Base field \(\Q(\sqrt{133}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 33\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[21,21,-w + 4]$ |
Dimension: | $1$ |
CM: | no |
Base change: | no |
Newspace dimension: | $34$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, -w + 6]$ | $\phantom{-}1$ |
3 | $[3, 3, -w - 5]$ | $\phantom{-}1$ |
4 | $[4, 2, 2]$ | $\phantom{-}3$ |
7 | $[7, 7, 3w - 19]$ | $-1$ |
11 | $[11, 11, -2w - 11]$ | $-3$ |
11 | $[11, 11, -2w + 13]$ | $\phantom{-}3$ |
13 | $[13, 13, w + 4]$ | $-6$ |
13 | $[13, 13, -w + 5]$ | $-6$ |
19 | $[19, 19, 5w - 31]$ | $-2$ |
23 | $[23, 23, -w - 7]$ | $\phantom{-}0$ |
23 | $[23, 23, w - 8]$ | $-6$ |
25 | $[25, 5, -5]$ | $-3$ |
31 | $[31, 31, -w - 1]$ | $\phantom{-}3$ |
31 | $[31, 31, w - 2]$ | $-9$ |
41 | $[41, 41, 6w + 31]$ | $\phantom{-}9$ |
41 | $[41, 41, 6w - 37]$ | $\phantom{-}3$ |
43 | $[43, 43, -3w - 17]$ | $\phantom{-}9$ |
43 | $[43, 43, -3w + 20]$ | $\phantom{-}0$ |
59 | $[59, 59, 3w - 17]$ | $-6$ |
59 | $[59, 59, 3w + 14]$ | $\phantom{-}0$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3,3,w + 5]$ | $-1$ |
$7$ | $[7,7,-3w - 16]$ | $1$ |