Base field 6.6.1312625.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 7x^{4} + 7x^{3} + 12x^{2} - 12x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[31, 31, -2w^{5} + 12w^{3} + w^{2} - 16w - 2]$ |
| Dimension: | $13$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $26$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{13} + 11x^{12} + 29x^{11} - 83x^{10} - 478x^{9} - 188x^{8} + 2036x^{7} + 2425x^{6} - 2789x^{5} - 4618x^{4} + 1084x^{3} + 2556x^{2} + 145x - 275\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, -w^{5} + 6w^{3} + w^{2} - 8w - 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w + 1]$ | $...$ |
| 16 | $[16, 2, -w^{5} + 6w^{3} + w^{2} - 7w - 2]$ | $...$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 4w - 3]$ | $...$ |
| 29 | $[29, 29, 2w^{5} - 13w^{3} + 19w - 2]$ | $...$ |
| 31 | $[31, 31, -2w^{5} + 12w^{3} + w^{2} - 16w - 2]$ | $\phantom{-}1$ |
| 41 | $[41, 41, -w^{5} + 7w^{3} + w^{2} - 12w - 2]$ | $...$ |
| 41 | $[41, 41, 2w^{5} + w^{4} - 13w^{3} - 5w^{2} + 19w + 4]$ | $...$ |
| 59 | $[59, 59, -w^{5} + 7w^{3} + w^{2} - 11w]$ | $...$ |
| 61 | $[61, 61, w^{5} - 7w^{3} + 10w]$ | $...$ |
| 61 | $[61, 61, -2w^{5} + 12w^{3} + w^{2} - 16w - 3]$ | $...$ |
| 71 | $[71, 71, -2w^{5} - w^{4} + 12w^{3} + 5w^{2} - 16w - 4]$ | $...$ |
| 71 | $[71, 71, -3w^{5} - w^{4} + 20w^{3} + 6w^{2} - 31w - 5]$ | $...$ |
| 71 | $[71, 71, -w^{5} + 7w^{3} - w^{2} - 12w + 2]$ | $...$ |
| 79 | $[79, 79, w^{5} + w^{4} - 7w^{3} - 5w^{2} + 10w + 4]$ | $...$ |
| 79 | $[79, 79, -w^{5} - w^{4} + 8w^{3} + 4w^{2} - 15w + 1]$ | $...$ |
| 79 | $[79, 79, 2w^{5} + w^{4} - 13w^{3} - 5w^{2} + 20w + 3]$ | $...$ |
| 89 | $[89, 89, 2w^{5} + w^{4} - 14w^{3} - 5w^{2} + 23w + 1]$ | $...$ |
| 89 | $[89, 89, -2w^{5} - w^{4} + 12w^{3} + 5w^{2} - 15w - 4]$ | $...$ |
| 89 | $[89, 89, 2w^{5} + w^{4} - 11w^{3} - 5w^{2} + 13w + 3]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $31$ | $[31, 31, -2w^{5} + 12w^{3} + w^{2} - 16w - 2]$ | $-1$ |