Base field 6.6.810448.1
Generator \(w\), with minimal polynomial \(x^{6} - 3x^{5} - 2x^{4} + 9x^{3} - 5x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[64, 2, 2]$ |
| Dimension: | $4$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $15$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{4} + 3x^{3} - 33x^{2} - 104x - 52\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, w^{3} - 2w^{2} - 2w + 3]$ | $\phantom{-}0$ |
| 25 | $[25, 5, w^{4} - 2w^{3} - 2w^{2} + 3w + 1]$ | $-\frac{7}{43}e^{3} - \frac{11}{43}e^{2} + \frac{216}{43}e + \frac{530}{43}$ |
| 25 | $[25, 5, -w^{5} + 3w^{4} + 2w^{3} - 8w^{2} - 2w + 2]$ | $\phantom{-}e$ |
| 25 | $[25, 5, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 5w + 4]$ | $\phantom{-}e$ |
| 27 | $[27, 3, -w^{3} + 2w^{2} + 3w - 2]$ | $-\frac{2}{43}e^{3} + \frac{3}{43}e^{2} + \frac{74}{43}e + \frac{4}{43}$ |
| 27 | $[27, 3, w^{5} - 2w^{4} - 5w^{3} + 8w^{2} + 6w - 4]$ | $-\frac{2}{43}e^{3} + \frac{3}{43}e^{2} + \frac{74}{43}e + \frac{4}{43}$ |
| 37 | $[37, 37, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 3w + 2]$ | $\phantom{-}\frac{3}{43}e^{3} + \frac{17}{43}e^{2} - \frac{111}{43}e - \frac{436}{43}$ |
| 37 | $[37, 37, -2w^{5} + 5w^{4} + 6w^{3} - 14w^{2} - 5w + 5]$ | $-\frac{18}{43}e^{3} - \frac{16}{43}e^{2} + \frac{580}{43}e + \frac{810}{43}$ |
| 37 | $[37, 37, w^{5} - 3w^{4} - 2w^{3} + 8w^{2} - 2]$ | $\phantom{-}\frac{3}{43}e^{3} + \frac{17}{43}e^{2} - \frac{111}{43}e - \frac{436}{43}$ |
| 67 | $[67, 67, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 7w - 2]$ | $-\frac{12}{43}e^{3} - \frac{25}{43}e^{2} + \frac{444}{43}e + \frac{712}{43}$ |
| 67 | $[67, 67, w^{5} - 2w^{4} - 5w^{3} + 7w^{2} + 7w - 5]$ | $\phantom{-}\frac{16}{43}e^{3} + \frac{19}{43}e^{2} - \frac{592}{43}e - \frac{720}{43}$ |
| 67 | $[67, 67, -2w^{5} + 6w^{4} + 4w^{3} - 16w^{2} - 3w + 5]$ | $\phantom{-}\frac{8}{43}e^{3} + \frac{31}{43}e^{2} - \frac{296}{43}e - \frac{704}{43}$ |
| 67 | $[67, 67, -2w^{5} + 4w^{4} + 8w^{3} - 12w^{2} - 9w + 6]$ | $\phantom{-}\frac{8}{43}e^{3} + \frac{31}{43}e^{2} - \frac{296}{43}e - \frac{704}{43}$ |
| 67 | $[67, 67, -w^{5} + 2w^{4} + 4w^{3} - 6w^{2} - 6w + 4]$ | $\phantom{-}\frac{16}{43}e^{3} + \frac{19}{43}e^{2} - \frac{592}{43}e - \frac{720}{43}$ |
| 67 | $[67, 67, w^{5} - 4w^{4} + 10w^{2} - 2w - 3]$ | $-\frac{12}{43}e^{3} - \frac{25}{43}e^{2} + \frac{444}{43}e + \frac{712}{43}$ |
| 107 | $[107, 107, w^{5} - 3w^{4} - w^{3} + 7w^{2} - 3w - 2]$ | $\phantom{-}\frac{11}{43}e^{3} + \frac{5}{43}e^{2} - \frac{278}{43}e - \frac{108}{43}$ |
| 107 | $[107, 107, w^{5} - 2w^{4} - 5w^{3} + 8w^{2} + 5w - 5]$ | $-\frac{3}{43}e^{3} - \frac{17}{43}e^{2} + \frac{240}{43}e + \frac{608}{43}$ |
| 107 | $[107, 107, 2w^{5} - 5w^{4} - 6w^{3} + 13w^{2} + 6w - 4]$ | $-\frac{3}{43}e^{3} - \frac{17}{43}e^{2} + \frac{68}{43}e + \frac{264}{43}$ |
| 107 | $[107, 107, 2w^{5} - 5w^{4} - 6w^{3} + 15w^{2} + 4w - 6]$ | $-\frac{3}{43}e^{3} - \frac{17}{43}e^{2} + \frac{68}{43}e + \frac{264}{43}$ |
| 107 | $[107, 107, -w^{5} + 3w^{4} + 3w^{3} - 9w^{2} - 3w + 2]$ | $-\frac{3}{43}e^{3} - \frac{17}{43}e^{2} + \frac{240}{43}e + \frac{608}{43}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $4$ | $[4, 2, w^{3} - 2w^{2} - 2w + 3]$ | $1$ |