Base field \(\Q(\sqrt{57}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 14\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[228, 114, -4w + 2]$ |
Dimension: | $1$ |
CM: | no |
Base change: | no |
Newspace dimension: | $42$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -w + 4]$ | $-1$ |
2 | $[2, 2, -w - 3]$ | $-1$ |
3 | $[3, 3, -4w - 13]$ | $\phantom{-}1$ |
7 | $[7, 7, -2w - 7]$ | $-4$ |
7 | $[7, 7, -2w + 9]$ | $-1$ |
19 | $[19, 19, 10w + 33]$ | $\phantom{-}1$ |
25 | $[25, 5, 5]$ | $-1$ |
29 | $[29, 29, -6w - 19]$ | $\phantom{-}6$ |
29 | $[29, 29, -6w + 25]$ | $-9$ |
41 | $[41, 41, 2w - 5]$ | $\phantom{-}3$ |
41 | $[41, 41, -2w - 3]$ | $\phantom{-}6$ |
43 | $[43, 43, 2w - 11]$ | $\phantom{-}5$ |
43 | $[43, 43, 2w + 9]$ | $-4$ |
53 | $[53, 53, 2w - 3]$ | $\phantom{-}0$ |
53 | $[53, 53, -2w - 1]$ | $\phantom{-}9$ |
59 | $[59, 59, 4w - 15]$ | $\phantom{-}0$ |
59 | $[59, 59, 4w + 11]$ | $-3$ |
61 | $[61, 61, -4w - 15]$ | $-1$ |
61 | $[61, 61, -4w + 19]$ | $-7$ |
71 | $[71, 71, 8w + 25]$ | $-3$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -w + 4]$ | $1$ |
$2$ | $[2, 2, -w - 3]$ | $1$ |
$3$ | $[3, 3, -4w - 13]$ | $-1$ |
$19$ | $[19, 19, 10w + 33]$ | $-1$ |