Base field 4.4.19773.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 11x^{2} - 9x + 3\); narrow class number \(4\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2]$ |
Level: | $[13, 13, w^{3} - 2w^{2} - 6w + 1]$ |
Dimension: | $2$ |
CM: | no |
Base change: | yes |
Newspace dimension: | $40$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - x - 5\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, w^{3} - 2w^{2} - 8w - 3]$ | $-e + 1$ |
3 | $[3, 3, w^{3} - 3w^{2} - 5w + 2]$ | $\phantom{-}e$ |
13 | $[13, 13, w^{3} - 2w^{2} - 6w + 1]$ | $-1$ |
16 | $[16, 2, 2]$ | $-4$ |
17 | $[17, 17, -2w^{3} + 5w^{2} + 14w - 1]$ | $-2e + 4$ |
17 | $[17, 17, -w^{3} + 3w^{2} + 5w - 4]$ | $\phantom{-}2e + 2$ |
17 | $[17, 17, -w^{3} + 2w^{2} + 8w + 1]$ | $-2e + 4$ |
17 | $[17, 17, w - 1]$ | $\phantom{-}2e + 2$ |
23 | $[23, 23, 2w^{3} - 6w^{2} - 11w + 7]$ | $-2e - 2$ |
23 | $[23, 23, w^{3} - 3w^{2} - 7w + 4]$ | $-2e - 2$ |
23 | $[23, 23, -w^{2} + 2w + 5]$ | $\phantom{-}2e - 4$ |
23 | $[23, 23, 3w^{3} - 8w^{2} - 20w + 5]$ | $\phantom{-}2e - 4$ |
61 | $[61, 61, -w^{3} + 2w^{2} + 9w + 1]$ | $\phantom{-}3e + 1$ |
61 | $[61, 61, -2w^{3} + 5w^{2} + 13w - 2]$ | $-3e + 4$ |
61 | $[61, 61, w^{3} - 2w^{2} - 9w - 2]$ | $\phantom{-}3e + 1$ |
61 | $[61, 61, 2w^{3} - 5w^{2} - 13w + 1]$ | $-3e + 4$ |
79 | $[79, 79, 4w^{3} - 10w^{2} - 28w + 5]$ | $-3e + 1$ |
79 | $[79, 79, w^{3} - 3w^{2} - 4w + 4]$ | $-3e + 1$ |
79 | $[79, 79, w^{3} - 4w^{2} - 2w + 10]$ | $\phantom{-}3e - 2$ |
79 | $[79, 79, 2w^{3} - 6w^{2} - 10w + 5]$ | $\phantom{-}3e - 2$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$13$ | $[13, 13, w^{3} - 2w^{2} - 6w + 1]$ | $1$ |