Base field 5.5.81589.1
Generator \(w\), with minimal polynomial \(x^{5} - 6x^{3} + 8x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[16, 2, w^{4} - w^{3} - 3w^{2} + 3w - 1]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} - x - 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{2} - 3]$ | $\phantom{-}e$ |
| 11 | $[11, 11, -w^{4} + 5w^{2} + w - 4]$ | $-2e + 3$ |
| 13 | $[13, 13, -w^{3} + w^{2} + 3w - 4]$ | $\phantom{-}2e + 3$ |
| 16 | $[16, 2, w^{4} - w^{3} - 3w^{2} + 3w - 1]$ | $\phantom{-}1$ |
| 17 | $[17, 17, w^{4} - 4w^{2} + 2]$ | $\phantom{-}4e - 4$ |
| 31 | $[31, 31, w^{4} - 4w^{2} - w + 3]$ | $-4e + 4$ |
| 43 | $[43, 43, -w^{3} + 4w - 2]$ | $\phantom{-}4$ |
| 53 | $[53, 53, w^{4} - 3w^{2} - 1]$ | $-2e + 5$ |
| 53 | $[53, 53, w^{4} - w^{3} - 4w^{2} + 2w + 1]$ | $-4e + 6$ |
| 53 | $[53, 53, -w^{3} - w^{2} + 3w + 4]$ | $-2e + 5$ |
| 61 | $[61, 61, -w^{3} + w^{2} + 5w - 2]$ | $-10e + 7$ |
| 61 | $[61, 61, w^{4} - 4w^{2} + w + 1]$ | $-6e + 5$ |
| 61 | $[61, 61, w^{3} + w^{2} - 4w - 3]$ | $\phantom{-}2$ |
| 67 | $[67, 67, -2w^{3} + w^{2} + 6w - 2]$ | $-2e - 11$ |
| 71 | $[71, 71, -2w^{3} + w^{2} + 7w - 3]$ | $\phantom{-}2$ |
| 71 | $[71, 71, 2w^{4} - 4w^{3} - 7w^{2} + 13w - 1]$ | $\phantom{-}12$ |
| 73 | $[73, 73, -w^{4} + 2w^{3} + 3w^{2} - 7w]$ | $\phantom{-}4e + 2$ |
| 73 | $[73, 73, w^{4} + w^{3} - 3w^{2} - 4w - 2]$ | $-8e + 3$ |
| 79 | $[79, 79, w^{4} - w^{3} - 5w^{2} + 4w + 6]$ | $\phantom{-}12e - 6$ |
| 83 | $[83, 83, -2w^{4} + w^{3} + 9w^{2} - 3w - 6]$ | $\phantom{-}4e - 13$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $16$ | $[16, 2, w^{4} - w^{3} - 3w^{2} + 3w - 1]$ | $-1$ |