Base field 3.3.473.1
Generator \(w\), with minimal polynomial \(x^{3} - 5x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[11, 11, -w^{2} + 3]$ |
| Dimension: | $4$ |
| 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:
| \(x^{4} - 2x^{3} - 7x^{2} + 9x - 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w - 1]$ | $-e^{3} + e^{2} + 8e - 3$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}e^{3} - 2e^{2} - 7e + 5$ |
| 9 | $[9, 3, -w^{2} + w + 4]$ | $-e^{3} + e^{2} + 9e - 3$ |
| 11 | $[11, 11, -w^{2} + 3]$ | $\phantom{-}1$ |
| 11 | $[11, 11, -w^{2} - w + 1]$ | $\phantom{-}e^{3} - 2e^{2} - 7e + 8$ |
| 13 | $[13, 13, w + 3]$ | $-e^{3} + 2e^{2} + 7e - 7$ |
| 17 | $[17, 17, -w^{2} + 2]$ | $\phantom{-}3e^{3} - 4e^{2} - 25e + 15$ |
| 25 | $[25, 5, w^{2} + w - 4]$ | $\phantom{-}3e^{3} - 4e^{2} - 22e + 11$ |
| 37 | $[37, 37, w^{2} + w - 5]$ | $-e^{2} + e$ |
| 41 | $[41, 41, 2w^{2} + w - 6]$ | $-3e^{3} + 4e^{2} + 27e - 13$ |
| 43 | $[43, 43, w^{2} - 3w - 2]$ | $\phantom{-}2e^{3} - 2e^{2} - 14e + 4$ |
| 43 | $[43, 43, -w + 4]$ | $-2e + 2$ |
| 71 | $[71, 71, w^{2} - 8]$ | $\phantom{-}e^{2} + 2e - 2$ |
| 73 | $[73, 73, 3w + 5]$ | $-2e^{3} + 4e^{2} + 14e - 18$ |
| 73 | $[73, 73, w^{2} - 2w - 5]$ | $\phantom{-}e^{3} - 2e^{2} - 11e + 11$ |
| 73 | $[73, 73, w^{2} - 2w - 7]$ | $-e^{3} + 2e^{2} + 7e + 3$ |
| 79 | $[79, 79, 2w^{2} + w - 9]$ | $\phantom{-}2e^{3} - 2e^{2} - 16e - 2$ |
| 83 | $[83, 83, 3w^{2} - 2w - 13]$ | $-4e^{3} + 6e^{2} + 28e - 18$ |
| 89 | $[89, 89, -w^{2} - 2w + 9]$ | $\phantom{-}e^{3} - e^{2} - 10e + 7$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, -w^{2} + 3]$ | $-1$ |