Base field 5.5.138136.1
Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 6x^{3} + 3x^{2} + 4x - 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[8, 2, w^{4} - 7w^{2} - 3w + 5]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + x^{3} - 5x^{2} - x + 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -2w^{4} + w^{3} + 12w^{2} + w - 5]$ | $-e - 1$ |
| 8 | $[8, 2, w^{4} - 7w^{2} - 3w + 5]$ | $-1$ |
| 19 | $[19, 19, -2w^{4} + w^{3} + 12w^{2} - 5]$ | $-e^{3} - e^{2} + 6e - 1$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 5w - 1]$ | $-e^{2} - e + 2$ |
| 29 | $[29, 29, 2w^{4} - 2w^{3} - 11w^{2} + 4w + 3]$ | $-e^{3} - 2e^{2} + 3$ |
| 31 | $[31, 31, -2w^{4} + w^{3} + 12w^{2} + 2w - 5]$ | $\phantom{-}e^{3} + 2e^{2} - 4e - 4$ |
| 37 | $[37, 37, -2w^{4} + 13w^{2} + 5w - 7]$ | $\phantom{-}e^{3} + 4e^{2} - 3e - 10$ |
| 53 | $[53, 53, 3w^{4} - 2w^{3} - 18w^{2} + 3w + 9]$ | $-3e^{3} - 4e^{2} + 11e + 3$ |
| 59 | $[59, 59, 2w^{4} - 13w^{2} - 6w + 5]$ | $\phantom{-}2e^{3} + 6e^{2} - 3e - 12$ |
| 61 | $[61, 61, -3w^{4} + 2w^{3} + 18w^{2} - 2w - 11]$ | $\phantom{-}e^{3} - 2e^{2} - 4e + 8$ |
| 61 | $[61, 61, w^{2} - w - 3]$ | $\phantom{-}2e^{3} - 12e + 5$ |
| 61 | $[61, 61, 6w^{4} - 2w^{3} - 38w^{2} - 6w + 23]$ | $\phantom{-}3e^{3} + 4e^{2} - 9e - 4$ |
| 67 | $[67, 67, -w^{4} + 7w^{2} + 4w - 5]$ | $-5e^{3} - 9e^{2} + 17e + 5$ |
| 67 | $[67, 67, -w^{4} + 6w^{2} + 2w - 1]$ | $-3e^{3} - 7e^{2} + 8e + 8$ |
| 71 | $[71, 71, -w^{2} + 3]$ | $\phantom{-}3e^{3} + 9e^{2} - 7e - 15$ |
| 73 | $[73, 73, 3w^{4} - w^{3} - 19w^{2} - 3w + 9]$ | $\phantom{-}2e^{3} + 3e^{2} - 5e - 4$ |
| 79 | $[79, 79, 3w^{4} - w^{3} - 19w^{2} - 4w + 11]$ | $-3e^{3} - 3e^{2} + 19e + 2$ |
| 83 | $[83, 83, -w^{4} - w^{3} + 7w^{2} + 8w - 3]$ | $\phantom{-}2e^{3} + 4e^{2} - 2e - 9$ |
| 97 | $[97, 97, -2w^{4} + w^{3} + 12w^{2} + 2w - 3]$ | $\phantom{-}3e^{3} + 3e^{2} - 14e - 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $8$ | $[8, 2, w^{4} - 7w^{2} - 3w + 5]$ | $1$ |