Base field \(\Q(\sqrt{217}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 54\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[8, 8, -223w + 1754]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w + 8]$ | $\phantom{-}0$ |
| 2 | $[2, 2, w + 7]$ | $-2$ |
| 3 | $[3, 3, -52w - 357]$ | $-1$ |
| 3 | $[3, 3, -52w + 409]$ | $\phantom{-}0$ |
| 7 | $[7, 7, 498w - 3917]$ | $\phantom{-}1$ |
| 13 | $[13, 13, 22w - 173]$ | $-6$ |
| 13 | $[13, 13, 22w + 151]$ | $\phantom{-}2$ |
| 17 | $[17, 17, -6w - 41]$ | $\phantom{-}3$ |
| 17 | $[17, 17, -6w + 47]$ | $\phantom{-}5$ |
| 25 | $[25, 5, -5]$ | $\phantom{-}2$ |
| 31 | $[31, 31, 1048w - 8243]$ | $-5$ |
| 61 | $[61, 61, 602w - 4735]$ | $-10$ |
| 61 | $[61, 61, 602w + 4133]$ | $\phantom{-}8$ |
| 67 | $[67, 67, -186w - 1277]$ | $\phantom{-}5$ |
| 67 | $[67, 67, -186w + 1463]$ | $-4$ |
| 71 | $[71, 71, 290w - 2281]$ | $-2$ |
| 71 | $[71, 71, 290w + 1991]$ | $\phantom{-}16$ |
| 73 | $[73, 73, 2w - 13]$ | $\phantom{-}0$ |
| 73 | $[73, 73, -2w - 11]$ | $-10$ |
| 83 | $[83, 83, -36w - 247]$ | $-10$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w + 8]$ | $-1$ |