Base field \(\Q(\sqrt{2}, \sqrt{3})\)
Generator \(w\), with minimal polynomial \(x^{4} - 4x^{2} + 1\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[64, 4, 2w^{3} - 6w]$ |
Dimension: | $2$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $5$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - 32\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w^{3} - 4w + 1]$ | $\phantom{-}0$ |
9 | $[9, 3, -w^{2} + 2]$ | $\phantom{-}2$ |
23 | $[23, 23, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}e$ |
23 | $[23, 23, w^{2} - w - 3]$ | $\phantom{-}e$ |
23 | $[23, 23, -w^{2} - w + 3]$ | $\phantom{-}e$ |
23 | $[23, 23, -w^{3} - w^{2} + 4w + 1]$ | $\phantom{-}e$ |
25 | $[25, 5, w^{3} - 5w + 1]$ | $\phantom{-}2$ |
25 | $[25, 5, w^{3} - 5w - 1]$ | $\phantom{-}2$ |
47 | $[47, 47, -3w^{3} + 2w^{2} + 12w - 8]$ | $-2e$ |
47 | $[47, 47, -2w^{3} - w^{2} + 6w]$ | $-2e$ |
47 | $[47, 47, 2w^{3} - w^{2} - 6w]$ | $-2e$ |
47 | $[47, 47, w^{2} + w - 5]$ | $-2e$ |
49 | $[49, 7, 2w^{3} - 6w - 1]$ | $\phantom{-}10$ |
49 | $[49, 7, -2w^{3} + 6w - 1]$ | $\phantom{-}10$ |
71 | $[71, 71, 2w^{3} - w^{2} - 7w + 1]$ | $-e$ |
71 | $[71, 71, 3w^{3} - w^{2} - 11w + 2]$ | $-e$ |
71 | $[71, 71, 4w^{3} - 2w^{2} - 14w + 5]$ | $-e$ |
71 | $[71, 71, -3w^{3} + 2w^{2} + 10w - 4]$ | $-e$ |
73 | $[73, 73, -w^{3} - 2w^{2} + 3w + 5]$ | $-6$ |
73 | $[73, 73, -w^{3} + 2w^{2} + 3w - 3]$ | $-6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2,2,w^{3}-4w+1]$ | $1$ |