Base field 4.4.16448.2
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 7x^{2} + 8x + 14\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[8,4,w^{2} - 3]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - 3x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{3} - 3w^{2} - 3w + 10]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w^{3} - 6w - 5]$ | $\phantom{-}0$ |
| 7 | $[7, 7, -w^{3} + 3w^{2} + 2w - 7]$ | $-e - 3$ |
| 7 | $[7, 7, -w^{3} + 5w + 3]$ | $-2e^{2} + e + 5$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 3w - 5]$ | $-2e + 3$ |
| 31 | $[31, 31, -w^{2} - w + 1]$ | $\phantom{-}5e^{2} + 2e - 11$ |
| 31 | $[31, 31, -w^{2} + 3w - 1]$ | $\phantom{-}e^{2} - 2e - 5$ |
| 31 | $[31, 31, -w^{3} + w^{2} + 4w + 1]$ | $-1$ |
| 41 | $[41, 41, -w^{3} + 3w^{2} + 2w - 9]$ | $\phantom{-}3e^{2} + e - 7$ |
| 41 | $[41, 41, w^{3} + w^{2} - 8w - 11]$ | $-e^{2} - 3e + 1$ |
| 47 | $[47, 47, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}4e^{2} + e - 8$ |
| 47 | $[47, 47, w^{3} - 2w^{2} - 3w + 3]$ | $-2e^{2} + 5e + 8$ |
| 49 | $[49, 7, 2w^{2} - 2w - 9]$ | $-2e^{2} + e + 3$ |
| 71 | $[71, 71, 5w^{3} - 16w^{2} - 17w + 61]$ | $-7e^{2} + 4e + 12$ |
| 71 | $[71, 71, -2w^{3} - 2w^{2} + 10w + 13]$ | $\phantom{-}e^{2} - 6e - 2$ |
| 73 | $[73, 73, 3w^{3} + w^{2} - 18w - 17]$ | $\phantom{-}6e^{2} - 8e - 19$ |
| 73 | $[73, 73, w^{3} - 5w - 1]$ | $-4e^{2} + 2e$ |
| 73 | $[73, 73, w^{3} - 7w - 3]$ | $\phantom{-}4e^{2} - 6e - 12$ |
| 73 | $[73, 73, -3w^{3} + 10w^{2} + 7w - 31]$ | $-6e^{2} + 8e + 13$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}5e^{2} - 3e - 15$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2,2,-w^{3} + 6w + 5]$ | $-1$ |