Base field \(\Q(\sqrt{321}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 80\); narrow class number \(6\) and class number \(3\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[4, 2, 2]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $78$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}1$ |
| 2 | $[2, 2, w + 1]$ | $-1$ |
| 3 | $[3, 3, -2w + 19]$ | $-2$ |
| 5 | $[5, 5, w]$ | $-3$ |
| 5 | $[5, 5, w + 4]$ | $\phantom{-}3$ |
| 13 | $[13, 13, w + 1]$ | $-4$ |
| 13 | $[13, 13, w + 11]$ | $-4$ |
| 17 | $[17, 17, w + 3]$ | $\phantom{-}6$ |
| 17 | $[17, 17, w + 13]$ | $-6$ |
| 19 | $[19, 19, w + 6]$ | $\phantom{-}2$ |
| 19 | $[19, 19, w + 12]$ | $\phantom{-}2$ |
| 37 | $[37, 37, w + 2]$ | $\phantom{-}2$ |
| 37 | $[37, 37, w + 34]$ | $\phantom{-}2$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}14$ |
| 59 | $[59, 59, -4w - 33]$ | $-9$ |
| 59 | $[59, 59, 4w - 37]$ | $\phantom{-}9$ |
| 61 | $[61, 61, w + 28]$ | $-10$ |
| 61 | $[61, 61, w + 32]$ | $-10$ |
| 71 | $[71, 71, w + 22]$ | $\phantom{-}6$ |
| 71 | $[71, 71, w + 48]$ | $-6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $-1$ |
| $2$ | $[2, 2, w + 1]$ | $1$ |