Base field 4.4.8525.1
Generator \(w\), with minimal polynomial \(x^4 - 2 x^3 - 8 x^2 + 9 x + 19\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[11, 11, w^2 - 2 w - 4]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^3 + 2 x^2 - 14 x - 32\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, -w + 2]$ | $-\frac{1}{2} e^2 + 5$ |
| 11 | $[11, 11, w^2 - 2 w - 4]$ | $\phantom{-}1$ |
| 11 | $[11, 11, -w^2 + 3]$ | $\phantom{-}e^2 - 10$ |
| 11 | $[11, 11, w^2 - 5]$ | $\phantom{-}\frac{1}{2} e^2 - e - 9$ |
| 16 | $[16, 2, 2]$ | $-e^2 + 9$ |
| 19 | $[19, 19, -w]$ | $\phantom{-}2 e^2 - 2 e - 26$ |
| 19 | $[19, 19, -w + 1]$ | $-\frac{3}{2} e^2 + e + 13$ |
| 31 | $[31, 31, -w^3 + 3 w^2 + 2 w - 9]$ | $\phantom{-}e^2 - 2 e - 16$ |
| 31 | $[31, 31, -w^2 + 2 w + 7]$ | $-e^2 + 4$ |
| 31 | $[31, 31, -w^3 + 5 w + 5]$ | $-e^2 + 14$ |
| 41 | $[41, 41, -w^3 + 2 w^2 + 4 w - 2]$ | $-\frac{1}{2} e^2 - e + 3$ |
| 41 | $[41, 41, -w^3 + w^2 + 5 w - 3]$ | $-2 e^2 + 2 e + 28$ |
| 59 | $[59, 59, -w^3 + w^2 + 6 w - 2]$ | $\phantom{-}2 e^2 - 2 e - 28$ |
| 59 | $[59, 59, -w^3 + w^2 + 4 w + 5]$ | $\phantom{-}5 e^2 - 6 e - 62$ |
| 59 | $[59, 59, w^3 - 5 w^2 - w + 18]$ | $-\frac{1}{2} e^2 - e + 7$ |
| 59 | $[59, 59, w^3 - 2 w^2 - 5 w + 4]$ | $-\frac{7}{2} e^2 + 3 e + 41$ |
| 81 | $[81, 3, -3]$ | $\phantom{-}\frac{3}{2} e^2 - e - 19$ |
| 89 | $[89, 89, -w^3 + 3 w^2 - 3]$ | $\phantom{-}3 e - 4$ |
| 89 | $[89, 89, -4 w^2 + 5 w + 20]$ | $-\frac{7}{2} e^2 + 2 e + 41$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, w^2 - 2 w - 4]$ | $-1$ |