7 \)) | \( -6 \) |
| \( 53 \) | 53.2 = (\( 2 i + 7 \)) | \( -6 \) |
| \( 61 \) | 61.1 = (\( -6 i - 5 \)) | \( -4 \) |
| \( 61 \) | 61.2 = (\( 5 i + 6 \)) | \( -4 \) |
| \( 73 \) | 73.1 = (\( -3 i - 8 \)) | \( -4 \) |
| \( 73 \) | 73.2 = (\( 3 i - 8 \)) | \( -4 \) |
| \( 89 \) | 89.1 = (\( -5 i + 8 \)) | \( -9 \) |