Base field \(\Q(\sqrt{481}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 120\); narrow class number \(2\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[3, 3, -2w - 21]$ |
| Dimension: | $40$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $126$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{40} - 62x^{38} + 1761x^{36} - 30375x^{34} + 355590x^{32} - 2990976x^{30} + 18666613x^{28} - 88018266x^{26} + 316369151x^{24} - 868545902x^{22} + 1814347440x^{20} - 2857600350x^{18} + 3344264944x^{16} - 2848792772x^{14} + 1717467146x^{12} - 705230205x^{10} + 186793286x^{8} - 29336844x^{6} + 2351980x^{4} - 67888x^{2} + 16\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $...$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -2w - 21]$ | $-1$ |
| 3 | $[3, 3, 2w - 23]$ | $...$ |
| 5 | $[5, 5, w]$ | $...$ |
| 5 | $[5, 5, w + 4]$ | $...$ |
| 13 | $[13, 13, w + 6]$ | $...$ |
| 19 | $[19, 19, w + 2]$ | $...$ |
| 19 | $[19, 19, w + 16]$ | $...$ |
| 31 | $[31, 31, w + 13]$ | $...$ |
| 31 | $[31, 31, w + 17]$ | $...$ |
| 37 | $[37, 37, w + 18]$ | $...$ |
| 49 | $[49, 7, -7]$ | $...$ |
| 53 | $[53, 53, -234w + 2683]$ | $...$ |
| 53 | $[53, 53, -234w - 2449]$ | $...$ |
| 59 | $[59, 59, w + 1]$ | $...$ |
| 59 | $[59, 59, w + 57]$ | $...$ |
| 89 | $[89, 89, w + 41]$ | $...$ |
| 89 | $[89, 89, w + 47]$ | $...$ |
| 97 | $[97, 97, w + 26]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, -2w - 21]$ | $1$ |