Base field 3.3.568.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x - 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[11, 11, -w^{2} + w + 1]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $11$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} + 2x^{4} - 6x^{3} - 9x^{2} + 8x + 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}e^{3} - 5e + 1$ |
| 5 | $[5, 5, w^{2} - w - 7]$ | $-e^{4} - e^{3} + 5e^{2} + 3e - 4$ |
| 11 | $[11, 11, -w^{2} + w + 1]$ | $-1$ |
| 17 | $[17, 17, -w^{2} + w + 3]$ | $\phantom{-}2e^{4} + 2e^{3} - 11e^{2} - 7e + 6$ |
| 25 | $[25, 5, -w^{2} - w - 1]$ | $\phantom{-}e^{2} - e - 8$ |
| 27 | $[27, 3, 3]$ | $-e^{4} - e^{3} + 4e^{2} + 4e$ |
| 29 | $[29, 29, -w^{2} + 3w - 1]$ | $\phantom{-}e^{2} + e - 6$ |
| 37 | $[37, 37, 3w^{2} - 5w - 13]$ | $-e^{3} + 7e - 4$ |
| 41 | $[41, 41, 2w - 1]$ | $\phantom{-}e^{4} - 4e^{2} - e - 4$ |
| 53 | $[53, 53, 5w^{2} - 9w - 21]$ | $-3e^{4} - 3e^{3} + 16e^{2} + 10e - 8$ |
| 53 | $[53, 53, 3w^{2} - 5w - 15]$ | $\phantom{-}e^{4} - 5e^{3} - 8e^{2} + 22e + 2$ |
| 53 | $[53, 53, w^{2} - 3w - 7]$ | $-e^{3} + 3e^{2} + 8e - 6$ |
| 59 | $[59, 59, w^{2} - 3w - 5]$ | $\phantom{-}2e^{4} + e^{3} - 9e^{2} - 4$ |
| 61 | $[61, 61, 2w^{2} - 4w - 9]$ | $-2e^{3} - 3e^{2} + 9e$ |
| 61 | $[61, 61, 2w - 7]$ | $-e^{4} + 2e^{3} + 5e^{2} - 10e + 2$ |
| 61 | $[61, 61, 2w - 5]$ | $\phantom{-}e^{4} + 2e^{3} - 6e^{2} - 11e + 2$ |
| 67 | $[67, 67, -w^{2} + w - 1]$ | $-e^{4} - 2e^{3} + 7e^{2} + 10e - 10$ |
| 71 | $[71, 71, -2w - 5]$ | $-4e^{3} - 2e^{2} + 16e - 2$ |
| 71 | $[71, 71, 3w^{2} - 3w - 19]$ | $-4e^{3} - 2e^{2} + 14e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, -w^{2} + w + 1]$ | $1$ |