Base field 6.6.1241125.1
Generator \(w\), with minimal polynomial \(x^{6} - 7x^{4} - 2x^{3} + 11x^{2} + 7x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[55, 55, w^{5} - 8w^{3} - 2w^{2} + 15w + 5]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $33$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 5x^{3} - 6x^{2} - 16x - 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, -2w^{5} + w^{4} + 13w^{3} - 2w^{2} - 19w - 5]$ | $\phantom{-}1$ |
| 9 | $[9, 3, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 23w + 6]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w - 1]$ | $-1$ |
| 25 | $[25, 5, w^{3} + w^{2} - 4w - 3]$ | $-\frac{2}{3}e^{2} - \frac{8}{3}e + \frac{1}{3}$ |
| 29 | $[29, 29, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w]$ | $-\frac{1}{3}e^{2} - \frac{1}{3}e + \frac{2}{3}$ |
| 41 | $[41, 41, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ | $-\frac{2}{3}e^{3} - 2e^{2} + 9e + \frac{14}{3}$ |
| 49 | $[49, 7, w^{5} - w^{4} - 7w^{3} + 4w^{2} + 11w + 1]$ | $\phantom{-}\frac{1}{3}e^{3} + 2e^{2} - \frac{28}{3}$ |
| 59 | $[59, 59, 2w^{5} - w^{4} - 14w^{3} + 2w^{2} + 24w + 7]$ | $\phantom{-}\frac{4}{3}e^{3} + \frac{17}{3}e^{2} - \frac{43}{3}e - \frac{38}{3}$ |
| 59 | $[59, 59, -w^{5} + 8w^{3} + 2w^{2} - 15w - 8]$ | $-\frac{2}{3}e^{3} - \frac{8}{3}e^{2} + \frac{19}{3}e + 1$ |
| 61 | $[61, 61, w^{5} - 7w^{3} - 2w^{2} + 12w + 4]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{5}{3}e^{2} - \frac{13}{3}e - \frac{29}{3}$ |
| 61 | $[61, 61, -w^{5} + 7w^{3} - 11w - 1]$ | $-3e - 5$ |
| 64 | $[64, 2, 2]$ | $\phantom{-}\frac{2}{3}e^{3} + \frac{10}{3}e^{2} - \frac{8}{3}e - \frac{25}{3}$ |
| 71 | $[71, 71, w^{3} + w^{2} - 5w - 3]$ | $\phantom{-}\frac{2}{3}e^{3} + \frac{7}{3}e^{2} - \frac{26}{3}e - \frac{7}{3}$ |
| 71 | $[71, 71, -3w^{5} + w^{4} + 21w^{3} - w^{2} - 33w - 9]$ | $\phantom{-}\frac{2}{3}e^{3} + 2e^{2} - 9e - \frac{2}{3}$ |
| 79 | $[79, 79, -2w^{5} + w^{4} + 13w^{3} - 3w^{2} - 19w - 5]$ | $\phantom{-}\frac{2}{3}e^{3} + 3e^{2} - 5e - \frac{20}{3}$ |
| 81 | $[81, 3, 2w^{5} - w^{4} - 13w^{3} + w^{2} + 19w + 8]$ | $\phantom{-}\frac{1}{3}e^{3} + 2e^{2} - \frac{1}{3}$ |
| 89 | $[89, 89, 2w^{5} - w^{4} - 13w^{3} + 2w^{2} + 20w + 7]$ | $-\frac{4}{3}e^{3} - \frac{19}{3}e^{2} + \frac{23}{3}e + 12$ |
| 89 | $[89, 89, -w^{5} + 8w^{3} + w^{2} - 16w - 5]$ | $\phantom{-}\frac{2}{3}e^{2} + \frac{14}{3}e - \frac{1}{3}$ |
| 89 | $[89, 89, -3w^{5} + w^{4} + 20w^{3} - 30w - 11]$ | $\phantom{-}\frac{1}{3}e^{3} + \frac{7}{3}e^{2} - \frac{5}{3}e - 14$ |
| 89 | $[89, 89, -w^{5} + 7w^{3} + 2w^{2} - 11w - 4]$ | $-\frac{4}{3}e^{3} - \frac{17}{3}e^{2} + \frac{34}{3}e + \frac{35}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $5$ | $[5, 5, -2w^{5} + w^{4} + 13w^{3} - 2w^{2} - 19w - 5]$ | $-1$ |
| $11$ | $[11, 11, w - 1]$ | $1$ |