Base field \(\Q(\sqrt{305}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 76\); narrow class number \(4\) and class number \(2\).
Form
Weight: | $[2, 2]$ |
Level: | $[9, 3, 3]$ |
Dimension: | $36$ |
CM: | no |
Base change: | no |
Newspace dimension: | $220$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{36} + 62x^{34} + 1751x^{32} + 29820x^{30} + 341671x^{28} + 2782337x^{26} + 16583216x^{24} + 73394825x^{22} + 242172389x^{20} + 592895173x^{18} + 1062894233x^{16} + 1364467204x^{14} + 1213873895x^{12} + 715822013x^{10} + 264232076x^{8} + 56453691x^{6} + 6138128x^{4} + 261755x^{2} + 2704\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $\phantom{-}e$ |
2 | $[2, 2, w + 1]$ | $...$ |
5 | $[5, 5, -4w + 37]$ | $...$ |
7 | $[7, 7, w + 2]$ | $...$ |
7 | $[7, 7, w + 4]$ | $...$ |
9 | $[9, 3, 3]$ | $-1$ |
17 | $[17, 17, w + 6]$ | $...$ |
17 | $[17, 17, w + 10]$ | $...$ |
19 | $[19, 19, -2w + 19]$ | $...$ |
19 | $[19, 19, -2w - 17]$ | $...$ |
23 | $[23, 23, w + 5]$ | $...$ |
23 | $[23, 23, w + 17]$ | $...$ |
37 | $[37, 37, w + 1]$ | $...$ |
37 | $[37, 37, w + 35]$ | $...$ |
41 | $[41, 41, -22w + 203]$ | $...$ |
41 | $[41, 41, -6w + 55]$ | $...$ |
43 | $[43, 43, w + 20]$ | $...$ |
43 | $[43, 43, w + 22]$ | $...$ |
53 | $[53, 53, w + 13]$ | $...$ |
53 | $[53, 53, w + 39]$ | $...$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$9$ | $[9, 3, 3]$ | $1$ |