Base field 4.4.6224.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - 2x + 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[13, 13, -w^{3} + 4w + 2]$ |
| Dimension: | $4$ |
| 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:
| \(x^{4} + 2x^{3} - 5x^{2} - 7x + 4\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{3} - w^{2} - 4w + 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $-e - 2$ |
| 7 | $[7, 7, -w^{3} + w^{2} + 3w - 2]$ | $-e^{3} - e^{2} + 4e$ |
| 13 | $[13, 13, -w^{3} + 4w + 2]$ | $\phantom{-}1$ |
| 19 | $[19, 19, w^{3} - w^{2} - 5w + 2]$ | $\phantom{-}e^{3} + e^{2} - 3e - 4$ |
| 29 | $[29, 29, -w^{2} - w + 3]$ | $\phantom{-}e^{3} + e^{2} - 5e - 6$ |
| 29 | $[29, 29, w^{2} - w - 1]$ | $\phantom{-}2e^{3} + 3e^{2} - 7e - 6$ |
| 37 | $[37, 37, -w^{2} + 2w + 2]$ | $\phantom{-}e^{3} + 3e^{2} - 10$ |
| 37 | $[37, 37, -w^{3} + 5w + 1]$ | $-e^{3} - e^{2} + 2e - 2$ |
| 41 | $[41, 41, -w^{3} + 2w^{2} + 3w - 7]$ | $\phantom{-}e^{3} - 6e + 2$ |
| 47 | $[47, 47, w^{3} - 2w^{2} - 4w + 2]$ | $\phantom{-}e^{3} - e^{2} - 2e + 8$ |
| 47 | $[47, 47, 2w^{3} - 3w^{2} - 8w + 6]$ | $-4e^{2} - 3e + 12$ |
| 59 | $[59, 59, -2w^{3} + w^{2} + 7w - 3]$ | $-e^{3} - 4e^{2} + e + 8$ |
| 67 | $[67, 67, w^{3} - 2w^{2} - 3w + 1]$ | $-e^{3} - 4e^{2} + 5e + 8$ |
| 73 | $[73, 73, -2w - 1]$ | $-3e^{3} - 3e^{2} + 12e + 6$ |
| 79 | $[79, 79, 2w^{2} - 2w - 9]$ | $-e^{3} + 2e^{2} + 5e - 12$ |
| 81 | $[81, 3, -3]$ | $-2e^{3} - 4e^{2} + 11e + 6$ |
| 97 | $[97, 97, -3w + 2]$ | $\phantom{-}e^{3} - e^{2} - 3e + 6$ |
| 101 | $[101, 101, w^{3} - 3w^{2} - w + 4]$ | $-4e^{2} - 3e + 10$ |
| 101 | $[101, 101, 2w^{3} - w^{2} - 9w + 1]$ | $\phantom{-}e^{3} - 11e - 2$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, -w^{3} + 4w + 2]$ | $-1$ |