Base field 4.4.19664.1
Generator \(w\), with minimal polynomial \(x^4 - 2 x^3 - 5 x^2 + 2 x + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[8, 4, w^2 - 2 w - 5]$ |
| 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:
| \(x^3 + x^2 - 4 x - 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -w - 1]$ | $\phantom{-}0$ |
| 5 | $[5, 5, -w^3 + 2 w^2 + 5 w - 1]$ | $-e + 1$ |
| 7 | $[7, 7, -w^3 + 2 w^2 + 5 w - 3]$ | $-2$ |
| 29 | $[29, 29, -w^2 + w + 3]$ | $\phantom{-}2 e^2 + e - 5$ |
| 29 | $[29, 29, 2 w^3 - 5 w^2 - 7 w + 9]$ | $-e^2 - 1$ |
| 31 | $[31, 31, -w^3 + 2 w^2 + 5 w + 1]$ | $\phantom{-}2 e - 2$ |
| 41 | $[41, 41, -w^3 + 4 w^2 - w - 3]$ | $-e^2 - 2 e + 3$ |
| 43 | $[43, 43, -w^3 + 3 w^2 + 2 w - 5]$ | $\phantom{-}2 e^2 - 2 e - 10$ |
| 47 | $[47, 47, w^2 - 3 w - 3]$ | $\phantom{-}2 e^2 - 2$ |
| 53 | $[53, 53, w^3 - 2 w^2 - 3 w + 1]$ | $\phantom{-}e^2 + 4 e + 3$ |
| 59 | $[59, 59, w^2 - w - 5]$ | $\phantom{-}2 e^2 - 8$ |
| 61 | $[61, 61, 5 w^3 - 12 w^2 - 19 w + 17]$ | $-e^2 + 4 e + 9$ |
| 67 | $[67, 67, 2 w^3 - 5 w^2 - 7 w + 5]$ | $\phantom{-}4 e + 2$ |
| 67 | $[67, 67, w^3 - 4 w^2 + w + 5]$ | $-4 e^2 - 2 e + 6$ |
| 67 | $[67, 67, 3 w^3 - 7 w^2 - 12 w + 11]$ | $-4 e^2 - 4 e + 8$ |
| 67 | $[67, 67, -2 w^3 + 4 w^2 + 8 w - 5]$ | $\phantom{-}4 e + 8$ |
| 71 | $[71, 71, -3 w^3 + 8 w^2 + 9 w - 9]$ | $\phantom{-}2 e^2 + 6 e - 10$ |
| 71 | $[71, 71, -w^3 + 3 w^2 + 2 w - 7]$ | $-6 e^2 - 2 e + 14$ |
| 79 | $[79, 79, 3 w^3 - 7 w^2 - 14 w + 15]$ | $-4 e - 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w - 1]$ | $-1$ |