Base field 4.4.10512.1
Generator \(w\), with minimal polynomial \(x^4 - 7 x^2 - 6 x + 1\); narrow class number \(4\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[36, 6, -w^3 + w^2 + 5 w + 4]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^2 - x - 26\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w^3 - w^2 - 5 w - 2]$ | $-1$ |
| 9 | $[9, 3, w^3 - w^2 - 5 w - 1]$ | $-1$ |
| 11 | $[11, 11, -w^3 + w^2 + 6 w + 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w - 1]$ | $-e + 1$ |
| 13 | $[13, 13, w^3 - 2 w^2 - 4 w + 2]$ | $\phantom{-}e + 1$ |
| 13 | $[13, 13, -w^2 + w + 4]$ | $-e + 2$ |
| 23 | $[23, 23, w^2 - 2 w - 2]$ | $\phantom{-}6$ |
| 23 | $[23, 23, w^3 - w^2 - 6 w - 3]$ | $\phantom{-}e - 2$ |
| 23 | $[23, 23, -w^2 + 2 w + 5]$ | $\phantom{-}6$ |
| 23 | $[23, 23, -w + 2]$ | $-e - 1$ |
| 37 | $[37, 37, 2 w^3 - 2 w^2 - 12 w - 1]$ | $-e + 6$ |
| 37 | $[37, 37, w^3 - 2 w^2 - 5 w + 2]$ | $\phantom{-}e + 5$ |
| 37 | $[37, 37, w^3 - 2 w^2 - 5 w + 3]$ | $-e + 6$ |
| 37 | $[37, 37, -w^3 + w^2 + 6 w - 2]$ | $\phantom{-}e + 5$ |
| 47 | $[47, 47, w^2 - 2 w - 1]$ | $-8$ |
| 47 | $[47, 47, w^2 - 2 w - 6]$ | $-8$ |
| 59 | $[59, 59, 2 w - 1]$ | $-e - 7$ |
| 59 | $[59, 59, -2 w^3 + 2 w^2 + 12 w + 3]$ | $\phantom{-}e - 8$ |
| 73 | $[73, 73, -w^3 + w^2 + 7 w + 1]$ | $-6$ |
| 83 | $[83, 83, -w^3 + w^2 + 4 w + 3]$ | $\phantom{-}2 e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, w^3 - w^2 - 5 w - 2]$ | $1$ |
| $9$ | $[9, 3, w^3 - w^2 - 5 w - 1]$ | $1$ |