Base field 4.4.16448.2
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 7x^{2} + 8x + 14\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[4, 2, w^{2} - w - 4]$ |
Dimension: | $2$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $7$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - x - 8\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w^{3} - 3w^{2} - 3w + 10]$ | $-1$ |
2 | $[2, 2, w^{3} - 6w - 5]$ | $-1$ |
7 | $[7, 7, -w^{3} + 3w^{2} + 2w - 7]$ | $\phantom{-}e$ |
7 | $[7, 7, -w^{3} + 5w + 3]$ | $\phantom{-}e$ |
31 | $[31, 31, -w^{3} + 2w^{2} + 3w - 5]$ | $-2e$ |
31 | $[31, 31, -w^{2} - w + 1]$ | $-2e$ |
31 | $[31, 31, -w^{2} + 3w - 1]$ | $-2e$ |
31 | $[31, 31, -w^{3} + w^{2} + 4w + 1]$ | $-2e$ |
41 | $[41, 41, -w^{3} + 3w^{2} + 2w - 9]$ | $\phantom{-}6$ |
41 | $[41, 41, w^{3} + w^{2} - 8w - 11]$ | $\phantom{-}6$ |
47 | $[47, 47, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}0$ |
47 | $[47, 47, w^{3} - 2w^{2} - 3w + 3]$ | $\phantom{-}0$ |
49 | $[49, 7, 2w^{2} - 2w - 9]$ | $\phantom{-}14$ |
71 | $[71, 71, 5w^{3} - 16w^{2} - 17w + 61]$ | $\phantom{-}3e$ |
71 | $[71, 71, -2w^{3} - 2w^{2} + 10w + 13]$ | $\phantom{-}3e$ |
73 | $[73, 73, 3w^{3} + w^{2} - 18w - 17]$ | $-2e - 6$ |
73 | $[73, 73, w^{3} - 5w - 1]$ | $-2e + 6$ |
73 | $[73, 73, w^{3} - 7w - 3]$ | $-2e + 6$ |
73 | $[73, 73, -3w^{3} + 10w^{2} + 7w - 31]$ | $-2e - 6$ |
81 | $[81, 3, -3]$ | $-3e + 10$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w^{3} - 3w^{2} - 3w + 10]$ | $1$ |
$2$ | $[2, 2, w^{3} - 6w - 5]$ | $1$ |