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: | $[7, 7, -w^3 + 2 w^2 + 5 w - 3]$ |
| Dimension: | $5$ |
| 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:
| \(x^5 + 2 x^4 - 4 x^3 - 6 x^2 + 4 x + 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e^2 + e - 2$ |
| 2 | $[2, 2, -w - 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w^3 + 2 w^2 + 5 w - 1]$ | $-e^2 - e + 2$ |
| 7 | $[7, 7, -w^3 + 2 w^2 + 5 w - 3]$ | $\phantom{-}1$ |
| 29 | $[29, 29, -w^2 + w + 3]$ | $-e^2 - 2 e$ |
| 29 | $[29, 29, 2 w^3 - 5 w^2 - 7 w + 9]$ | $-e^4 - 3 e^3 + 2 e^2 + 6 e + 2$ |
| 31 | $[31, 31, -w^3 + 2 w^2 + 5 w + 1]$ | $\phantom{-}e^3 + 2 e^2 - e - 4$ |
| 41 | $[41, 41, -w^3 + 4 w^2 - w - 3]$ | $\phantom{-}e^4 - 2 e^3 - 9 e^2 + 6 e + 10$ |
| 43 | $[43, 43, -w^3 + 3 w^2 + 2 w - 5]$ | $-e^4 - 2 e^3 + 4 e^2 + 6 e - 6$ |
| 47 | $[47, 47, w^2 - 3 w - 3]$ | $\phantom{-}2 e^4 + 5 e^3 - 2 e^2 - 8 e - 6$ |
| 53 | $[53, 53, w^3 - 2 w^2 - 3 w + 1]$ | $-2 e^4 - 2 e^3 + 8 e^2 + 2 e - 6$ |
| 59 | $[59, 59, w^2 - w - 5]$ | $-4 e^4 - 7 e^3 + 10 e^2 + 11 e - 2$ |
| 61 | $[61, 61, 5 w^3 - 12 w^2 - 19 w + 17]$ | $-2 e^4 - 2 e^3 + 10 e^2 + 2 e - 10$ |
| 67 | $[67, 67, 2 w^3 - 5 w^2 - 7 w + 5]$ | $\phantom{-}2 e^4 + 3 e^3 - 5 e^2 - 2 e$ |
| 67 | $[67, 67, w^3 - 4 w^2 + w + 5]$ | $-3 e^3 + 11 e - 8$ |
| 67 | $[67, 67, 3 w^3 - 7 w^2 - 12 w + 11]$ | $-4 e^4 - 7 e^3 + 13 e^2 + 16 e - 8$ |
| 67 | $[67, 67, -2 w^3 + 4 w^2 + 8 w - 5]$ | $-3 e - 2$ |
| 71 | $[71, 71, -3 w^3 + 8 w^2 + 9 w - 9]$ | $-e^4 - 2 e^3 + 4 e^2 + 4 e - 10$ |
| 71 | $[71, 71, -w^3 + 3 w^2 + 2 w - 7]$ | $\phantom{-}4 e^4 + 6 e^3 - 18 e^2 - 17 e + 10$ |
| 79 | $[79, 79, 3 w^3 - 7 w^2 - 14 w + 15]$ | $\phantom{-}3 e^3 + 3 e^2 - 10 e - 8$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, -w^3 + 2 w^2 + 5 w - 3]$ | $-1$ |