Base field 4.4.19664.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 2x + 2\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[8, 2, -w^{3} + 3w^{2} + 2w - 4]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - 2\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $\phantom{-}0$ |
2 | $[2, 2, -w - 1]$ | $\phantom{-}1$ |
5 | $[5, 5, -w^{3} + 2w^{2} + 5w - 1]$ | $\phantom{-}e$ |
7 | $[7, 7, -w^{3} + 2w^{2} + 5w - 3]$ | $\phantom{-}e + 2$ |
29 | $[29, 29, -w^{2} + w + 3]$ | $-2e$ |
29 | $[29, 29, 2w^{3} - 5w^{2} - 7w + 9]$ | $\phantom{-}6e + 2$ |
31 | $[31, 31, -w^{3} + 2w^{2} + 5w + 1]$ | $-2e - 4$ |
41 | $[41, 41, -w^{3} + 4w^{2} - w - 3]$ | $-3e + 2$ |
43 | $[43, 43, -w^{3} + 3w^{2} + 2w - 5]$ | $\phantom{-}e + 4$ |
47 | $[47, 47, w^{2} - 3w - 3]$ | $-4e + 2$ |
53 | $[53, 53, w^{3} - 2w^{2} - 3w + 1]$ | $-3e - 4$ |
59 | $[59, 59, w^{2} - w - 5]$ | $\phantom{-}3e - 4$ |
61 | $[61, 61, 5w^{3} - 12w^{2} - 19w + 17]$ | $-5e$ |
67 | $[67, 67, 2w^{3} - 5w^{2} - 7w + 5]$ | $-5e$ |
67 | $[67, 67, w^{3} - 4w^{2} + w + 5]$ | $-2e - 2$ |
67 | $[67, 67, 3w^{3} - 7w^{2} - 12w + 11]$ | $\phantom{-}4$ |
67 | $[67, 67, -2w^{3} + 4w^{2} + 8w - 5]$ | $\phantom{-}2e + 6$ |
71 | $[71, 71, -3w^{3} + 8w^{2} + 9w - 9]$ | $\phantom{-}5e + 2$ |
71 | $[71, 71, -w^{3} + 3w^{2} + 2w - 7]$ | $\phantom{-}7e - 2$ |
79 | $[79, 79, 3w^{3} - 7w^{2} - 14w + 15]$ | $-4e + 6$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w]$ | $-1$ |
$2$ | $[2, 2, -w - 1]$ | $-1$ |