Base field 6.6.300125.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 7x^{4} + 2x^{3} + 7x^{2} - 2x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[125, 5, 4w^{5} - w^{4} - 29w^{3} - 13w^{2} + 19w + 2]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} + 10x + 17\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 29 | $[29, 29, -9w^{5} + 3w^{4} + 64w^{3} + 26w^{2} - 40w - 10]$ | $-1$ |
| 29 | $[29, 29, w^{5} - 7w^{3} - 5w^{2} + 2w + 2]$ | $-1$ |
| 29 | $[29, 29, w^{4} - w^{3} - 6w^{2} + 2]$ | $-1$ |
| 29 | $[29, 29, 5w^{5} - w^{4} - 36w^{3} - 19w^{2} + 21w + 9]$ | $-1$ |
| 29 | $[29, 29, -w^{5} + w^{4} + 7w^{3} - 2w^{2} - 6w + 1]$ | $-1$ |
| 29 | $[29, 29, 2w^{5} - 15w^{3} - 10w^{2} + 11w + 5]$ | $-1$ |
| 41 | $[41, 41, 5w^{5} - w^{4} - 36w^{3} - 18w^{2} + 21w + 5]$ | $\phantom{-}e$ |
| 41 | $[41, 41, -5w^{5} + 2w^{4} + 36w^{3} + 11w^{2} - 25w - 2]$ | $\phantom{-}e$ |
| 41 | $[41, 41, 6w^{5} - w^{4} - 44w^{3} - 23w^{2} + 30w + 8]$ | $\phantom{-}e$ |
| 41 | $[41, 41, 13w^{5} - 4w^{4} - 93w^{3} - 39w^{2} + 59w + 16]$ | $\phantom{-}e$ |
| 41 | $[41, 41, -4w^{5} + 30w^{3} + 19w^{2} - 19w - 8]$ | $\phantom{-}e$ |
| 41 | $[41, 41, w^{5} - 7w^{3} - 6w^{2} + 2w + 3]$ | $\phantom{-}e$ |
| 49 | $[49, 7, -5w^{5} + w^{4} + 36w^{3} + 19w^{2} - 22w - 6]$ | $-3e - 10$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}e - 8$ |
| 71 | $[71, 71, -8w^{5} + w^{4} + 58w^{3} + 34w^{2} - 34w - 16]$ | $-3e - 19$ |
| 71 | $[71, 71, -6w^{5} + 2w^{4} + 42w^{3} + 18w^{2} - 23w - 6]$ | $-3e - 19$ |
| 71 | $[71, 71, -8w^{5} + 2w^{4} + 58w^{3} + 27w^{2} - 38w - 10]$ | $-3e - 19$ |
| 71 | $[71, 71, 4w^{5} - 30w^{3} - 19w^{2} + 20w + 8]$ | $-3e - 19$ |
| 71 | $[71, 71, -10w^{5} + 3w^{4} + 72w^{3} + 30w^{2} - 48w - 10]$ | $-3e - 19$ |
| 71 | $[71, 71, -8w^{5} + 2w^{4} + 58w^{3} + 26w^{2} - 37w - 8]$ | $-3e - 19$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $125$ | $[125, 5, 4w^{5} - w^{4} - 29w^{3} - 13w^{2} + 19w + 2]$ | $-1$ |