Base field 4.4.19664.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 2x + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[10, 10, w^{3} - 2w^{2} - 4w + 3]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + x^{3} - 6x^{2} - 4x + 6\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, -w - 1]$ | $-1$ |
| 5 | $[5, 5, -w^{3} + 2w^{2} + 5w - 1]$ | $-1$ |
| 7 | $[7, 7, -w^{3} + 2w^{2} + 5w - 3]$ | $\phantom{-}e^{3} - 3e + 2$ |
| 29 | $[29, 29, -w^{2} + w + 3]$ | $\phantom{-}2e^{3} - e^{2} - 7e + 6$ |
| 29 | $[29, 29, 2w^{3} - 5w^{2} - 7w + 9]$ | $-2e^{2} - 2e + 6$ |
| 31 | $[31, 31, -w^{3} + 2w^{2} + 5w + 1]$ | $-e^{3} - e^{2} + 4e + 8$ |
| 41 | $[41, 41, -w^{3} + 4w^{2} - w - 3]$ | $\phantom{-}e^{2} + e - 6$ |
| 43 | $[43, 43, -w^{3} + 3w^{2} + 2w - 5]$ | $-e^{3} + e^{2} + 2e - 4$ |
| 47 | $[47, 47, w^{2} - 3w - 3]$ | $\phantom{-}e^{3} + e^{2} - 4e$ |
| 53 | $[53, 53, w^{3} - 2w^{2} - 3w + 1]$ | $-e^{3} - 3e^{2} + 6e + 6$ |
| 59 | $[59, 59, w^{2} - w - 5]$ | $-e^{3} - e^{2} + 4e$ |
| 61 | $[61, 61, 5w^{3} - 12w^{2} - 19w + 17]$ | $-3e^{3} - e^{2} + 14e + 2$ |
| 67 | $[67, 67, 2w^{3} - 5w^{2} - 7w + 5]$ | $-e^{3} - 3e^{2} + 14$ |
| 67 | $[67, 67, w^{3} - 4w^{2} + w + 5]$ | $\phantom{-}2e^{3} - 6e + 8$ |
| 67 | $[67, 67, 3w^{3} - 7w^{2} - 12w + 11]$ | $-2e^{3} + 8e + 2$ |
| 67 | $[67, 67, -2w^{3} + 4w^{2} + 8w - 5]$ | $-e^{3} + 4e^{2} + 7e - 10$ |
| 71 | $[71, 71, -3w^{3} + 8w^{2} + 9w - 9]$ | $-3e^{2} + e + 12$ |
| 71 | $[71, 71, -w^{3} + 3w^{2} + 2w - 7]$ | $-3e^{2} + e + 12$ |
| 79 | $[79, 79, 3w^{3} - 7w^{2} - 14w + 15]$ | $-3e^{3} + e^{2} + 12e - 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, -w - 1]$ | $1$ |
| $5$ | $[5, 5, -w^{3} + 2w^{2} + 5w - 1]$ | $1$ |