Base field \(\Q(\sqrt{57}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 14\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[76, 38, 20w + 66]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 4]$ | $\phantom{-}1$ |
| 2 | $[2, 2, -w - 3]$ | $\phantom{-}1$ |
| 3 | $[3, 3, -4w - 13]$ | $-1$ |
| 7 | $[7, 7, -2w - 7]$ | $\phantom{-}3$ |
| 7 | $[7, 7, -2w + 9]$ | $\phantom{-}3$ |
| 19 | $[19, 19, 10w + 33]$ | $-1$ |
| 25 | $[25, 5, 5]$ | $\phantom{-}6$ |
| 29 | $[29, 29, -6w - 19]$ | $-5$ |
| 29 | $[29, 29, -6w + 25]$ | $-5$ |
| 41 | $[41, 41, 2w - 5]$ | $-8$ |
| 41 | $[41, 41, -2w - 3]$ | $-8$ |
| 43 | $[43, 43, 2w - 11]$ | $\phantom{-}4$ |
| 43 | $[43, 43, 2w + 9]$ | $\phantom{-}4$ |
| 53 | $[53, 53, 2w - 3]$ | $-1$ |
| 53 | $[53, 53, -2w - 1]$ | $-1$ |
| 59 | $[59, 59, 4w - 15]$ | $\phantom{-}15$ |
| 59 | $[59, 59, 4w + 11]$ | $\phantom{-}15$ |
| 61 | $[61, 61, -4w - 15]$ | $\phantom{-}2$ |
| 61 | $[61, 61, -4w + 19]$ | $\phantom{-}2$ |
| 71 | $[71, 71, 8w + 25]$ | $\phantom{-}2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w + 4]$ | $-1$ |
| $2$ | $[2, 2, -w - 3]$ | $-1$ |
| $19$ | $[19, 19, 10w + 33]$ | $1$ |