Base field 6.6.980125.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 6x^{4} + 6x^{3} + 7x^{2} - 5x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[19, 19, -w^{5} - w^{4} + 5w^{3} + 4w^{2} - 5w - 3]$ |
| Dimension: | $2$ |
| 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:
| \(x^{2} + x - 5\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -w^{2} + 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w^{4} + w^{3} - 4w^{2} - 3w + 2]$ | $-e - 1$ |
| 11 | $[11, 11, -w^{5} + 6w^{3} - w^{2} - 7w + 1]$ | $-e - 4$ |
| 19 | $[19, 19, -w^{5} - w^{4} + 5w^{3} + 4w^{2} - 5w - 3]$ | $\phantom{-}1$ |
| 29 | $[29, 29, -2w^{4} - w^{3} + 9w^{2} + 2w - 5]$ | $-e + 5$ |
| 31 | $[31, 31, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 7w + 1]$ | $\phantom{-}4e + 2$ |
| 41 | $[41, 41, 2w^{5} + w^{4} - 10w^{3} - 3w^{2} + 7w + 2]$ | $-8$ |
| 41 | $[41, 41, w^{5} - w^{4} - 6w^{3} + 5w^{2} + 6w - 3]$ | $-8$ |
| 41 | $[41, 41, w^{5} - 6w^{3} + w^{2} + 7w - 2]$ | $\phantom{-}e - 3$ |
| 59 | $[59, 59, -w^{5} - w^{4} + 4w^{3} + 4w^{2} - 2w - 3]$ | $-4e$ |
| 59 | $[59, 59, w^{5} - w^{4} - 5w^{3} + 6w^{2} + 2w - 4]$ | $\phantom{-}2$ |
| 59 | $[59, 59, -w^{5} + 4w^{3} - w^{2} - w + 1]$ | $\phantom{-}e - 5$ |
| 61 | $[61, 61, -w^{4} + 4w^{2} - 2w - 2]$ | $\phantom{-}2e - 8$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}2e - 1$ |
| 71 | $[71, 71, 2w^{5} + w^{4} - 10w^{3} - 3w^{2} + 9w + 3]$ | $\phantom{-}2e$ |
| 81 | $[81, 3, w^{5} + 2w^{4} - 4w^{3} - 8w^{2} + 2w + 3]$ | $-2e + 4$ |
| 89 | $[89, 89, -w^{5} + 6w^{3} - 7w]$ | $\phantom{-}6$ |
| 89 | $[89, 89, w^{5} + w^{4} - 5w^{3} - 4w^{2} + 6w + 2]$ | $-3e - 6$ |
| 101 | $[101, 101, w^{5} - 4w^{3} + 2w^{2} + w - 3]$ | $-5e + 2$ |
| 101 | $[101, 101, w^{5} + 2w^{4} - 4w^{3} - 8w^{2} + 3w + 4]$ | $\phantom{-}6e + 6$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, -w^{5} - w^{4} + 5w^{3} + 4w^{2} - 5w - 3]$ | $-1$ |