Base field \(\Q(\sqrt{7}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 7\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[63, 21, 3w]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $2$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 3]$ | $-1$ |
| 3 | $[3, 3, w - 2]$ | $-1$ |
| 3 | $[3, 3, w + 2]$ | $-1$ |
| 7 | $[7, 7, w]$ | $\phantom{-}1$ |
| 19 | $[19, 19, 2w - 3]$ | $-4$ |
| 19 | $[19, 19, 2w + 3]$ | $-4$ |
| 25 | $[25, 5, 5]$ | $-6$ |
| 29 | $[29, 29, -w - 6]$ | $-2$ |
| 29 | $[29, 29, w - 6]$ | $-2$ |
| 31 | $[31, 31, 4w + 9]$ | $\phantom{-}0$ |
| 31 | $[31, 31, -4w + 9]$ | $\phantom{-}0$ |
| 37 | $[37, 37, -3w + 10]$ | $\phantom{-}6$ |
| 37 | $[37, 37, -6w + 17]$ | $\phantom{-}6$ |
| 47 | $[47, 47, -3w - 4]$ | $\phantom{-}0$ |
| 47 | $[47, 47, 3w - 4]$ | $\phantom{-}0$ |
| 53 | $[53, 53, 2w - 9]$ | $\phantom{-}6$ |
| 53 | $[53, 53, 2w + 9]$ | $\phantom{-}6$ |
| 59 | $[59, 59, 3w - 2]$ | $-12$ |
| 59 | $[59, 59, -3w - 2]$ | $-12$ |
| 83 | $[83, 83, -6w - 13]$ | $\phantom{-}12$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w - 2]$ | $1$ |
| $3$ | $[3, 3, w + 2]$ | $1$ |
| $7$ | $[7, 7, w]$ | $-1$ |