Base field 3.3.756.1
Generator \(w\), with minimal polynomial \(x^{3} - 6x - 2\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[7, 7, w - 1]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $7$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - 3x^{4} - 3x^{3} + 12x^{2} - 4x - 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 1]$ | $-e^{4} + 2e^{3} + 4e^{2} - 6e$ |
| 7 | $[7, 7, -w + 3]$ | $\phantom{-}e^{4} - 2e^{3} - 5e^{2} + 8e + 2$ |
| 7 | $[7, 7, w - 1]$ | $\phantom{-}1$ |
| 11 | $[11, 11, -w - 3]$ | $-e^{2} + 2e + 2$ |
| 13 | $[13, 13, -w^{2} + w + 3]$ | $\phantom{-}e^{3} - 2e^{2} - 4e + 4$ |
| 19 | $[19, 19, -w^{2} - w + 1]$ | $\phantom{-}e^{3} - 6e - 2$ |
| 23 | $[23, 23, -w^{2} + 3]$ | $-2e + 4$ |
| 29 | $[29, 29, 2w + 3]$ | $\phantom{-}e^{4} - 2e^{3} - 5e^{2} + 6e + 4$ |
| 31 | $[31, 31, 2w^{2} - 2w - 9]$ | $-e^{4} + e^{3} + 4e^{2} - 2$ |
| 53 | $[53, 53, -w^{2} - 1]$ | $-e^{4} + 3e^{3} + 4e^{2} - 14e + 8$ |
| 61 | $[61, 61, 2w - 3]$ | $-e^{4} + 6e^{2} - 2$ |
| 67 | $[67, 67, w^{2} - 2w - 5]$ | $\phantom{-}2e^{4} - 7e^{3} - 7e^{2} + 28e - 4$ |
| 67 | $[67, 67, -w^{2} + w + 9]$ | $-3e^{4} + 5e^{3} + 15e^{2} - 14e - 8$ |
| 67 | $[67, 67, -w^{2} + 3w + 3]$ | $-3e^{4} + 9e^{3} + 10e^{2} - 34e + 2$ |
| 71 | $[71, 71, w^{2} + w - 7]$ | $-e^{4} + e^{3} + 6e^{2} - 6$ |
| 73 | $[73, 73, -2w^{2} + 3w + 7]$ | $-2e^{4} + 3e^{3} + 10e^{2} - 6e - 8$ |
| 89 | $[89, 89, w^{2} - 2w - 7]$ | $\phantom{-}e^{4} + e^{3} - 10e^{2} - 6e + 12$ |
| 89 | $[89, 89, -2w^{2} + 1]$ | $\phantom{-}5e^{4} - 9e^{3} - 24e^{2} + 28e + 8$ |
| 89 | $[89, 89, -3w^{2} + 19]$ | $\phantom{-}4e^{4} - 11e^{3} - 16e^{2} + 40e - 4$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w - 1]$ | $-1$ |