Base field 6.6.966125.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 6x^{4} + 4x^{3} + 8x^{2} - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[29, 29, -w^{4} + 4w^{2} + 1]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $14$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 28x^{4} + 244x^{2} - 648\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 5 | $[5, 5, w - 1]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w^{3} - 3w]$ | $-\frac{1}{9}e^{5} + \frac{19}{9}e^{3} - \frac{91}{9}e$ |
| 19 | $[19, 19, -w^{5} + w^{4} + 5w^{3} - 4w^{2} - 5w]$ | $-\frac{1}{6}e^{5} + \frac{8}{3}e^{3} - \frac{23}{3}e$ |
| 25 | $[25, 5, w^{5} - 2w^{4} - 6w^{3} + 8w^{2} + 8w]$ | $\phantom{-}\frac{1}{18}e^{5} - \frac{5}{9}e^{3} - \frac{4}{9}e$ |
| 29 | $[29, 29, -w^{4} + 4w^{2} + 1]$ | $-1$ |
| 31 | $[31, 31, w^{5} - 2w^{4} - 5w^{3} + 9w^{2} + 3w - 4]$ | $\phantom{-}0$ |
| 31 | $[31, 31, -w^{2} + 2]$ | $-\frac{1}{6}e^{5} + \frac{11}{3}e^{3} - \frac{50}{3}e$ |
| 59 | $[59, 59, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 4w - 2]$ | $\phantom{-}\frac{4}{9}e^{5} - \frac{76}{9}e^{3} + \frac{319}{9}e$ |
| 59 | $[59, 59, w^{4} - w^{3} - 5w^{2} + 3w + 4]$ | $\phantom{-}e^{2} - 8$ |
| 59 | $[59, 59, -w^{4} - w^{3} + 4w^{2} + 5w]$ | $\phantom{-}e^{4} - 20e^{2} + 88$ |
| 61 | $[61, 61, w^{5} - w^{4} - 4w^{3} + 5w^{2} - 4]$ | $\phantom{-}\frac{5}{18}e^{5} - \frac{43}{9}e^{3} + \frac{142}{9}e$ |
| 64 | $[64, 2, 2]$ | $\phantom{-}\frac{1}{2}e^{4} - 10e^{2} + 47$ |
| 71 | $[71, 71, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 6w]$ | $-2e^{2} + 16$ |
| 71 | $[71, 71, -w^{5} + 2w^{4} + 4w^{3} - 9w^{2} + w + 4]$ | $\phantom{-}\frac{1}{9}e^{5} - \frac{19}{9}e^{3} + \frac{73}{9}e$ |
| 71 | $[71, 71, 2w^{5} - 3w^{4} - 9w^{3} + 13w^{2} + 4w - 4]$ | $\phantom{-}\frac{1}{6}e^{5} - \frac{11}{3}e^{3} + \frac{59}{3}e$ |
| 71 | $[71, 71, w^{3} - 5w]$ | $-e^{4} + 20e^{2} - 84$ |
| 79 | $[79, 79, w^{5} - w^{4} - 4w^{3} + 4w^{2} + w - 2]$ | $-\frac{7}{18}e^{5} + \frac{71}{9}e^{3} - \frac{314}{9}e$ |
| 89 | $[89, 89, w^{3} - w^{2} - 4w + 1]$ | $\phantom{-}e^{4} - 20e^{2} + 86$ |
| 101 | $[101, 101, -2w^{5} + 3w^{4} + 11w^{3} - 13w^{2} - 12w + 2]$ | $\phantom{-}\frac{1}{9}e^{5} - \frac{10}{9}e^{3} - \frac{44}{9}e$ |
| 101 | $[101, 101, 2w^{5} - 2w^{4} - 13w^{3} + 7w^{2} + 20w + 4]$ | $-e^{4} + 19e^{2} - 82$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $29$ | $[29, 29, -w^{4} + 4w^{2} + 1]$ | $1$ |