Base field 3.3.404.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 5x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[7, 7, -w + 2]$ |
| Dimension: | $3$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $3$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{3} - 2x^{2} - 2x + 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w^{2} - 2w - 2]$ | $-e^{2} + 2e + 2$ |
| 7 | $[7, 7, -w + 2]$ | $\phantom{-}1$ |
| 9 | $[9, 3, w^{2} - 2]$ | $-2e^{2} + 2e + 2$ |
| 11 | $[11, 11, -w^{2} + 2w + 4]$ | $\phantom{-}2e^{2} - 4e - 4$ |
| 29 | $[29, 29, -2w + 1]$ | $\phantom{-}2e^{2} - 2e - 2$ |
| 37 | $[37, 37, 2w^{2} - 4w - 3]$ | $\phantom{-}2e + 2$ |
| 37 | $[37, 37, -w^{2} + 3w + 3]$ | $\phantom{-}e^{2} - 4e - 4$ |
| 37 | $[37, 37, 2w^{2} - w - 8]$ | $\phantom{-}2e^{2} - 10$ |
| 41 | $[41, 41, w^{2} - 4w + 2]$ | $-e^{2} - 4e + 8$ |
| 43 | $[43, 43, -2w^{2} + 2w + 7]$ | $\phantom{-}4e^{2} - 12$ |
| 43 | $[43, 43, -2w^{2} + 3w + 6]$ | $\phantom{-}4e^{2} - 6e - 4$ |
| 43 | $[43, 43, -w^{2} + 6]$ | $-2e^{2} + 4e$ |
| 49 | $[49, 7, w^{2} + w - 3]$ | $-2e^{2} - 4e + 10$ |
| 53 | $[53, 53, 2w^{2} - 5w - 4]$ | $\phantom{-}e^{2}$ |
| 59 | $[59, 59, 2w - 3]$ | $-e^{2} + 2e - 2$ |
| 61 | $[61, 61, -w - 4]$ | $-4e^{2} + 6e + 10$ |
| 67 | $[67, 67, -2w^{2} - w + 2]$ | $\phantom{-}4e^{2} - 8e - 4$ |
| 73 | $[73, 73, 2w^{2} - 3w - 12]$ | $\phantom{-}4e^{2} - 10e - 2$ |
| 83 | $[83, 83, -2w - 5]$ | $\phantom{-}4e^{2} - 6e - 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, -w + 2]$ | $-1$ |