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: | $[396, 66, 24w - 78]$ |
Dimension: | $1$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w - 2]$ | $-1$ |
2 | $[2, 2, -w + 3]$ | $-1$ |
3 | $[3, 3, 2w - 7]$ | $\phantom{-}0$ |
11 | $[11, 11, 4w - 13]$ | $\phantom{-}1$ |
17 | $[17, 17, -2w + 5]$ | $\phantom{-}6$ |
17 | $[17, 17, 2w + 3]$ | $\phantom{-}6$ |
25 | $[25, 5, 5]$ | $-10$ |
29 | $[29, 29, -2w + 3]$ | $\phantom{-}6$ |
29 | $[29, 29, 2w + 1]$ | $\phantom{-}6$ |
31 | $[31, 31, -2w + 9]$ | $-4$ |
31 | $[31, 31, 2w + 7]$ | $-4$ |
37 | $[37, 37, -4w - 11]$ | $\phantom{-}2$ |
37 | $[37, 37, 4w - 15]$ | $\phantom{-}2$ |
41 | $[41, 41, -10w + 33]$ | $-6$ |
41 | $[41, 41, 6w - 19]$ | $-6$ |
49 | $[49, 7, -7]$ | $-10$ |
67 | $[67, 67, 2w - 11]$ | $\phantom{-}8$ |
67 | $[67, 67, -2w - 9]$ | $\phantom{-}8$ |
83 | $[83, 83, 4w + 5]$ | $\phantom{-}12$ |
83 | $[83, 83, 4w - 9]$ | $\phantom{-}12$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w - 2]$ | $1$ |
$2$ | $[2, 2, -w + 3]$ | $1$ |
$3$ | $[3, 3, 2w - 7]$ | $-1$ |
$11$ | $[11, 11, 4w - 13]$ | $-1$ |