Base field: \(\Q(\sqrt{-2}) \)
Generator \(a\), with minimal polynomial \(x^2 + 2\); class number \(1\).
Form
| Weight: | 2 | |
| Level: | 144.2 = \( \left(12\right) \) | |
| Level norm: | 144 | |
| Dimension: | 1 | |
| CM: | no | |
| Base change: | yes | 48.2.a.a , 192.2.a.d |
| Newspace: | 2.0.8.1-144.2 (dimension 1) | |
| Sign of functional equation: | $+1$ | |
| Analytic rank: | \(0\) | |
| L-ratio: | 1 |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| \( 2 \) | 2.1 = (\( a \)) | \( -1 \) |
| \( 3 \) | 3.1 = (\( -a - 1 \)) | \( -1 \) |
| \( 3 \) | 3.2 = (\( a - 1 \)) | \( -1 \) |
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.
| $N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
|---|---|---|
| \( 11 \) | 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 = (\( a - 9 \)) | \( 4 \) |