Base field \(\Q(\sqrt{41}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 10\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[400, 20, 20]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 4]$ | $\phantom{-}0$ |
| 2 | $[2, 2, -w - 3]$ | $\phantom{-}0$ |
| 5 | $[5, 5, -2w - 5]$ | $-1$ |
| 5 | $[5, 5, -2w + 7]$ | $-1$ |
| 9 | $[9, 3, 3]$ | $-2$ |
| 23 | $[23, 23, 2w - 9]$ | $\phantom{-}6$ |
| 23 | $[23, 23, -2w - 7]$ | $\phantom{-}6$ |
| 31 | $[31, 31, -6w - 17]$ | $-4$ |
| 31 | $[31, 31, 6w - 23]$ | $-4$ |
| 37 | $[37, 37, 2w - 3]$ | $\phantom{-}2$ |
| 37 | $[37, 37, -2w - 1]$ | $\phantom{-}2$ |
| 41 | $[41, 41, 2w - 1]$ | $\phantom{-}6$ |
| 43 | $[43, 43, -4w - 9]$ | $-10$ |
| 43 | $[43, 43, 4w - 13]$ | $-10$ |
| 49 | $[49, 7, -7]$ | $-10$ |
| 59 | $[59, 59, 2w - 11]$ | $\phantom{-}12$ |
| 59 | $[59, 59, -2w - 9]$ | $\phantom{-}12$ |
| 61 | $[61, 61, -4w + 17]$ | $\phantom{-}2$ |
| 61 | $[61, 61, 4w + 13]$ | $\phantom{-}2$ |
| 73 | $[73, 73, 8w + 23]$ | $\phantom{-}2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w - 4]$ | $-1$ |
| $2$ | $[2, 2, -w - 3]$ | $-1$ |
| $5$ | $[5, 5, -2w - 5]$ | $1$ |
| $5$ | $[5, 5, -2w + 7]$ | $1$ |