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: | $[11, 11, w - 1]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $12$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 6x^{3} - 9x^{2} - 54x - 27\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 11 | $[11, 11, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w + 2]$ | $\phantom{-}\frac{1}{18}e^{3} + \frac{1}{2}e^{2} - \frac{1}{2}e - 7$ |
| 11 | $[11, 11, w^{5} - 3w^{4} - 3w^{3} + 9w^{2} + 4w - 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w - 1]$ | $\phantom{-}1$ |
| 19 | $[19, 19, w^{3} - w^{2} - 4w]$ | $-\frac{1}{3}e^{3} - \frac{3}{2}e^{2} + \frac{9}{2}e + \frac{17}{2}$ |
| 19 | $[19, 19, -w^{5} + 2w^{4} + 6w^{3} - 7w^{2} - 10w + 1]$ | $-\frac{1}{6}e^{2} - \frac{1}{2}e + \frac{5}{2}$ |
| 29 | $[29, 29, w^{5} - 3w^{4} - 3w^{3} + 9w^{2} + 3w - 3]$ | $-\frac{2}{9}e^{3} - \frac{4}{3}e^{2} + 2e + 6$ |
| 29 | $[29, 29, -w^{5} + 3w^{4} + 3w^{3} - 7w^{2} - 6w - 2]$ | $\phantom{-}\frac{1}{6}e^{3} + \frac{2}{3}e^{2} - 4e - \frac{9}{2}$ |
| 29 | $[29, 29, w^{5} - 3w^{4} - 2w^{3} + 6w^{2} + 2w + 1]$ | $\phantom{-}\frac{2}{9}e^{3} + e^{2} - 4e - 12$ |
| 29 | $[29, 29, -w^{4} + 4w^{3} - 9w]$ | $-\frac{1}{6}e^{3} - e^{2} + e + \frac{11}{2}$ |
| 31 | $[31, 31, w^{4} - 3w^{3} - 2w^{2} + 6w + 1]$ | $\phantom{-}\frac{1}{9}e^{3} + \frac{1}{2}e^{2} - \frac{1}{2}e - \frac{1}{2}$ |
| 41 | $[41, 41, -2w^{5} + 6w^{4} + 5w^{3} - 15w^{2} - 6w + 3]$ | $-\frac{1}{18}e^{3} + e - \frac{13}{2}$ |
| 59 | $[59, 59, -2w^{5} + 6w^{4} + 6w^{3} - 16w^{2} - 11w + 1]$ | $\phantom{-}\frac{2}{9}e^{3} + \frac{5}{3}e^{2} - 10$ |
| 61 | $[61, 61, -2w^{5} + 6w^{4} + 5w^{3} - 14w^{2} - 7w]$ | $-\frac{1}{3}e^{3} - 2e^{2} + 4e + 9$ |
| 61 | $[61, 61, 2w^{5} - 5w^{4} - 8w^{3} + 13w^{2} + 13w + 1]$ | $-\frac{5}{9}e^{3} - \frac{5}{2}e^{2} + \frac{17}{2}e + \frac{29}{2}$ |
| 61 | $[61, 61, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w - 1]$ | $\phantom{-}\frac{5}{9}e^{3} + \frac{11}{6}e^{2} - \frac{19}{2}e - \frac{25}{2}$ |
| 61 | $[61, 61, w^{3} - 2w^{2} - 3w - 1]$ | $\phantom{-}\frac{2}{9}e^{3} + \frac{5}{3}e^{2} - 9$ |
| 64 | $[64, 2, -2]$ | $-\frac{1}{9}e^{3} - \frac{1}{6}e^{2} + \frac{7}{2}e + \frac{13}{2}$ |
| 79 | $[79, 79, -3w^{5} + 9w^{4} + 7w^{3} - 21w^{2} - 9w + 2]$ | $\phantom{-}\frac{1}{6}e^{2} - \frac{1}{2}e - \frac{13}{2}$ |
| 89 | $[89, 89, w^{5} - 3w^{4} - 2w^{3} + 6w^{2} + 3w + 3]$ | $\phantom{-}\frac{1}{18}e^{3} + \frac{9}{2}$ |
| 101 | $[101, 101, -w^{5} + 4w^{4} - w^{3} - 8w^{2} + 5w]$ | $-\frac{1}{9}e^{3} + e - 1$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $11$ | $[11, 11, w - 1]$ | $-1$ |