Base field 6.6.1997632.1
Generator \(w\), with minimal polynomial \(x^{6} - 8x^{4} + 19x^{2} - 13\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[13, 13, w]$ |
| Dimension: | $2$ |
| 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:
| \(x^{2} - 8x + 14\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 8 | $[8, 2, w^{4} - 5w^{2} - w + 4]$ | $\phantom{-}0$ |
| 13 | $[13, 13, w]$ | $\phantom{-}1$ |
| 13 | $[13, 13, -w^{2} + w + 3]$ | $\phantom{-}e$ |
| 13 | $[13, 13, w^{2} + w - 3]$ | $-e$ |
| 27 | $[27, 3, w^{5} - 6w^{3} + w^{2} + 8w - 2]$ | $\phantom{-}4e - 18$ |
| 27 | $[27, 3, w^{5} - 6w^{3} - w^{2} + 8w + 2]$ | $\phantom{-}4e - 18$ |
| 29 | $[29, 29, w^{4} - 6w^{2} + w + 8]$ | $-e + 6$ |
| 29 | $[29, 29, -w^{4} + 6w^{2} + w - 8]$ | $\phantom{-}e - 6$ |
| 41 | $[41, 41, w^{3} - w^{2} - 3w + 4]$ | $-6e + 20$ |
| 41 | $[41, 41, w^{5} + w^{4} - 6w^{3} - 5w^{2} + 8w + 3]$ | $\phantom{-}3e - 6$ |
| 41 | $[41, 41, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 8w + 3]$ | $-3e + 6$ |
| 41 | $[41, 41, w^{5} - w^{4} - 6w^{3} + 5w^{2} + 8w - 6]$ | $-6e + 20$ |
| 43 | $[43, 43, -w^{4} + 6w^{2} - w - 9]$ | $\phantom{-}2e - 4$ |
| 43 | $[43, 43, -w^{4} + 6w^{2} + w - 9]$ | $-2e + 4$ |
| 49 | $[49, 7, w^{4} - 5w^{2} + 7]$ | $-12$ |
| 97 | $[97, 97, w^{4} + w^{3} - 5w^{2} - 3w + 4]$ | $-3e + 10$ |
| 97 | $[97, 97, w^{4} + w^{3} - 5w^{2} - 3w + 3]$ | $\phantom{-}3e - 12$ |
| 97 | $[97, 97, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ | $-3e + 12$ |
| 97 | $[97, 97, -w^{4} + w^{3} + 5w^{2} - 3w - 4]$ | $\phantom{-}3e - 10$ |
| 113 | $[113, 113, w^{5} - w^{4} - 6w^{3} + 6w^{2} + 7w - 9]$ | $-7e + 36$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, w]$ | $-1$ |