Base field 5.5.161121.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 6x^{3} + 3x^{2} + 5x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[9, 3, -w^{4} + w^{3} + 6w^{2} - 4w - 5]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $5$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} + 4x - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w^{4} - w^{3} - 6w^{2} + 3w + 4]$ | $-1$ |
| 3 | $[3, 3, w - 1]$ | $\phantom{-}1$ |
| 9 | $[9, 3, -2w^{4} + 3w^{3} + 11w^{2} - 12w - 5]$ | $\phantom{-}e$ |
| 17 | $[17, 17, 2w^{4} - 2w^{3} - 11w^{2} + 7w + 6]$ | $\phantom{-}4$ |
| 31 | $[31, 31, -w^{4} + 2w^{3} + 5w^{2} - 7w - 4]$ | $\phantom{-}2$ |
| 31 | $[31, 31, -2w^{4} + 3w^{3} + 11w^{2} - 12w - 7]$ | $\phantom{-}6$ |
| 32 | $[32, 2, 2]$ | $-e - 5$ |
| 37 | $[37, 37, w^{4} - 2w^{3} - 4w^{2} + 7w]$ | $\phantom{-}2e + 8$ |
| 41 | $[41, 41, 2w^{4} - 3w^{3} - 11w^{2} + 10w + 6]$ | $\phantom{-}2$ |
| 43 | $[43, 43, -w^{4} + 2w^{3} + 4w^{2} - 6w]$ | $\phantom{-}2e + 4$ |
| 43 | $[43, 43, 3w^{4} - 4w^{3} - 16w^{2} + 15w + 7]$ | $\phantom{-}e + 2$ |
| 47 | $[47, 47, w^{2} - 3]$ | $-3e - 4$ |
| 67 | $[67, 67, -2w^{4} + 3w^{3} + 10w^{2} - 11w - 5]$ | $-2e - 6$ |
| 71 | $[71, 71, 4w^{4} - 5w^{3} - 22w^{2} + 18w + 12]$ | $-e + 4$ |
| 79 | $[79, 79, -2w^{4} + 3w^{3} + 12w^{2} - 12w - 9]$ | $-e - 8$ |
| 79 | $[79, 79, 3w^{4} - 3w^{3} - 16w^{2} + 8w + 4]$ | $-2e - 8$ |
| 83 | $[83, 83, w^{4} - 2w^{3} - 6w^{2} + 8w + 7]$ | $\phantom{-}2e + 8$ |
| 97 | $[97, 97, -2w^{4} + 3w^{3} + 9w^{2} - 8w - 4]$ | $\phantom{-}2$ |
| 107 | $[107, 107, 2w^{4} - 3w^{3} - 11w^{2} + 10w + 9]$ | $-3e - 2$ |
| 107 | $[107, 107, w^{4} - w^{3} - 5w^{2} + 4w]$ | $-2e + 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w^{4} - w^{3} - 6w^{2} + 3w + 4]$ | $1$ |
| $3$ | $[3, 3, w - 1]$ | $-1$ |