Base field \(\Q(\sqrt{33}) \)
Generator \(w\), with minimal polynomial \(x^2 - x - 8\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[576, 48, -12 w + 48]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 2]$ | $\phantom{-}0$ |
| 2 | $[2, 2, -w + 3]$ | $\phantom{-}0$ |
| 3 | $[3, 3, 2 w - 7]$ | $\phantom{-}0$ |
| 11 | $[11, 11, 4 w - 13]$ | $-2$ |
| 17 | $[17, 17, -2 w + 5]$ | $-8$ |
| 17 | $[17, 17, 2 w + 3]$ | $\phantom{-}2$ |
| 25 | $[25, 5, 5]$ | $-2$ |
| 29 | $[29, 29, -2 w + 3]$ | $-8$ |
| 29 | $[29, 29, 2 w + 1]$ | $-2$ |
| 31 | $[31, 31, -2 w + 9]$ | $\phantom{-}8$ |
| 31 | $[31, 31, 2 w + 7]$ | $-4$ |
| 37 | $[37, 37, -4 w - 11]$ | $\phantom{-}6$ |
| 37 | $[37, 37, 4 w - 15]$ | $-10$ |
| 41 | $[41, 41, -10 w + 33]$ | $\phantom{-}4$ |
| 41 | $[41, 41, 6 w - 19]$ | $\phantom{-}6$ |
| 49 | $[49, 7, -7]$ | $\phantom{-}2$ |
| 67 | $[67, 67, 2 w - 11]$ | $\phantom{-}12$ |
| 67 | $[67, 67, -2 w - 9]$ | $\phantom{-}4$ |
| 83 | $[83, 83, 4 w + 5]$ | $-12$ |
| 83 | $[83, 83, 4 w - 9]$ | $\phantom{-}0$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w - 2]$ | $1$ |
| $2$ | $[2, 2, -w + 3]$ | $-1$ |
| $3$ | $[3, 3, 2 w - 7]$ | $-1$ |