Base field 4.4.11324.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 4x + 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[13, 13, -w^{2} + 3]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $19$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} + 2x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -w^{3} + 4w + 1]$ | $-e - 2$ |
| 5 | $[5, 5, w + 1]$ | $\phantom{-}e + 1$ |
| 13 | $[13, 13, -w^{2} + 3]$ | $\phantom{-}1$ |
| 17 | $[17, 17, -w^{3} + w^{2} + 3w - 1]$ | $\phantom{-}e - 3$ |
| 19 | $[19, 19, -w^{3} + 3w - 1]$ | $-e - 3$ |
| 23 | $[23, 23, -w + 3]$ | $\phantom{-}2$ |
| 31 | $[31, 31, -w^{2} - 2w + 1]$ | $\phantom{-}4e + 2$ |
| 41 | $[41, 41, w^{3} + w^{2} - 5w - 3]$ | $-4e - 4$ |
| 43 | $[43, 43, 2w - 1]$ | $-e - 7$ |
| 53 | $[53, 53, -w - 3]$ | $-2e + 8$ |
| 53 | $[53, 53, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}4e + 2$ |
| 61 | $[61, 61, w^{3} - 3w - 5]$ | $-e + 5$ |
| 67 | $[67, 67, w^{3} + w^{2} - 5w - 1]$ | $-4e + 6$ |
| 81 | $[81, 3, -3]$ | $-2$ |
| 83 | $[83, 83, -w^{3} + 5w - 3]$ | $-e + 1$ |
| 89 | $[89, 89, w^{2} + 1]$ | $\phantom{-}5e + 3$ |
| 97 | $[97, 97, w^{3} - w^{2} - 5w + 1]$ | $-2e - 2$ |
| 97 | $[97, 97, 3w^{3} - 5w^{2} - 14w + 21]$ | $-10e - 12$ |
| 97 | $[97, 97, w^{3} - 3w - 3]$ | $-3e - 9$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $13$ | $[13, 13, -w^{2} + 3]$ | $-1$ |