Base field \(\Q(\sqrt{409}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 102\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[9, 9, -2w + 21]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $133$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -219w + 2324]$ | $\phantom{-}1$ |
| 2 | $[2, 2, -219w - 2105]$ | $\phantom{-}2$ |
| 3 | $[3, 3, 11066w + 106365]$ | $\phantom{-}0$ |
| 3 | $[3, 3, -11066w + 117431]$ | $-1$ |
| 5 | $[5, 5, -18w - 173]$ | $-2$ |
| 5 | $[5, 5, -18w + 191]$ | $\phantom{-}2$ |
| 17 | $[17, 17, -8w + 85]$ | $\phantom{-}3$ |
| 17 | $[17, 17, 8w + 77]$ | $\phantom{-}6$ |
| 23 | $[23, 23, -286w + 3035]$ | $\phantom{-}1$ |
| 23 | $[23, 23, -286w - 2749]$ | $\phantom{-}5$ |
| 41 | $[41, 41, 1600w + 15379]$ | $\phantom{-}12$ |
| 41 | $[41, 41, 1600w - 16979]$ | $-9$ |
| 49 | $[49, 7, -7]$ | $-4$ |
| 53 | $[53, 53, -116w + 1231]$ | $-6$ |
| 53 | $[53, 53, 116w + 1115]$ | $\phantom{-}3$ |
| 71 | $[71, 71, -126240w + 1339643]$ | $\phantom{-}6$ |
| 71 | $[71, 71, 126240w + 1213403]$ | $-12$ |
| 83 | $[83, 83, 12w - 127]$ | $\phantom{-}13$ |
| 83 | $[83, 83, -12w - 115]$ | $-7$ |
| 89 | $[89, 89, 285678w + 2745901]$ | $-10$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, 11066w + 106365]$ | $1$ |