Base field 3.3.1593.1
Generator \(w\), with minimal polynomial \(x^{3} - 9x - 7\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[7, 7, -w^{2} + 2w + 3]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} - x - 5\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e$ |
| 5 | $[5, 5, w^{2} - 2w - 4]$ | $\phantom{-}1$ |
| 7 | $[7, 7, w]$ | $-e + 1$ |
| 7 | $[7, 7, w + 3]$ | $-e + 1$ |
| 7 | $[7, 7, -w^{2} + 2w + 3]$ | $-1$ |
| 8 | $[8, 2, 2]$ | $-e$ |
| 13 | $[13, 13, w^{2} - 3w - 2]$ | $\phantom{-}e - 5$ |
| 17 | $[17, 17, w - 2]$ | $\phantom{-}e - 4$ |
| 25 | $[25, 5, -w^{2} - w + 3]$ | $-2e + 3$ |
| 29 | $[29, 29, w^{2} - 2w - 6]$ | $\phantom{-}2e - 1$ |
| 31 | $[31, 31, w^{2} - 5]$ | $\phantom{-}e - 9$ |
| 37 | $[37, 37, -w^{2} - 2w + 2]$ | $\phantom{-}8$ |
| 41 | $[41, 41, w^{2} - 8]$ | $-e - 9$ |
| 43 | $[43, 43, w^{2} - w - 4]$ | $\phantom{-}e - 5$ |
| 53 | $[53, 53, 2w^{2} - 5w - 4]$ | $-e + 10$ |
| 59 | $[59, 59, w^{2} - 3]$ | $-3$ |
| 59 | $[59, 59, w^{2} - 3w - 5]$ | $\phantom{-}3e$ |
| 61 | $[61, 61, -w^{2} + 2w + 12]$ | $-2e - 3$ |
| 67 | $[67, 67, -2w^{2} + 6w + 3]$ | $-2e - 1$ |
| 71 | $[71, 71, w^{2} - w - 11]$ | $\phantom{-}2e + 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, -w^{2} + 2w + 3]$ | $1$ |