Base field 4.4.18736.1
Generator \(w\), with minimal polynomial \(x^4 - 2 x^3 - 5 x^2 + 4 x + 5\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[9, 9, w^3 - 3 w^2 - 2 w + 7]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^2 - 7\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w - 1]$ | $\phantom{-}0$ |
| 4 | $[4, 2, -w^3 + 2 w^2 + 4 w - 3]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w]$ | $\phantom{-}0$ |
| 7 | $[7, 7, w - 2]$ | $-4$ |
| 11 | $[11, 11, w^2 - 2 w - 4]$ | $\phantom{-}3$ |
| 23 | $[23, 23, -w^2 + 2 w + 1]$ | $\phantom{-}0$ |
| 23 | $[23, 23, w^3 - 2 w^2 - 3 w + 3]$ | $\phantom{-}0$ |
| 27 | $[27, 3, -w^3 + w^2 + 6 w + 2]$ | $-e$ |
| 31 | $[31, 31, -w^3 + 3 w^2 + w - 1]$ | $-10$ |
| 31 | $[31, 31, -w^3 + 2 w^2 + 4 w - 4]$ | $-2 e$ |
| 37 | $[37, 37, w^2 - 2 w - 6]$ | $-4$ |
| 37 | $[37, 37, w^3 - 2 w^2 - 3 w + 2]$ | $\phantom{-}4 e$ |
| 43 | $[43, 43, w^2 - 3 w - 2]$ | $-2 e$ |
| 61 | $[61, 61, -w^3 + 2 w^2 + 2 w - 2]$ | $-2 e$ |
| 73 | $[73, 73, w^3 - 3 w^2 - 2 w + 3]$ | $-5 e$ |
| 83 | $[83, 83, -w - 3]$ | $\phantom{-}12$ |
| 89 | $[89, 89, -w^3 + 3 w^2 + 2 w - 2]$ | $-3 e$ |
| 89 | $[89, 89, 2 w - 1]$ | $\phantom{-}0$ |
| 101 | $[101, 101, w^3 - 4 w^2 + w + 7]$ | $\phantom{-}0$ |
| 101 | $[101, 101, 2 w^2 - 3 w - 3]$ | $-6 e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w - 1]$ | $-1$ |