Base field \(\Q(\sqrt{129}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 32\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[8,4,2w + 10]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 6]$ | $\phantom{-}1$ |
| 2 | $[2, 2, -w - 5]$ | $\phantom{-}0$ |
| 3 | $[3, 3, -28w - 145]$ | $-1$ |
| 5 | $[5, 5, -6w - 31]$ | $\phantom{-}0$ |
| 5 | $[5, 5, -6w + 37]$ | $\phantom{-}3$ |
| 13 | $[13, 13, -4w - 21]$ | $\phantom{-}2$ |
| 13 | $[13, 13, 4w - 25]$ | $-1$ |
| 29 | $[29, 29, -2w + 11]$ | $-6$ |
| 29 | $[29, 29, -2w - 9]$ | $\phantom{-}9$ |
| 31 | $[31, 31, 50w + 259]$ | $\phantom{-}8$ |
| 31 | $[31, 31, 50w - 309]$ | $\phantom{-}8$ |
| 43 | $[43, 43, -106w - 549]$ | $\phantom{-}8$ |
| 49 | $[49, 7, -7]$ | $-4$ |
| 67 | $[67, 67, 2w - 15]$ | $-4$ |
| 67 | $[67, 67, -2w - 13]$ | $-10$ |
| 71 | $[71, 71, -40w + 247]$ | $\phantom{-}9$ |
| 71 | $[71, 71, 40w + 207]$ | $-6$ |
| 79 | $[79, 79, 14w - 87]$ | $-10$ |
| 79 | $[79, 79, 14w + 73]$ | $-1$ |
| 89 | $[89, 89, 10w + 51]$ | $\phantom{-}15$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,w + 5]$ | $-1$ |
| $2$ | $[2,2,w - 6]$ | $-1$ |