Base field 4.4.4752.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 3x^{2} + 4x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[13, 13, w^{3} - 2w^{2} - w + 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $4$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} - 12x^{2} + 34\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w - 1]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w^{3} + w^{2} + 3w]$ | $-e^{2} + 7$ |
| 11 | $[11, 11, -w^{2} + 3]$ | $\phantom{-}e^{3} - 6e$ |
| 13 | $[13, 13, w^{3} - 2w^{2} - w + 1]$ | $-1$ |
| 13 | $[13, 13, w^{3} - w^{2} - 2w + 1]$ | $-3e^{2} + 20$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 4w - 2]$ | $-e$ |
| 23 | $[23, 23, w^{3} - 2w^{2} - 3w + 2]$ | $\phantom{-}2e^{3} - 12e$ |
| 47 | $[47, 47, -w^{3} + 2w^{2} + 3w - 1]$ | $-e^{3} + 7e$ |
| 47 | $[47, 47, -w^{3} + w^{2} + 4w - 3]$ | $\phantom{-}2e^{3} - 13e$ |
| 59 | $[59, 59, w^{2} - 5]$ | $-e^{3} + 3e$ |
| 59 | $[59, 59, w^{2} - 2w - 4]$ | $-e^{3} + 10e$ |
| 61 | $[61, 61, -w^{3} + 2w^{2} + 4w - 4]$ | $\phantom{-}2e^{2} - 12$ |
| 61 | $[61, 61, w^{3} - w^{2} - 5w + 1]$ | $\phantom{-}2e^{2} - 12$ |
| 71 | $[71, 71, w^{3} - w^{2} - 2w - 2]$ | $-3e^{3} + 17e$ |
| 71 | $[71, 71, -w^{3} + 2w^{2} + w - 4]$ | $\phantom{-}4e$ |
| 73 | $[73, 73, 2w^{2} - w - 5]$ | $\phantom{-}6e^{2} - 36$ |
| 73 | $[73, 73, w^{3} - 2w^{2} - 2w + 6]$ | $\phantom{-}6e^{2} - 36$ |
| 83 | $[83, 83, -2w^{3} + 3w^{2} + 6w - 6]$ | $\phantom{-}e^{3} - 9e$ |
| 83 | $[83, 83, -2w^{3} + 4w^{2} + 5w - 5]$ | $-e^{3} + 2e$ |
| 83 | $[83, 83, -2w^{3} + 2w^{2} + 7w - 2]$ | $-5e^{3} + 31e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, w^{3} - 2w^{2} - w + 1]$ | $1$ |