Base field 6.6.905177.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 7x^{4} + 9x^{3} + 7x^{2} - 9x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[49, 7, -w^{5} - w^{4} + 6w^{3} + 3w^{2} - 7w]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} + 2x - 7\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 8 | $[8, 2, -2w^{5} - w^{4} + 13w^{3} + w^{2} - 16w - 1]$ | $\phantom{-}e$ |
| 8 | $[8, 2, -3w^{5} - w^{4} + 19w^{3} - 2w^{2} - 20w + 1]$ | $-e - 2$ |
| 13 | $[13, 13, -w^{2} + 3]$ | $\phantom{-}2$ |
| 29 | $[29, 29, -w^{5} - w^{4} + 5w^{3} + 2w^{2} - 3w - 1]$ | $-6$ |
| 41 | $[41, 41, -2w^{5} + 13w^{3} - 4w^{2} - 12w]$ | $\phantom{-}2e - 4$ |
| 41 | $[41, 41, 4w^{5} + 2w^{4} - 25w^{3} - 2w^{2} + 26w + 5]$ | $-2e - 8$ |
| 43 | $[43, 43, -w^{2} - w + 2]$ | $-2e + 2$ |
| 43 | $[43, 43, 2w^{5} + w^{4} - 13w^{3} - 2w^{2} + 14w + 5]$ | $\phantom{-}2e + 6$ |
| 43 | $[43, 43, -w^{5} + 7w^{3} - w^{2} - 8w - 3]$ | $-2e + 2$ |
| 43 | $[43, 43, 2w^{5} + w^{4} - 13w^{3} - 2w^{2} + 15w + 3]$ | $\phantom{-}2e + 6$ |
| 49 | $[49, 7, -w^{5} - w^{4} + 6w^{3} + 3w^{2} - 7w]$ | $\phantom{-}1$ |
| 71 | $[71, 71, -5w^{5} - 2w^{4} + 32w^{3} - w^{2} - 35w - 2]$ | $-4e - 4$ |
| 71 | $[71, 71, 2w^{5} + w^{4} - 13w^{3} - 2w^{2} + 14w + 6]$ | $-2e - 2$ |
| 71 | $[71, 71, -3w^{5} - 2w^{4} + 19w^{3} + 5w^{2} - 22w - 7]$ | $\phantom{-}2e + 2$ |
| 71 | $[71, 71, 4w^{5} + 2w^{4} - 25w^{3} - 2w^{2} + 26w + 6]$ | $\phantom{-}4e + 4$ |
| 83 | $[83, 83, -2w^{5} - w^{4} + 12w^{3} - 12w + 1]$ | $\phantom{-}2e - 2$ |
| 83 | $[83, 83, -2w^{5} - w^{4} + 13w^{3} - 16w + 1]$ | $\phantom{-}2e - 10$ |
| 83 | $[83, 83, -4w^{5} - 2w^{4} + 26w^{3} + 3w^{2} - 29w - 6]$ | $-2e - 14$ |
| 83 | $[83, 83, 2w^{5} - 13w^{3} + 5w^{2} + 13w - 1]$ | $-2e - 6$ |
| 97 | $[97, 97, -3w^{5} + 20w^{3} - 8w^{2} - 22w + 5]$ | $\phantom{-}2e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $49$ | $[49,7,-w^{5}-w^{4}+6w^{3}+3w^{2}-7w]$ | $-1$ |