Base field 6.6.434581.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 4x^{4} + 5x^{3} + 4x^{2} - 2x - 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[64, 2, -2]$ |
| Dimension: | $2$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $10$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{2} + 2x - 17\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 13 | $[13, 13, -w^{5} + 3w^{4} + 2w^{3} - 9w^{2} + w + 4]$ | $\phantom{-}e$ |
| 13 | $[13, 13, -w^{2} + w + 2]$ | $-e - 2$ |
| 27 | $[27, 3, 2w^{5} - 4w^{4} - 7w^{3} + 9w^{2} + 4w - 2]$ | $-\frac{1}{3}e - \frac{19}{3}$ |
| 27 | $[27, 3, -2w^{5} + 5w^{4} + 5w^{3} - 12w^{2} - w + 5]$ | $\phantom{-}\frac{1}{3}e - \frac{17}{3}$ |
| 29 | $[29, 29, w^{3} - 2w^{2} - 2w + 3]$ | $-\frac{2}{3}e - \frac{5}{3}$ |
| 29 | $[29, 29, 2w^{5} - 4w^{4} - 7w^{3} + 8w^{2} + 4w - 2]$ | $\phantom{-}\frac{2}{3}e - \frac{1}{3}$ |
| 43 | $[43, 43, -w^{5} + 3w^{4} + w^{3} - 6w^{2} + 3w + 1]$ | $-\frac{2}{3}e + \frac{10}{3}$ |
| 43 | $[43, 43, -w^{4} + w^{3} + 5w^{2} - 4]$ | $\phantom{-}\frac{2}{3}e + \frac{14}{3}$ |
| 49 | $[49, 7, w^{5} - 4w^{4} + 11w^{2} - 3w - 4]$ | $-9$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}1$ |
| 71 | $[71, 71, 2w^{5} - 6w^{4} - 4w^{3} + 17w^{2} - w - 6]$ | $\phantom{-}\frac{1}{3}e + \frac{1}{3}$ |
| 71 | $[71, 71, 2w^{4} - 4w^{3} - 6w^{2} + 7w + 2]$ | $-\frac{5}{3}e - \frac{23}{3}$ |
| 71 | $[71, 71, -w^{5} + 3w^{4} + 2w^{3} - 7w^{2} - w]$ | $-\frac{1}{3}e - \frac{1}{3}$ |
| 71 | $[71, 71, -2w^{5} + 5w^{4} + 6w^{3} - 14w^{2} - 3w + 5]$ | $\phantom{-}\frac{5}{3}e - \frac{13}{3}$ |
| 83 | $[83, 83, -3w^{5} + 7w^{4} + 9w^{3} - 17w^{2} - 5w + 5]$ | $\phantom{-}\frac{5}{3}e - \frac{1}{3}$ |
| 83 | $[83, 83, 3w^{5} - 6w^{4} - 10w^{3} + 12w^{2} + 5w - 2]$ | $\phantom{-}3e + 3$ |
| 83 | $[83, 83, -2w^{5} + 5w^{4} + 5w^{3} - 11w^{2} - 3w + 3]$ | $-\frac{5}{3}e - \frac{11}{3}$ |
| 83 | $[83, 83, 3w^{5} - 7w^{4} - 8w^{3} + 15w^{2} + 2w - 4]$ | $-3e - 3$ |
| 97 | $[97, 97, -3w^{5} + 6w^{4} + 10w^{3} - 12w^{2} - 5w + 3]$ | $-\frac{2}{3}e - \frac{35}{3}$ |
| 97 | $[97, 97, w^{5} - 2w^{4} - 4w^{3} + 5w^{2} + 5w - 3]$ | $-\frac{5}{3}e - \frac{8}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $64$ | $[64, 2, -2]$ | $-1$ |