Base field 5.5.38569.1
Generator \(w\), with minimal polynomial \(x^{5} - 5x^{3} + 4x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[59, 59, w^{4} + w^{3} - 6w^{2} - 4w + 4]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} - 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, -w^{2} + 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -w^{3} + w^{2} + 4w - 2]$ | $-4$ |
| 11 | $[11, 11, w^{3} - 3w]$ | $\phantom{-}\frac{1}{2}e$ |
| 13 | $[13, 13, w^{4} - 5w^{2} + 2]$ | $-2e$ |
| 17 | $[17, 17, w^{3} - 3w - 1]$ | $-e$ |
| 32 | $[32, 2, 2]$ | $-5$ |
| 37 | $[37, 37, w^{4} + w^{3} - 5w^{2} - 5w + 4]$ | $-\frac{3}{2}e$ |
| 43 | $[43, 43, w^{2} + w - 3]$ | $-8$ |
| 43 | $[43, 43, -w^{4} + w^{3} + 4w^{2} - 2w - 2]$ | $\phantom{-}e$ |
| 47 | $[47, 47, -w^{4} - w^{3} + 6w^{2} + 4w - 5]$ | $-12$ |
| 59 | $[59, 59, w^{4} + w^{3} - 6w^{2} - 4w + 4]$ | $-1$ |
| 67 | $[67, 67, -w^{3} + w^{2} + 3w - 4]$ | $\phantom{-}\frac{5}{2}e$ |
| 73 | $[73, 73, w^{4} - 3w^{2} - w - 1]$ | $\phantom{-}\frac{9}{2}e$ |
| 73 | $[73, 73, -2w^{4} - w^{3} + 9w^{2} + 5w - 6]$ | $-3e$ |
| 79 | $[79, 79, -3w^{4} + 13w^{2} + 2w - 7]$ | $-10$ |
| 79 | $[79, 79, -w^{3} + 5w]$ | $-4$ |
| 79 | $[79, 79, -w^{4} + 3w^{2} + 1]$ | $\phantom{-}\frac{5}{2}e$ |
| 83 | $[83, 83, -2w^{4} - 2w^{3} + 11w^{2} + 7w - 8]$ | $-6$ |
| 89 | $[89, 89, -w^{4} - 2w^{3} + 4w^{2} + 7w - 3]$ | $\phantom{-}\frac{5}{2}e$ |
| 101 | $[101, 101, -w^{4} + 5w^{2} - w - 4]$ | $-18$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $59$ | $[59, 59, w^{4} + w^{3} - 6w^{2} - 4w + 4]$ | $1$ |