Base field 3.3.1129.1
Generator \(w\), with minimal polynomial \(x^{3} - 7x - 3\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[19, 19, -w^{2} - w + 4]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $36$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 10x^{6} + 24x^{4} - 18x^{2} + 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, w]$ | $-e^{6} + 9e^{4} - 15e^{2} + 4$ |
| 3 | $[3, 3, w + 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}e^{7} - 8e^{5} + 7e^{3} + 4e$ |
| 8 | $[8, 2, 2]$ | $\phantom{-}e^{6} - 9e^{4} + 15e^{2} - 5$ |
| 11 | $[11, 11, -w^{2} + 5]$ | $-3e^{7} + 26e^{5} - 38e^{3} + 9e$ |
| 13 | $[13, 13, w^{2} - w - 7]$ | $\phantom{-}3e^{7} - 27e^{5} + 46e^{3} - 17e$ |
| 17 | $[17, 17, -w^{2} + w + 4]$ | $\phantom{-}e^{3} - 6e$ |
| 19 | $[19, 19, -w^{2} - w + 4]$ | $-1$ |
| 29 | $[29, 29, 2w^{2} - 2w - 11]$ | $-e^{7} + 10e^{5} - 24e^{3} + 18e$ |
| 31 | $[31, 31, w^{2} - 2w - 4]$ | $-3e^{7} + 25e^{5} - 30e^{3} - e$ |
| 37 | $[37, 37, -2w^{2} + 3w + 7]$ | $\phantom{-}e^{7} - 11e^{5} + 33e^{3} - 33e$ |
| 41 | $[41, 41, w^{2} - 2]$ | $-2e^{7} + 16e^{5} - 16e^{3}$ |
| 59 | $[59, 59, 2w^{2} - 13]$ | $\phantom{-}7e^{6} - 61e^{4} + 90e^{2} - 18$ |
| 61 | $[61, 61, w^{2} + w - 10]$ | $\phantom{-}e^{4} - 5e^{2} - 2$ |
| 67 | $[67, 67, 2w^{2} - w - 11]$ | $\phantom{-}2e^{7} - 17e^{5} + 23e^{3} - 3e$ |
| 73 | $[73, 73, -w^{2} - 1]$ | $-3e^{6} + 25e^{4} - 30e^{2}$ |
| 83 | $[83, 83, w^{2} - w - 10]$ | $-8e^{6} + 68e^{4} - 91e^{2} + 6$ |
| 89 | $[89, 89, -w^{2} + 4w - 2]$ | $\phantom{-}e^{6} - 8e^{4} + 4e^{2} + 14$ |
| 97 | $[97, 97, w^{2} - 2w - 7]$ | $\phantom{-}4e^{7} - 37e^{5} + 69e^{3} - 31e$ |
| 97 | $[97, 97, -w^{2} - 4w - 5]$ | $\phantom{-}4e^{6} - 34e^{4} + 46e^{2} - 18$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, -w^{2} - w + 4]$ | $1$ |