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