Base field 4.4.7488.1
Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 4x^{2} + 2x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[13,13,w^{3} - 2w^{2} - 4w + 4]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $8$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} - 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w^{3} + 2w^{2} + 4w - 1]$ | $\phantom{-}e$ |
| 9 | $[9, 3, w^{3} - 2w^{2} - 3w + 1]$ | $-2$ |
| 11 | $[11, 11, -w^{3} + 2w^{2} + 4w]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -w + 2]$ | $-2e$ |
| 13 | $[13, 13, w + 2]$ | $-4$ |
| 13 | $[13, 13, w^{3} - 2w^{2} - 4w + 4]$ | $\phantom{-}1$ |
| 13 | $[13, 13, -w^{2} + 2w + 2]$ | $-1$ |
| 37 | $[37, 37, -w^{3} + 2w^{2} + 5w - 3]$ | $-10$ |
| 37 | $[37, 37, w^{3} - 2w^{2} - 5w + 1]$ | $-1$ |
| 47 | $[47, 47, -2w^{3} + 2w^{2} + 10w + 5]$ | $-2e$ |
| 47 | $[47, 47, w^{2} - w - 5]$ | $-5e$ |
| 59 | $[59, 59, -w^{3} + 3w^{2} + 3w - 6]$ | $\phantom{-}2e$ |
| 59 | $[59, 59, w^{3} - 3w^{2} - 3w + 2]$ | $\phantom{-}8e$ |
| 71 | $[71, 71, -2w^{3} + 4w^{2} + 7w]$ | $\phantom{-}0$ |
| 71 | $[71, 71, w^{3} - 2w^{2} - 2w - 2]$ | $-9e$ |
| 73 | $[73, 73, w^{3} - 2w^{2} - 4w - 2]$ | $-1$ |
| 73 | $[73, 73, w - 4]$ | $-10$ |
| 83 | $[83, 83, w^{3} - w^{2} - 6w + 1]$ | $-8e$ |
| 83 | $[83, 83, w^{2} - 3w - 3]$ | $\phantom{-}7e$ |
| 97 | $[97, 97, -3w^{3} + 5w^{2} + 12w + 1]$ | $-10$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13,13,w^{3} - 2w^{2} - 4w + 4]$ | $-1$ |