Base field 4.4.13824.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} + 6\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[13, 13, w^{3} - 4w + 1]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $20$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 7x^{4} + 13x^{2} - 5\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w^{2} + w + 2]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w^{2} - w - 3]$ | $-e^{3} + 3e$ |
| 11 | $[11, 11, -w^{2} + w + 1]$ | $\phantom{-}e^{5} - 5e^{3} + 4e$ |
| 11 | $[11, 11, -w^{2} - w + 1]$ | $-e^{5} + 6e^{3} - 8e$ |
| 13 | $[13, 13, w^{3} - 4w + 1]$ | $\phantom{-}1$ |
| 13 | $[13, 13, -w^{3} + 4w + 1]$ | $-e^{4} + 3e^{2} - 1$ |
| 25 | $[25, 5, -w^{2} - 2w + 1]$ | $\phantom{-}e^{4} - 8e^{2} + 9$ |
| 25 | $[25, 5, w^{2} - 2w - 1]$ | $\phantom{-}4e^{2} - 11$ |
| 37 | $[37, 37, w^{3} - 3w - 1]$ | $-2e^{4} + 9e^{2} - 7$ |
| 37 | $[37, 37, w^{3} - 3w + 1]$ | $-2e^{4} + 9e^{2} - 7$ |
| 59 | $[59, 59, w^{2} - w - 5]$ | $-2e^{5} + 8e^{3} - 2e$ |
| 59 | $[59, 59, -w^{2} - w + 5]$ | $\phantom{-}3e^{5} - 12e^{3} + 4e$ |
| 61 | $[61, 61, -w^{3} + w^{2} + 4w - 7]$ | $\phantom{-}e^{4} - 2e^{2} + 3$ |
| 61 | $[61, 61, w^{3} - 3w^{2} - 6w + 11]$ | $\phantom{-}6e^{4} - 28e^{2} + 18$ |
| 73 | $[73, 73, 2w^{2} - w - 5]$ | $\phantom{-}5e^{4} - 23e^{2} + 16$ |
| 73 | $[73, 73, 2w - 1]$ | $\phantom{-}3e^{4} - 15e^{2} + 9$ |
| 73 | $[73, 73, -2w - 1]$ | $-6e^{4} + 27e^{2} - 21$ |
| 73 | $[73, 73, 2w^{2} + w - 5]$ | $\phantom{-}2e^{4} - 8e^{2} - 4$ |
| 83 | $[83, 83, 2w^{3} + w^{2} - 9w - 7]$ | $-4e^{5} + 26e^{3} - 34e$ |
| 83 | $[83, 83, -2w^{3} + w^{2} + 7w + 1]$ | $\phantom{-}2e^{5} - 9e^{3} + 5e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13,13,w^{3}-4w+1]$ | $-1$ |