Base field 4.4.4352.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - 4x + 2\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[23, 23, -2w^{3} + 2w^{2} + 9w + 1]$ |
| Dimension: | $2$ |
| 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:
| \(x^{2} + x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w]$ | $\phantom{-}e$ |
| 7 | $[7, 7, -w^{3} + w^{2} + 5w + 1]$ | $-3$ |
| 7 | $[7, 7, -w + 1]$ | $-3$ |
| 17 | $[17, 17, -w^{3} + 2w^{2} + 4w - 3]$ | $\phantom{-}2e + 1$ |
| 23 | $[23, 23, -2w^{3} + 2w^{2} + 9w + 1]$ | $\phantom{-}1$ |
| 23 | $[23, 23, -w^{3} + w^{2} + 3w + 1]$ | $-3e$ |
| 31 | $[31, 31, w^{2} - w - 1]$ | $\phantom{-}6e + 3$ |
| 31 | $[31, 31, w^{3} - 2w^{2} - 3w + 5]$ | $-3e - 3$ |
| 41 | $[41, 41, w^{3} - 3w^{2} - 2w + 7]$ | $\phantom{-}e - 5$ |
| 41 | $[41, 41, w^{3} - 3w^{2} - 2w + 5]$ | $-2e + 4$ |
| 49 | $[49, 7, 2w^{3} - 2w^{2} - 8w - 1]$ | $-8e - 3$ |
| 71 | $[71, 71, -2w^{3} + 3w^{2} + 8w - 1]$ | $\phantom{-}3e - 3$ |
| 71 | $[71, 71, w^{2} - 5]$ | $\phantom{-}3e - 3$ |
| 73 | $[73, 73, -3w^{3} + 4w^{2} + 11w - 3]$ | $\phantom{-}11e + 8$ |
| 73 | $[73, 73, 2w^{3} - w^{2} - 9w - 3]$ | $-7e - 4$ |
| 79 | $[79, 79, 3w^{3} - 4w^{2} - 13w + 3]$ | $\phantom{-}3e - 6$ |
| 79 | $[79, 79, w^{2} + w - 3]$ | $\phantom{-}3$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}9e$ |
| 89 | $[89, 89, -w^{3} + 3w^{2} + 3w - 11]$ | $-13e - 3$ |
| 89 | $[89, 89, 3w^{3} - 2w^{2} - 14w - 3]$ | $-e + 5$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $23$ | $[23, 23, -2w^{3} + 2w^{2} + 9w + 1]$ | $-1$ |