Base field 3.3.788.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 7x - 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[9, 3, w^{2} - w - 7]$ |
| Dimension: | $5$ |
| 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:
| \(x^{5} + 2x^{4} - 6x^{3} - 8x^{2} + 8x + 1\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w]$ | $-e - 1$ |
| 5 | $[5, 5, -w^{2} + 2w + 4]$ | $\phantom{-}e^{3} + e^{2} - 4e - 2$ |
| 9 | $[9, 3, w^{2} - w - 7]$ | $-1$ |
| 11 | $[11, 11, -w^{2} + 2w + 2]$ | $\phantom{-}e^{4} + 2e^{3} - 5e^{2} - 7e + 3$ |
| 13 | $[13, 13, w - 2]$ | $-e^{4} - 3e^{3} + 4e^{2} + 11e - 5$ |
| 17 | $[17, 17, w^{2} - 2w - 8]$ | $-e^{2} - e + 2$ |
| 25 | $[25, 5, -w^{2} + 2]$ | $-e^{3} - 2e^{2} + 5e + 4$ |
| 31 | $[31, 31, 3w^{2} - 5w - 19]$ | $-e^{3} - e^{2} + 3e + 3$ |
| 53 | $[53, 53, 2w^{2} - 3w - 10]$ | $-e^{4} - 3e^{3} + 5e^{2} + 13e - 4$ |
| 53 | $[53, 53, w^{2} - 3w - 5]$ | $\phantom{-}2e^{4} + 3e^{3} - 12e^{2} - 11e + 8$ |
| 53 | $[53, 53, 2w - 1]$ | $\phantom{-}e^{4} - 5e^{2} - 6$ |
| 59 | $[59, 59, 2w^{2} - 4w - 11]$ | $\phantom{-}e^{4} + 4e^{3} - 3e^{2} - 16e + 2$ |
| 59 | $[59, 59, 2w^{2} - 6w - 5]$ | $-e^{4} - 2e^{3} + 4e^{2} + 7e - 2$ |
| 59 | $[59, 59, 2w + 5]$ | $-2e^{2} - 3e + 3$ |
| 67 | $[67, 67, w^{2} - 3w - 7]$ | $\phantom{-}2e^{4} + 4e^{3} - 11e^{2} - 18e + 7$ |
| 71 | $[71, 71, 2w^{2} - 2w - 13]$ | $-2e^{4} - 3e^{3} + 13e^{2} + 13e - 13$ |
| 73 | $[73, 73, 2w^{2} - 4w - 7]$ | $\phantom{-}e^{4} + 3e^{3} - e^{2} - 8e - 7$ |
| 79 | $[79, 79, -w^{2} + 10]$ | $\phantom{-}e^{3} - e^{2} - 5e + 1$ |
| 89 | $[89, 89, 2w^{2} - w - 10]$ | $\phantom{-}3e^{4} + 7e^{3} - 16e^{2} - 27e + 11$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $9$ | $[9, 3, w^{2} - w - 7]$ | $1$ |