Base field 3.3.993.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 6x + 3\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[21, 21, w^{2} - 1]$ |
| Dimension: | $7$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{7} - 4x^{6} - 6x^{5} + 33x^{4} - 69x^{2} + 35x + 12\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 3 | $[3, 3, -w]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w - 1]$ | $\phantom{-}1$ |
| 5 | $[5, 5, -w + 2]$ | $-e^{6} + 3e^{5} + 8e^{4} - 21e^{3} - 19e^{2} + 32e + 6$ |
| 7 | $[7, 7, w + 1]$ | $-1$ |
| 8 | $[8, 2, 2]$ | $-e^{6} + 3e^{5} + 9e^{4} - 23e^{3} - 25e^{2} + 39e + 9$ |
| 13 | $[13, 13, w^{2} - w - 4]$ | $\phantom{-}e^{6} - 3e^{5} - 8e^{4} + 20e^{3} + 22e^{2} - 27e - 14$ |
| 17 | $[17, 17, -w^{2} + 2w + 1]$ | $\phantom{-}e^{6} - 2e^{5} - 12e^{4} + 18e^{3} + 39e^{2} - 35e - 18$ |
| 25 | $[25, 5, -w^{2} - w + 4]$ | $\phantom{-}e^{6} - 3e^{5} - 9e^{4} + 22e^{3} + 26e^{2} - 33e - 10$ |
| 31 | $[31, 31, w^{2} - w - 1]$ | $\phantom{-}e^{6} - 3e^{5} - 8e^{4} + 21e^{3} + 20e^{2} - 34e - 8$ |
| 31 | $[31, 31, 2w^{2} - w - 14]$ | $-e^{6} + 2e^{5} + 12e^{4} - 18e^{3} - 39e^{2} + 36e + 16$ |
| 31 | $[31, 31, w^{2} - 2]$ | $-e^{6} + 3e^{5} + 8e^{4} - 21e^{3} - 19e^{2} + 30e + 8$ |
| 37 | $[37, 37, -3w^{2} + w + 19]$ | $-2e^{3} + 4e^{2} + 8e - 10$ |
| 49 | $[49, 7, w^{2} - 2w - 4]$ | $\phantom{-}e^{6} - 3e^{5} - 7e^{4} + 18e^{3} + 14e^{2} - 21e - 2$ |
| 53 | $[53, 53, -w - 4]$ | $\phantom{-}e^{6} - 2e^{5} - 14e^{4} + 24e^{3} + 45e^{2} - 57e - 6$ |
| 61 | $[61, 61, 2w^{2} + w - 7]$ | $-e^{6} + 3e^{5} + 7e^{4} - 18e^{3} - 16e^{2} + 19e + 10$ |
| 71 | $[71, 71, 2w^{2} - 2w - 13]$ | $-e^{6} + 3e^{5} + 11e^{4} - 28e^{3} - 34e^{2} + 57e + 12$ |
| 73 | $[73, 73, w - 5]$ | $\phantom{-}e^{6} - e^{5} - 17e^{4} + 18e^{3} + 62e^{2} - 49e - 26$ |
| 83 | $[83, 83, w^{2} - 3w - 2]$ | $\phantom{-}2e^{4} - 7e^{3} - 8e^{2} + 29e$ |
| 89 | $[89, 89, w^{2} + 2w - 4]$ | $-e^{5} + 5e^{4} - 23e^{2} + 15e + 6$ |
| 97 | $[97, 97, -w^{2} + 2w + 7]$ | $\phantom{-}2e^{4} - 4e^{3} - 12e^{2} + 14e + 10$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3, 3, w - 1]$ | $-1$ |
| $7$ | $[7, 7, w + 1]$ | $1$ |