Base field 5.5.179024.1
Generator \(w\), with minimal polynomial \(x^{5} - 8x^{3} + 6x - 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2]$ |
| Level: | $[9, 9, 4w^{4} + 2w^{3} - 31w^{2} - 16w + 17]$ |
| 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:
| \(x^{5} - 9x^{3} - 2x^{2} + 16x + 8\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, 2w^{4} + w^{3} - 15w^{2} - 7w + 7]$ | $\phantom{-}0$ |
| 11 | $[11, 11, 2w^{4} + w^{3} - 16w^{2} - 9w + 9]$ | $-e^{4} + 8e^{2} - 8$ |
| 17 | $[17, 17, w^{4} + w^{3} - 8w^{2} - 6w + 5]$ | $-e^{3} + 6e + 2$ |
| 29 | $[29, 29, w^{4} - 8w^{2} + 3]$ | $\phantom{-}e^{3} + 2e^{2} - 6e - 10$ |
| 43 | $[43, 43, 6w^{4} + 3w^{3} - 46w^{2} - 24w + 21]$ | $\phantom{-}2e^{2} - 4$ |
| 43 | $[43, 43, 2w^{4} + w^{3} - 15w^{2} - 6w + 7]$ | $\phantom{-}e^{3} - 4e$ |
| 47 | $[47, 47, 3w^{4} + w^{3} - 23w^{2} - 9w + 11]$ | $-e^{4} + 2e^{3} + 8e^{2} - 12e - 12$ |
| 47 | $[47, 47, w^{4} + w^{3} - 8w^{2} - 7w + 3]$ | $-2e^{4} + 14e^{2} - 12$ |
| 49 | $[49, 7, -w^{4} + 8w^{2} + 2w - 5]$ | $\phantom{-}2e^{4} - 2e^{3} - 16e^{2} + 8e + 18$ |
| 53 | $[53, 53, -6w^{4} - 3w^{3} + 46w^{2} + 23w - 23]$ | $\phantom{-}e^{4} - 8e^{2} - 2e + 10$ |
| 53 | $[53, 53, 2w^{4} + w^{3} - 15w^{2} - 7w + 5]$ | $\phantom{-}2e + 2$ |
| 59 | $[59, 59, 13w^{4} + 7w^{3} - 101w^{2} - 54w + 55]$ | $-2e^{4} + 2e^{3} + 16e^{2} - 12e - 20$ |
| 67 | $[67, 67, 5w^{4} + 3w^{3} - 39w^{2} - 23w + 19]$ | $-e^{3} + 4e + 4$ |
| 67 | $[67, 67, 4w^{4} + 2w^{3} - 32w^{2} - 16w + 19]$ | $\phantom{-}2e^{4} - e^{3} - 12e^{2} + 4e + 8$ |
| 71 | $[71, 71, 4w^{4} + 3w^{3} - 31w^{2} - 22w + 15]$ | $\phantom{-}e^{4} - 2e^{3} - 8e^{2} + 12e + 16$ |
| 71 | $[71, 71, 9w^{4} + 5w^{3} - 70w^{2} - 38w + 39]$ | $-2e^{2} + 4$ |
| 71 | $[71, 71, 4w^{4} + w^{3} - 31w^{2} - 8w + 17]$ | $-2e^{2} + 4$ |
| 81 | $[81, 3, -5w^{4} - 2w^{3} + 38w^{2} + 17w - 19]$ | $-2e^{4} + 2e^{3} + 14e^{2} - 6e - 10$ |
| 83 | $[83, 83, -3w^{4} - w^{3} + 24w^{2} + 9w - 13]$ | $-2e^{3} + 2e^{2} + 12e - 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, 2w^{4} + w^{3} - 15w^{2} - 7w + 7]$ | $-1$ |