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: | $[6,6,-67w + 711]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $57$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} - 2x - 6\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -219w + 2324]$ | $-1$ |
| 2 | $[2, 2, -219w - 2105]$ | $\phantom{-}1$ |
| 3 | $[3, 3, 11066w + 106365]$ | $\phantom{-}1$ |
| 3 | $[3, 3, -11066w + 117431]$ | $\phantom{-}2$ |
| 5 | $[5, 5, -18w - 173]$ | $-e + 2$ |
| 5 | $[5, 5, -18w + 191]$ | $\phantom{-}e$ |
| 17 | $[17, 17, -8w + 85]$ | $\phantom{-}2e$ |
| 17 | $[17, 17, 8w + 77]$ | $\phantom{-}4$ |
| 23 | $[23, 23, -286w + 3035]$ | $\phantom{-}2$ |
| 23 | $[23, 23, -286w - 2749]$ | $-2e + 4$ |
| 41 | $[41, 41, 1600w + 15379]$ | $\phantom{-}3e - 4$ |
| 41 | $[41, 41, 1600w - 16979]$ | $-e + 6$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}e + 4$ |
| 53 | $[53, 53, -116w + 1231]$ | $\phantom{-}e - 4$ |
| 53 | $[53, 53, 116w + 1115]$ | $-e + 10$ |
| 71 | $[71, 71, -126240w + 1339643]$ | $\phantom{-}0$ |
| 71 | $[71, 71, 126240w + 1213403]$ | $-2e - 8$ |
| 83 | $[83, 83, 12w - 127]$ | $\phantom{-}10$ |
| 83 | $[83, 83, -12w - 115]$ | $-12$ |
| 89 | $[89, 89, 285678w + 2745901]$ | $\phantom{-}3e - 12$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,219w + 2105]$ | $-1$ |
| $3$ | $[3,3,11066w + 106365]$ | $-1$ |