Base field 6.6.966125.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 6x^{4} + 4x^{3} + 8x^{2} - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[59, 59, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w - 2]$ |
| Dimension: | $6$ |
| 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:
| \(x^{6} + 12x^{5} + 53x^{4} + 104x^{3} + 84x^{2} + 16x - 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w - 1]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w^{3} - 3w]$ | $-e - 3$ |
| 19 | $[19, 19, -w^{5} + w^{4} + 5w^{3} - 4w^{2} - 5w]$ | $-e^{5} - 12e^{4} - 51e^{3} - 88e^{2} - 49e - 2$ |
| 25 | $[25, 5, w^{5} - 2w^{4} - 6w^{3} + 8w^{2} + 8w]$ | $-e^{5} - 10e^{4} - 33e^{3} - 40e^{2} - 15e - 4$ |
| 29 | $[29, 29, -w^{4} + 4w^{2} + 1]$ | $\phantom{-}2e^{3} + 11e^{2} + 13e + 2$ |
| 31 | $[31, 31, w^{5} - 2w^{4} - 5w^{3} + 9w^{2} + 3w - 4]$ | $-e^{3} - 4e^{2} + e + 4$ |
| 31 | $[31, 31, -w^{2} + 2]$ | $\phantom{-}2e^{5} + 20e^{4} + 69e^{3} + 93e^{2} + 34e - 8$ |
| 59 | $[59, 59, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w - 2]$ | $\phantom{-}1$ |
| 59 | $[59, 59, w^{4} - w^{3} - 5w^{2} + 3w + 4]$ | $-2e^{2} - 6e - 2$ |
| 59 | $[59, 59, -w^{4} - w^{3} + 4w^{2} + 5w]$ | $\phantom{-}2e^{5} + 20e^{4} + 70e^{3} + 100e^{2} + 48e + 5$ |
| 61 | $[61, 61, w^{5} - w^{4} - 4w^{3} + 5w^{2} - 4]$ | $-2e^{3} - 14e^{2} - 23e + 2$ |
| 64 | $[64, 2, 2]$ | $\phantom{-}2e^{5} + 21e^{4} + 75e^{3} + 103e^{2} + 43e + 6$ |
| 71 | $[71, 71, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 6w]$ | $-2e^{5} - 19e^{4} - 62e^{3} - 77e^{2} - 20e + 5$ |
| 71 | $[71, 71, -w^{5} + 2w^{4} + 4w^{3} - 9w^{2} + w + 4]$ | $\phantom{-}4e^{4} + 31e^{3} + 70e^{2} + 37e - 8$ |
| 71 | $[71, 71, 2w^{5} - 3w^{4} - 9w^{3} + 13w^{2} + 4w - 4]$ | $-3e^{5} - 27e^{4} - 78e^{3} - 72e^{2} + 2e + 6$ |
| 71 | $[71, 71, w^{3} - 5w]$ | $-2e^{5} - 17e^{4} - 42e^{3} - 19e^{2} + 26e + 11$ |
| 79 | $[79, 79, w^{5} - w^{4} - 4w^{3} + 4w^{2} + w - 2]$ | $\phantom{-}3e^{5} + 31e^{4} + 106e^{3} + 126e^{2} + 21e - 13$ |
| 89 | $[89, 89, w^{3} - w^{2} - 4w + 1]$ | $-2e^{5} - 20e^{4} - 70e^{3} - 103e^{2} - 60e - 6$ |
| 101 | $[101, 101, -2w^{5} + 3w^{4} + 11w^{3} - 13w^{2} - 12w + 2]$ | $-2e^{4} - 15e^{3} - 29e^{2} - 2e + 4$ |
| 101 | $[101, 101, 2w^{5} - 2w^{4} - 13w^{3} + 7w^{2} + 20w + 4]$ | $\phantom{-}2e^{5} + 18e^{4} + 50e^{3} + 40e^{2} - 4e + 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $59$ | $[59, 59, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w - 2]$ | $-1$ |