Base field \(\Q(\sqrt{353}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 88\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[4, 2, 2]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $21$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 10]$ | $-1$ |
| 2 | $[2, 2, w + 9]$ | $\phantom{-}1$ |
| 9 | $[9, 3, 3]$ | $\phantom{-}2$ |
| 11 | $[11, 11, -10w + 99]$ | $-3$ |
| 11 | $[11, 11, 10w + 89]$ | $\phantom{-}5$ |
| 17 | $[17, 17, -66w - 587]$ | $-7$ |
| 17 | $[17, 17, -66w + 653]$ | $-3$ |
| 19 | $[19, 19, -28w + 277]$ | $\phantom{-}4$ |
| 19 | $[19, 19, 28w + 249]$ | $-4$ |
| 23 | $[23, 23, -8w - 71]$ | $\phantom{-}0$ |
| 23 | $[23, 23, 8w - 79]$ | $-2$ |
| 25 | $[25, 5, -5]$ | $-3$ |
| 29 | $[29, 29, -2w + 19]$ | $\phantom{-}0$ |
| 29 | $[29, 29, 2w + 17]$ | $-6$ |
| 41 | $[41, 41, -6w - 53]$ | $\phantom{-}3$ |
| 41 | $[41, 41, 6w - 59]$ | $-5$ |
| 43 | $[43, 43, -4w + 39]$ | $-1$ |
| 43 | $[43, 43, 4w + 35]$ | $-5$ |
| 47 | $[47, 47, 2w - 21]$ | $\phantom{-}2$ |
| 47 | $[47, 47, -2w - 19]$ | $\phantom{-}6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w + 10]$ | $1$ |
| $2$ | $[2, 2, w + 9]$ | $-1$ |