Base field \(\Q(\sqrt{22}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 22\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[144, 12, 12]$ |
Dimension: | $1$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $44$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, -3w + 14]$ | $\phantom{-}0$ |
3 | $[3, 3, -w + 5]$ | $\phantom{-}1$ |
3 | $[3, 3, w + 5]$ | $\phantom{-}1$ |
7 | $[7, 7, 2w + 9]$ | $\phantom{-}0$ |
7 | $[7, 7, 2w - 9]$ | $\phantom{-}0$ |
11 | $[11, 11, -7w + 33]$ | $-4$ |
13 | $[13, 13, -w - 3]$ | $\phantom{-}2$ |
13 | $[13, 13, -w + 3]$ | $\phantom{-}2$ |
25 | $[25, 5, -5]$ | $-6$ |
29 | $[29, 29, 3w + 13]$ | $-6$ |
29 | $[29, 29, -3w + 13]$ | $-6$ |
59 | $[59, 59, -w - 9]$ | $-4$ |
59 | $[59, 59, w - 9]$ | $-4$ |
61 | $[61, 61, 11w - 51]$ | $\phantom{-}2$ |
61 | $[61, 61, 25w - 117]$ | $\phantom{-}2$ |
67 | $[67, 67, 9w - 43]$ | $\phantom{-}4$ |
67 | $[67, 67, -9w - 43]$ | $\phantom{-}4$ |
79 | $[79, 79, 2w - 3]$ | $-8$ |
79 | $[79, 79, -2w - 3]$ | $-8$ |
89 | $[89, 89, 4w - 21]$ | $-6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, -3w + 14]$ | $-1$ |
$3$ | $[3, 3, -w + 5]$ | $-1$ |
$3$ | $[3, 3, w + 5]$ | $-1$ |