Base field 4.4.8468.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 5x^{2} + 3x + 4\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[22, 22, -w + 3]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - 8x^{3} - 2x^{2} + 10x + 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{3} - 4w - 2]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w - 1]$ | $-1$ |
| 11 | $[11, 11, -w^{3} + 5w + 1]$ | $-1$ |
| 17 | $[17, 17, -w^{3} + 3w + 1]$ | $\phantom{-}2e$ |
| 23 | $[23, 23, w^{3} + w^{2} - 4w - 5]$ | $\phantom{-}e^{4} - 2e^{3} - 6e^{2} + 9e + 6$ |
| 29 | $[29, 29, -w^{3} + w^{2} + 2w - 1]$ | $-e^{3} - e^{2} + 6e + 6$ |
| 29 | $[29, 29, w^{3} + w^{2} - 6w - 5]$ | $-2e^{4} + e^{3} + 15e^{2} - 4e - 12$ |
| 29 | $[29, 29, w^{3} - w^{2} - 4w + 1]$ | $-e^{3} + e^{2} + 6e$ |
| 47 | $[47, 47, w^{3} - 3w - 3]$ | $-2e^{3} + 14e$ |
| 53 | $[53, 53, 2w^{2} - 2w - 5]$ | $-e^{3} - e^{2} + 6e + 6$ |
| 53 | $[53, 53, -w^{3} + 2w^{2} + 5w - 7]$ | $\phantom{-}2e^{4} - 14e^{2} - 2e + 12$ |
| 59 | $[59, 59, 2w^{3} - 8w - 3]$ | $\phantom{-}2e^{4} - 2e^{3} - 12e^{2} + 6e + 6$ |
| 59 | $[59, 59, w^{3} - w^{2} - 2w + 3]$ | $\phantom{-}e^{4} - 10e^{2} + e + 12$ |
| 67 | $[67, 67, 2w - 1]$ | $-2e^{4} + 2e^{3} + 14e^{2} - 4e - 10$ |
| 71 | $[71, 71, 2w^{2} - 5]$ | $\phantom{-}e^{4} - 6e^{2} - 5e + 6$ |
| 73 | $[73, 73, -w^{3} + w^{2} + 4w + 1]$ | $\phantom{-}2$ |
| 73 | $[73, 73, -2w^{3} + 8w + 1]$ | $\phantom{-}e^{4} - 2e^{3} - 4e^{2} + 7e - 4$ |
| 73 | $[73, 73, -w^{3} + 5w - 1]$ | $\phantom{-}3e^{3} - 3e^{2} - 14e + 8$ |
| 79 | $[79, 79, w^{2} - w + 1]$ | $-2e^{4} + 16e^{2} - 10$ |
| 79 | $[79, 79, w^{3} + w^{2} - 4w - 7]$ | $-e^{4} + 2e^{3} + 6e^{2} - 9e - 10$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w - 1]$ | $1$ |
| $11$ | $[11, 11, -w^{3} + 5w + 1]$ | $1$ |