Base field \(\Q(\sqrt{301}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 75\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[36, 6, 6]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $122$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 9]$ | $-1$ |
| 3 | $[3, 3, w + 8]$ | $-1$ |
| 4 | $[4, 2, 2]$ | $-1$ |
| 5 | $[5, 5, -6w + 55]$ | $\phantom{-}3$ |
| 5 | $[5, 5, -6w - 49]$ | $-3$ |
| 7 | $[7, 7, -23w - 188]$ | $\phantom{-}1$ |
| 11 | $[11, 11, 5w - 46]$ | $\phantom{-}3$ |
| 11 | $[11, 11, -5w - 41]$ | $-3$ |
| 19 | $[19, 19, w + 7]$ | $-7$ |
| 19 | $[19, 19, -w + 8]$ | $\phantom{-}5$ |
| 23 | $[23, 23, 2w - 19]$ | $\phantom{-}0$ |
| 23 | $[23, 23, 2w + 17]$ | $\phantom{-}0$ |
| 43 | $[43, 43, 57w - 523]$ | $-4$ |
| 53 | $[53, 53, 28w - 257]$ | $\phantom{-}12$ |
| 53 | $[53, 53, 28w + 229]$ | $\phantom{-}12$ |
| 61 | $[61, 61, -13w + 119]$ | $-10$ |
| 61 | $[61, 61, 13w + 106]$ | $\phantom{-}2$ |
| 67 | $[67, 67, -9w + 83]$ | $-14$ |
| 67 | $[67, 67, -9w - 74]$ | $-2$ |
| 73 | $[73, 73, -w - 1]$ | $-4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w - 9]$ | $1$ |
| $3$ | $[3, 3, w + 8]$ | $1$ |
| $4$ | $[4, 2, 2]$ | $1$ |