Base field: \(\Q(\sqrt{-7}) \)
Generator \(a\), with minimal polynomial \(x^2 - x + 2\); class number \(1\).
Form
Weight: | 2 | |
Level: | 38025.1 = \( \left(195\right) \) | |
Level norm: | 38025 | |
Dimension: | 1 | |
CM: | no | |
Base change: | yes | 195.2.a.a , 9555.2.a.b |
Newspace: | 2.0.7.1-38025.1 (dimension 9) | |
Sign of functional equation: | $+1$ | |
Analytic rank: | \(0\) | |
L-ratio: | 193 |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
\( 9 \) | 9.1 = (\( 3 \)) | \( -1 \) |
\( 25 \) | 25.1 = (\( 5 \)) | \( -1 \) |
\( 169 \) | 169.1 = (\( 13 \)) | \( -1 \) |
Hecke eigenvalues
The Hecke eigenvalue field is $\Q$. The eigenvalue of the Hecke operator $T_{\mathfrak{p}}$ is $a_{\mathfrak{p}}$. The database contains 200 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.
$N(\mathfrak{p})$ | $\mathfrak{p}$ | $a_{\mathfrak{p}}$ |
---|---|---|
\( 2 \) | 2.1 = (\( a \)) | \( -1 \) |
\( 2 \) | 2.2 = (\( -a + 1 \)) | \( -1 \) |
\( 7 \) | 7.1 = (\( -2 a + 1 \)) | \( 0 \) |
\( 11 \) | 11.1 = (\( -2 a + 3 \)) | \( 4 \) |
\( 11 \) | 11.2 = (\( 2 a + 1 \)) | \( 4 \) |
\( 23 \) | 23.1 = (\( -2 a + 5 \)) | \( 8 \) |
\( 23 \) | 23.2 = (\( 2 a + 3 \)) | \( 8 \) |
\( 29 \) | 29.1 = (\( -4 a + 1 \)) | \( -2 \) |
\( 29 \) | 29.2 = (\( 4 a - 3 \)) | \( -2 \) |
\( 37 \) | 37.1 = (\( -4 a + 5 \)) | \( 6 \) |
\( 37 \) | 37.2 = (\( 4 a + 1 \)) | \( 6 \) |
\( 43 \) | 43.1 = (\( -2 a + 7 \)) | \( -4 \) |
\( 43 \) | 43.2 = (\( 2 a + 5 \)) | \( -4 \) |
\( 53 \) | 53.1 = (\( -4 a - 3 \)) | \( 6 \) |
\( 53 \) | 53.2 = (\( 4 a - 7 \)) | \( 6 \) |
\( 67 \) | 67.1 = (\( -6 a + 1 \)) | \( -4 \) |
\( 67 \) | 67.2 = (\( 6 a - 5 \)) | \( -4 \) |
\( 71 \) | 71.1 = (\( -2 a + 9 \)) | \( 0 \) |
\( 71 \) | 71.2 = (\( 2 a + 7 \)) | \( 0 \) |
\( 79 \) | 79.1 = (\( -6 a + 7 \)) | \( 16 \) |
\( 79 \) | 79.2 = (\( 6 a + 1 \)) | \( 16 \) |