Base field 6.6.592661.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 5x^{4} + 4x^{3} + 5x^{2} - 2x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[67, 67, -2w^{5} + w^{4} + 9w^{3} - 3w^{2} - 7w]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $16$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 4x^{3} - 5x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w^{5} - 5w^{3} + 4w]$ | $\phantom{-}e$ |
| 13 | $[13, 13, -w^{3} + 3w]$ | $-2e^{3} - 9e^{2} - 4e + 7$ |
| 25 | $[25, 5, w^{4} - w^{3} - 4w^{2} + 2w + 2]$ | $\phantom{-}e^{3} + 4e^{2} - 5$ |
| 31 | $[31, 31, -w^{5} + 5w^{3} - 5w + 1]$ | $\phantom{-}e^{3} + 4e^{2} - 2e - 4$ |
| 31 | $[31, 31, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ | $\phantom{-}2e^{3} + 9e^{2} + 7e - 6$ |
| 37 | $[37, 37, w^{4} - 5w^{2} + w + 3]$ | $-3e^{3} - 12e^{2} - 3e + 5$ |
| 43 | $[43, 43, -2w^{5} + w^{4} + 9w^{3} - 3w^{2} - 6w]$ | $\phantom{-}2e^{3} + 7e^{2} - 2e - 12$ |
| 47 | $[47, 47, w^{5} - w^{4} - 4w^{3} + 4w^{2} - 2]$ | $-e^{3} - 5e^{2} - 2e$ |
| 49 | $[49, 7, -w^{4} + 4w^{2} + w - 3]$ | $\phantom{-}e^{2} + 5e - 2$ |
| 53 | $[53, 53, -w^{4} + w^{3} + 4w^{2} - 3w - 4]$ | $\phantom{-}3e^{2} + 10e - 2$ |
| 59 | $[59, 59, w^{4} - 5w^{2} - w + 5]$ | $\phantom{-}2e^{3} + 9e^{2} + 4e - 2$ |
| 61 | $[61, 61, w^{3} - w^{2} - 3w]$ | $\phantom{-}e^{3} + 3e^{2} - 6e - 10$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}3e^{3} + 14e^{2} + 6e - 14$ |
| 67 | $[67, 67, -2w^{5} + w^{4} + 9w^{3} - 3w^{2} - 7w]$ | $\phantom{-}1$ |
| 67 | $[67, 67, 2w^{5} - w^{4} - 10w^{3} + 4w^{2} + 9w - 1]$ | $\phantom{-}3e^{3} + 14e^{2} + 5e - 17$ |
| 73 | $[73, 73, w^{5} - w^{4} - 4w^{3} + 5w^{2} + w - 3]$ | $\phantom{-}e^{3} + 6e^{2} + 6e - 13$ |
| 73 | $[73, 73, 3w^{5} - 3w^{4} - 13w^{3} + 11w^{2} + 7w - 3]$ | $-e^{3} - 8e^{2} - 12e + 5$ |
| 83 | $[83, 83, -2w^{5} + 3w^{4} + 9w^{3} - 11w^{2} - 6w + 2]$ | $\phantom{-}e^{2} - 3e - 12$ |
| 97 | $[97, 97, -2w^{4} + w^{3} + 9w^{2} - 3w - 4]$ | $-e^{2} + 2$ |
| 101 | $[101, 101, -2w^{5} + 3w^{4} + 9w^{3} - 11w^{2} - 6w + 4]$ | $\phantom{-}e^{3} + 9e^{2} + 13e - 7$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $67$ | $[67, 67, -2w^{5} + w^{4} + 9w^{3} - 3w^{2} - 7w]$ | $-1$ |