Base field \(\Q(\zeta_{11})^+\)
Generator \(w\), with minimal polynomial \(x^5 - x^4 - 4 x^3 + 3 x^2 + 3 x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[67,67,2 w^2 - w - 4]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $2$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^2 - 24\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 11 | $[11, 11, w^4 + w^3 - 4 w^2 - 3 w + 2]$ | $\phantom{-}e$ |
| 23 | $[23, 23, -w^4 + 3 w^2 + 1]$ | $-\frac{1}{2} e - 5$ |
| 23 | $[23, 23, -w^4 + 3 w^2 + w - 2]$ | $\phantom{-}4$ |
| 23 | $[23, 23, w^4 - w^3 - 3 w^2 + 3 w + 2]$ | $-e + 1$ |
| 23 | $[23, 23, -w^4 + w^3 + 4 w^2 - 3 w - 1]$ | $\phantom{-}\frac{1}{2} e + 3$ |
| 23 | $[23, 23, -w^2 + w + 3]$ | $\phantom{-}e + 2$ |
| 32 | $[32, 2, 2]$ | $-\frac{1}{2} e - 1$ |
| 43 | $[43, 43, -2 w^4 + w^3 + 6 w^2 - 2 w - 1]$ | $\phantom{-}9$ |
| 43 | $[43, 43, -w^4 + 2 w^2 + w + 1]$ | $\phantom{-}4$ |
| 43 | $[43, 43, w^3 + w^2 - 4 w - 2]$ | $\phantom{-}e - 3$ |
| 43 | $[43, 43, 2 w^4 - w^3 - 7 w^2 + 3 w + 3]$ | $\phantom{-}4$ |
| 43 | $[43, 43, w^4 - w^3 - 4 w^2 + 4 w + 2]$ | $-2 e - 2$ |
| 67 | $[67, 67, 2 w^4 - 7 w^2 + 2]$ | $\phantom{-}e - 4$ |
| 67 | $[67, 67, w^4 - 2 w^3 - 3 w^2 + 6 w + 2]$ | $\phantom{-}1$ |
| 67 | $[67, 67, 2 w^4 - 7 w^2 - w + 4]$ | $-2 e - 3$ |
| 67 | $[67, 67, w^4 - 2 w^3 - 4 w^2 + 6 w + 2]$ | $-2$ |
| 67 | $[67, 67, -w^4 + w^3 + 5 w^2 - 3 w - 3]$ | $-2 e + 2$ |
| 89 | $[89, 89, w^3 + w^2 - 4 w - 1]$ | $-e - 8$ |
| 89 | $[89, 89, -2 w^4 + w^3 + 7 w^2 - 3 w - 2]$ | $-\frac{5}{2} e - 5$ |
| 89 | $[89, 89, -w^4 + w^3 + 4 w^2 - 4 w - 3]$ | $\phantom{-}e + 8$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $67$ | $[67,67,2 w^2 - w - 4]$ | $-1$ |