Base field 3.3.1076.1
Generator \(w\), with minimal polynomial \(x^{3} - 8x - 6\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[7, 7, -2w^{2} + 5w + 5]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 7x^{4} - x^{3} + 12x^{2} + 4x - 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, -w - 2]$ | $\phantom{-}e$ |
| 3 | $[3, 3, -w^{2} + 2w + 3]$ | $\phantom{-}e^{3} - 4e$ |
| 7 | $[7, 7, -2w^{2} + 5w + 5]$ | $\phantom{-}1$ |
| 9 | $[9, 3, -w^{2} + 5]$ | $-e^{5} + 6e^{3} - 7e + 2$ |
| 13 | $[13, 13, -w^{2} + 3w + 1]$ | $\phantom{-}e^{4} + e^{3} - 5e^{2} - 3e + 4$ |
| 13 | $[13, 13, 2w + 5]$ | $-2e^{5} + 2e^{4} + 11e^{3} - 9e^{2} - 12e + 4$ |
| 13 | $[13, 13, w - 1]$ | $-2e^{4} - e^{3} + 10e^{2} + 3e - 6$ |
| 17 | $[17, 17, w^{2} - w - 5]$ | $\phantom{-}e^{5} - e^{4} - 6e^{3} + 6e^{2} + 7e - 2$ |
| 19 | $[19, 19, w^{2} - 2w - 5]$ | $-e^{5} + 7e^{3} + e^{2} - 10e - 4$ |
| 29 | $[29, 29, w^{2} - 7]$ | $\phantom{-}2e^{4} - 11e^{2} + e + 8$ |
| 31 | $[31, 31, 2w^{2} - 3w - 11]$ | $\phantom{-}4e^{5} - e^{4} - 22e^{3} + 5e^{2} + 22e - 2$ |
| 49 | $[49, 7, -2w^{2} - 4w + 1]$ | $-e^{3} - e^{2} + 9e + 4$ |
| 59 | $[59, 59, w^{2} - 2w - 11]$ | $\phantom{-}2e^{5} - 5e^{4} - 12e^{3} + 24e^{2} + 16e - 16$ |
| 71 | $[71, 71, -2w + 7]$ | $\phantom{-}e^{3} + 3e^{2} - 6e - 8$ |
| 73 | $[73, 73, w^{2} - 3w - 13]$ | $-2e^{5} + e^{4} + 13e^{3} - 5e^{2} - 20e + 2$ |
| 73 | $[73, 73, 2w^{2} - 2w - 17]$ | $\phantom{-}3e^{5} - 4e^{4} - 23e^{3} + 19e^{2} + 38e - 6$ |
| 73 | $[73, 73, -w^{2} - 4w - 5]$ | $\phantom{-}e^{5} - 2e^{4} - 9e^{3} + 4e^{2} + 20e + 8$ |
| 79 | $[79, 79, 2w - 1]$ | $-2e^{5} + 5e^{4} + 16e^{3} - 18e^{2} - 32e - 2$ |
| 79 | $[79, 79, w^{2} + w - 5]$ | $-4e^{4} + e^{3} + 20e^{2} - 12$ |
| 79 | $[79, 79, w - 5]$ | $-3e^{5} + 2e^{4} + 17e^{3} - 12e^{2} - 22e + 10$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, -2w^{2} + 5w + 5]$ | $-1$ |