Base field 6.6.1995125.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 6x^{4} + 6x^{3} + 12x^{2} + x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[19, 19, -w^{5} + 2w^{4} + 6w^{3} - 7w^{2} - 10w + 1]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $24$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} + 10x^{4} + 28x^{3} + 8x^{2} - 48x - 36\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 11 | $[11, 11, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w + 2]$ | $-\frac{1}{6}e^{4} - \frac{7}{6}e^{3} - \frac{2}{3}e^{2} + \frac{11}{3}e + 1$ |
| 11 | $[11, 11, w^{5} - 3w^{4} - 3w^{3} + 9w^{2} + 4w - 2]$ | $-\frac{1}{3}e^{4} - \frac{17}{6}e^{3} - \frac{16}{3}e^{2} + \frac{10}{3}e + 8$ |
| 11 | $[11, 11, w - 1]$ | $\phantom{-}e$ |
| 19 | $[19, 19, w^{3} - w^{2} - 4w]$ | $\phantom{-}\frac{1}{3}e^{4} + \frac{7}{3}e^{3} + \frac{7}{3}e^{2} - \frac{19}{3}e - 9$ |
| 19 | $[19, 19, -w^{5} + 2w^{4} + 6w^{3} - 7w^{2} - 10w + 1]$ | $\phantom{-}1$ |
| 29 | $[29, 29, w^{5} - 3w^{4} - 3w^{3} + 9w^{2} + 3w - 3]$ | $-\frac{1}{2}e^{4} - \frac{9}{2}e^{3} - 9e^{2} + 5e + 12$ |
| 29 | $[29, 29, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 6w - 2]$ | $-\frac{2}{3}e^{4} - \frac{17}{3}e^{3} - \frac{29}{3}e^{2} + \frac{38}{3}e + 19$ |
| 29 | $[29, 29, w^{5} - 3w^{4} - 2w^{3} + 6w^{2} + 2w + 1]$ | $\phantom{-}\frac{1}{3}e^{4} + \frac{17}{6}e^{3} + \frac{16}{3}e^{2} - \frac{10}{3}e - 11$ |
| 29 | $[29, 29, -w^{4} + 4w^{3} - 9w]$ | $\phantom{-}\frac{1}{3}e^{4} + \frac{7}{3}e^{3} + \frac{7}{3}e^{2} - \frac{16}{3}e - 8$ |
| 31 | $[31, 31, w^{4} - 3w^{3} - 2w^{2} + 6w + 1]$ | $-\frac{1}{6}e^{4} - \frac{5}{3}e^{3} - \frac{14}{3}e^{2} - \frac{1}{3}e + 9$ |
| 41 | $[41, 41, -2w^{5} + 6w^{4} + 5w^{3} - 15w^{2} - 6w + 3]$ | $\phantom{-}\frac{1}{2}e^{4} + 4e^{3} + 6e^{2} - 8e - 15$ |
| 59 | $[59, 59, -2w^{5} + 6w^{4} + 6w^{3} - 16w^{2} - 11w + 1]$ | $\phantom{-}\frac{1}{6}e^{4} + \frac{7}{6}e^{3} + \frac{5}{3}e^{2} + \frac{7}{3}e + 2$ |
| 61 | $[61, 61, -2w^{5} + 6w^{4} + 5w^{3} - 14w^{2} - 7w]$ | $-\frac{2}{3}e^{4} - \frac{17}{3}e^{3} - \frac{35}{3}e^{2} + \frac{11}{3}e + 21$ |
| 61 | $[61, 61, 2w^{5} - 5w^{4} - 8w^{3} + 13w^{2} + 13w + 1]$ | $\phantom{-}\frac{1}{3}e^{4} + \frac{13}{3}e^{3} + \frac{43}{3}e^{2} + \frac{5}{3}e - 21$ |
| 61 | $[61, 61, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w - 1]$ | $-\frac{1}{3}e^{4} - \frac{11}{6}e^{3} - \frac{1}{3}e^{2} + \frac{10}{3}e + 1$ |
| 61 | $[61, 61, w^{3} - 2w^{2} - 3w - 1]$ | $\phantom{-}\frac{2}{3}e^{4} + \frac{14}{3}e^{3} + \frac{14}{3}e^{2} - \frac{20}{3}e + 4$ |
| 64 | $[64, 2, -2]$ | $-\frac{1}{3}e^{4} - \frac{7}{3}e^{3} - \frac{10}{3}e^{2} + \frac{4}{3}e + 1$ |
| 79 | $[79, 79, -3w^{5} + 9w^{4} + 7w^{3} - 21w^{2} - 9w + 2]$ | $-\frac{1}{2}e^{3} - 4e^{2} - 5e - 1$ |
| 89 | $[89, 89, w^{5} - 3w^{4} - 2w^{3} + 6w^{2} + 3w + 3]$ | $\phantom{-}\frac{11}{6}e^{4} + \frac{46}{3}e^{3} + \frac{82}{3}e^{2} - \frac{64}{3}e - 41$ |
| 101 | $[101, 101, -w^{5} + 4w^{4} - w^{3} - 8w^{2} + 5w]$ | $-\frac{3}{2}e^{4} - \frac{25}{2}e^{3} - 22e^{2} + 21e + 42$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $19$ | $[19, 19, -w^{5} + 2w^{4} + 6w^{3} - 7w^{2} - 10w + 1]$ | $-1$ |