Base field 3.3.837.1
Generator \(w\), with minimal polynomial \(x^{3} - 6x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2]$ |
| Level: | $[16, 4, -w^{2} + w + 5]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $17$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} + 4x^{5} - 3x^{4} - 23x^{3} - 6x^{2} + 27x + 9\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w^{2} - 2w - 1]$ | $\phantom{-}e$ |
| 3 | $[3, 3, w + 2]$ | $\phantom{-}\frac{1}{3}e^{5} + \frac{1}{3}e^{4} - 3e^{3} - \frac{5}{3}e^{2} + 6e$ |
| 4 | $[4, 2, w^{2} + w - 3]$ | $\phantom{-}0$ |
| 5 | $[5, 5, -w + 2]$ | $-e^{2} - e + 3$ |
| 13 | $[13, 13, -2w - 5]$ | $-\frac{4}{3}e^{5} - \frac{7}{3}e^{4} + 9e^{3} + \frac{35}{3}e^{2} - 13e - 10$ |
| 25 | $[25, 5, -w^{2} - 2w + 2]$ | $-\frac{1}{3}e^{5} - \frac{4}{3}e^{4} + 3e^{3} + \frac{29}{3}e^{2} - 9e - 13$ |
| 31 | $[31, 31, -w^{2} + 2]$ | $\phantom{-}\frac{5}{3}e^{5} + \frac{11}{3}e^{4} - 9e^{3} - \frac{43}{3}e^{2} + 11e + 2$ |
| 31 | $[31, 31, -2w + 1]$ | $\phantom{-}\frac{2}{3}e^{5} + \frac{5}{3}e^{4} - 5e^{3} - \frac{31}{3}e^{2} + 10e + 8$ |
| 37 | $[37, 37, 2w + 3]$ | $-\frac{1}{3}e^{5} - \frac{1}{3}e^{4} + 2e^{3} - \frac{1}{3}e^{2} - 4e - 1$ |
| 41 | $[41, 41, -w - 4]$ | $\phantom{-}e^{5} + e^{4} - 8e^{3} - 4e^{2} + 14e - 3$ |
| 43 | $[43, 43, 2w^{2} - 2w - 7]$ | $\phantom{-}\frac{5}{3}e^{5} + \frac{14}{3}e^{4} - 8e^{3} - \frac{64}{3}e^{2} + 7e + 14$ |
| 47 | $[47, 47, -2w^{2} - w + 8]$ | $\phantom{-}e^{5} + 2e^{4} - 8e^{3} - 10e^{2} + 19e + 9$ |
| 53 | $[53, 53, 3w^{2} - 6w - 2]$ | $-e^{5} - e^{4} + 7e^{3} + 4e^{2} - 9e - 6$ |
| 53 | $[53, 53, -2w^{2} + 3w + 18]$ | $-e^{5} - 4e^{4} + 4e^{3} + 21e^{2} - 15$ |
| 53 | $[53, 53, 2w - 3]$ | $-3e^{5} - 6e^{4} + 18e^{3} + 26e^{2} - 24e - 12$ |
| 59 | $[59, 59, 2w^{2} - 3w - 4]$ | $-e^{3} - 4e^{2} + 2e + 12$ |
| 61 | $[61, 61, w^{2} - 2w - 4]$ | $\phantom{-}2e^{3} + 3e^{2} - 9e - 4$ |
| 71 | $[71, 71, 4w + 9]$ | $-e^{5} - e^{4} + 10e^{3} + 7e^{2} - 21e - 9$ |
| 73 | $[73, 73, 2w^{2} - 9]$ | $-\frac{1}{3}e^{5} - \frac{4}{3}e^{4} + e^{3} + \frac{17}{3}e^{2} - 3e - 4$ |
| 79 | $[79, 79, w^{2} - 4w + 2]$ | $\phantom{-}\frac{5}{3}e^{5} + \frac{8}{3}e^{4} - 13e^{3} - \frac{43}{3}e^{2} + 24e + 8$ |
Atkin-Lehner eigenvalues
The Atkin-Lehner eigenvalues for this form are not in the database.