Base field 4.4.15317.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 5x + 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[8, 8, -w^{2} + 2w]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 3x^{3} - 5x^{2} + 16x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}0$ |
| 2 | $[2, 2, -w + 1]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w^{2} + w + 1]$ | $\phantom{-}e^{3} - 6e - 2$ |
| 19 | $[19, 19, -w^{3} + 5w + 3]$ | $-3e^{3} + 2e^{2} + 16e - 3$ |
| 19 | $[19, 19, w^{3} - 3w^{2} - 2w + 7]$ | $\phantom{-}3e^{3} - 20e - 3$ |
| 43 | $[43, 43, -w^{3} + 3w^{2} + 2w - 5]$ | $-4e^{3} + 25e + 7$ |
| 43 | $[43, 43, -w^{3} + w^{2} + 2w - 1]$ | $-5e^{3} + 2e^{2} + 31e - 8$ |
| 43 | $[43, 43, w^{3} - 2w^{2} - w + 1]$ | $-e^{3} + 5e + 8$ |
| 43 | $[43, 43, -w^{3} + 5w + 1]$ | $-4e^{3} + 4e^{2} + 21e - 9$ |
| 47 | $[47, 47, -w^{3} + w^{2} + 2w + 1]$ | $-4e^{3} + 3e^{2} + 25e - 8$ |
| 47 | $[47, 47, w^{3} - 5w - 5]$ | $-e^{2} - e + 10$ |
| 47 | $[47, 47, -w^{3} + 3w^{2} + 2w - 9]$ | $-2e^{3} + 3e^{2} + 11e - 12$ |
| 47 | $[47, 47, w^{3} - 2w^{2} - w + 3]$ | $-4e^{3} + 3e^{2} + 21e - 4$ |
| 49 | $[49, 7, -w^{3} + w^{2} + 6w + 1]$ | $\phantom{-}2e^{3} + e^{2} - 12e - 9$ |
| 49 | $[49, 7, -w^{3} + 2w^{2} + 5w - 7]$ | $-2e^{3} + e^{2} + 10e + 5$ |
| 53 | $[53, 53, 2w - 1]$ | $-2e$ |
| 67 | $[67, 67, -w^{3} + w^{2} + 4w - 3]$ | $\phantom{-}e^{3} - 2e^{2} - 6e + 3$ |
| 67 | $[67, 67, -w^{3} + 2w^{2} + 3w - 1]$ | $\phantom{-}5e^{3} - 2e^{2} - 30e + 7$ |
| 81 | $[81, 3, -3]$ | $-e^{3} - 2e^{2} + 7e + 6$ |
| 83 | $[83, 83, 2w^{3} - 4w^{2} - 6w + 9]$ | $\phantom{-}3e^{3} - 3e^{2} - 20e + 8$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w]$ | $1$ |