Base field 5.5.186037.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 6x^{3} + 2x^{2} + 5x - 2\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2]$ |
Level: | $[2, 2, w]$ |
Dimension: | $2$ |
CM: | no |
Base change: | no |
Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{2} - 12\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w]$ | $-1$ |
7 | $[7, 7, w^{4} - w^{3} - 6w^{2} + w + 5]$ | $\phantom{-}0$ |
13 | $[13, 13, -w^{4} + w^{3} + 6w^{2} - w - 3]$ | $\phantom{-}e$ |
16 | $[16, 2, w^{4} - w^{3} - 6w^{2} + 2w + 5]$ | $-5$ |
19 | $[19, 19, -w^{4} + 7w^{2} + 2w - 3]$ | $-2e$ |
23 | $[23, 23, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}2e$ |
23 | $[23, 23, -w^{4} + 7w^{2} + 4w - 7]$ | $-2e$ |
25 | $[25, 5, -w^{2} + w + 3]$ | $-e$ |
31 | $[31, 31, w^{2} - w - 1]$ | $-8$ |
31 | $[31, 31, w^{4} - 6w^{2} - 2w + 3]$ | $\phantom{-}2e$ |
31 | $[31, 31, w^{3} - 2w^{2} - 4w + 3]$ | $-8$ |
67 | $[67, 67, 2w^{3} - 3w^{2} - 8w + 3]$ | $\phantom{-}0$ |
79 | $[79, 79, -w^{4} + 6w^{2} + 3w - 1]$ | $\phantom{-}8$ |
83 | $[83, 83, 2w^{4} - 14w^{2} - 7w + 11]$ | $-12$ |
83 | $[83, 83, w^{4} - 2w^{3} - 4w^{2} + 6w + 1]$ | $-4e$ |
83 | $[83, 83, -w^{4} + 8w^{2} + 3w - 7]$ | $-12$ |
97 | $[97, 97, w^{4} - 2w^{3} - 4w^{2} + 4w + 1]$ | $\phantom{-}e$ |
101 | $[101, 101, 2w^{4} - 14w^{2} - 6w + 11]$ | $-6$ |
101 | $[101, 101, -w^{4} + 8w^{2} + 2w - 9]$ | $\phantom{-}e$ |
107 | $[107, 107, -w^{3} + 2w^{2} + 4w - 1]$ | $\phantom{-}0$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$2$ | $[2, 2, w]$ | $1$ |