Base field \(\Q(\sqrt{58}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 58\); narrow class number \(2\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[9, 3, 3]$ |
Dimension: | $15$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $74$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{15} - 31x^{13} - x^{12} + 386x^{11} + 23x^{10} - 2462x^{9} - 204x^{8} + 8492x^{7} + 916x^{6} - 15320x^{5} - 2284x^{4} + 12648x^{3} + 2768x^{2} - 3328x - 768\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $\phantom{-}e$ |
3 | $[3, 3, w + 1]$ | $-1$ |
3 | $[3, 3, w + 2]$ | $-1$ |
7 | $[7, 7, -2w + 15]$ | $...$ |
7 | $[7, 7, -2w - 15]$ | $...$ |
11 | $[11, 11, w + 5]$ | $...$ |
11 | $[11, 11, w + 6]$ | $...$ |
19 | $[19, 19, w + 1]$ | $...$ |
19 | $[19, 19, w + 18]$ | $...$ |
23 | $[23, 23, w + 9]$ | $...$ |
23 | $[23, 23, -w + 9]$ | $...$ |
25 | $[25, 5, 5]$ | $...$ |
29 | $[29, 29, w]$ | $...$ |
37 | $[37, 37, w + 13]$ | $...$ |
37 | $[37, 37, w + 24]$ | $...$ |
43 | $[43, 43, w + 12]$ | $...$ |
43 | $[43, 43, w + 31]$ | $...$ |
61 | $[61, 61, w + 27]$ | $...$ |
61 | $[61, 61, w + 34]$ | $...$ |
71 | $[71, 71, 12w - 91]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3, 3, w + 1]$ | $1$ |
$3$ | $[3, 3, w + 2]$ | $1$ |