Base field 4.4.17428.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 6x^{2} + 4x + 6\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[8, 8, -w^{3} - w^{2} + 5w + 5]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 14x^{6} + x^{5} + 58x^{4} - 11x^{3} - 65x^{2} + 24x - 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w - 2]$ | $\phantom{-}e$ |
| 2 | $[2, 2, w + 1]$ | $\phantom{-}0$ |
| 3 | $[3, 3, -w^{2} + w + 3]$ | $-\frac{5}{6}e^{7} - \frac{1}{6}e^{6} + \frac{71}{6}e^{5} + \frac{4}{3}e^{4} - \frac{149}{3}e^{3} + \frac{5}{6}e^{2} + \frac{169}{3}e - \frac{31}{3}$ |
| 27 | $[27, 3, -w^{3} - 2w^{2} + 3w + 5]$ | $-\frac{2}{3}e^{7} - \frac{1}{3}e^{6} + \frac{26}{3}e^{5} + \frac{11}{3}e^{4} - \frac{94}{3}e^{3} - \frac{28}{3}e^{2} + \frac{80}{3}e + \frac{4}{3}$ |
| 29 | $[29, 29, w^{3} + w^{2} - 2w - 1]$ | $-\frac{5}{6}e^{7} - \frac{1}{6}e^{6} + \frac{71}{6}e^{5} + \frac{4}{3}e^{4} - \frac{152}{3}e^{3} + \frac{11}{6}e^{2} + \frac{187}{3}e - \frac{43}{3}$ |
| 31 | $[31, 31, -w^{2} - w + 1]$ | $\phantom{-}\frac{5}{3}e^{7} + \frac{1}{3}e^{6} - \frac{68}{3}e^{5} - \frac{11}{3}e^{4} + \frac{271}{3}e^{3} + \frac{16}{3}e^{2} - \frac{290}{3}e + \frac{44}{3}$ |
| 31 | $[31, 31, w^{3} - 2w^{2} - 5w + 7]$ | $-\frac{5}{6}e^{7} - \frac{1}{6}e^{6} + \frac{71}{6}e^{5} + \frac{4}{3}e^{4} - \frac{152}{3}e^{3} - \frac{1}{6}e^{2} + \frac{187}{3}e - \frac{19}{3}$ |
| 37 | $[37, 37, -w^{3} + 3w + 1]$ | $-\frac{7}{6}e^{7} + \frac{1}{6}e^{6} + \frac{97}{6}e^{5} - \frac{7}{3}e^{4} - \frac{199}{3}e^{3} + \frac{73}{6}e^{2} + \frac{227}{3}e - \frac{65}{3}$ |
| 41 | $[41, 41, -w^{2} + w + 5]$ | $\phantom{-}\frac{2}{3}e^{7} + \frac{1}{3}e^{6} - \frac{26}{3}e^{5} - \frac{8}{3}e^{4} + \frac{94}{3}e^{3} + \frac{1}{3}e^{2} - \frac{80}{3}e + \frac{38}{3}$ |
| 41 | $[41, 41, -w^{3} + w^{2} + 4w - 1]$ | $-e^{7} + 14e^{5} - e^{4} - 59e^{3} + 9e^{2} + 70e - 14$ |
| 43 | $[43, 43, -2w - 1]$ | $-\frac{10}{3}e^{7} - \frac{2}{3}e^{6} + \frac{139}{3}e^{5} + \frac{19}{3}e^{4} - \frac{569}{3}e^{3} - \frac{11}{3}e^{2} + \frac{622}{3}e - \frac{112}{3}$ |
| 47 | $[47, 47, w^{2} + w - 5]$ | $-\frac{5}{6}e^{7} - \frac{1}{6}e^{6} + \frac{65}{6}e^{5} + \frac{4}{3}e^{4} - \frac{119}{3}e^{3} - \frac{1}{6}e^{2} + \frac{103}{3}e - \frac{13}{3}$ |
| 47 | $[47, 47, 2w^{3} - 3w^{2} - 9w + 11]$ | $-\frac{5}{6}e^{7} - \frac{1}{6}e^{6} + \frac{71}{6}e^{5} + \frac{4}{3}e^{4} - \frac{149}{3}e^{3} + \frac{5}{6}e^{2} + \frac{175}{3}e - \frac{25}{3}$ |
| 53 | $[53, 53, w^{3} + 2w^{2} - 5w - 5]$ | $\phantom{-}\frac{7}{3}e^{7} + \frac{2}{3}e^{6} - \frac{97}{3}e^{5} - \frac{19}{3}e^{4} + \frac{398}{3}e^{3} + \frac{17}{3}e^{2} - \frac{448}{3}e + \frac{94}{3}$ |
| 59 | $[59, 59, w^{3} + w^{2} - 4w - 1]$ | $\phantom{-}e^{7} - 14e^{5} + e^{4} + 57e^{3} - 11e^{2} - 60e + 22$ |
| 59 | $[59, 59, w^{3} + w^{2} - 4w - 5]$ | $-\frac{2}{3}e^{7} - \frac{1}{3}e^{6} + \frac{29}{3}e^{5} + \frac{8}{3}e^{4} - \frac{127}{3}e^{3} - \frac{1}{3}e^{2} + \frac{152}{3}e - \frac{38}{3}$ |
| 71 | $[71, 71, 2w^{3} - 4w^{2} - 10w + 19]$ | $\phantom{-}\frac{2}{3}e^{7} - \frac{2}{3}e^{6} - \frac{29}{3}e^{5} + \frac{22}{3}e^{4} + \frac{127}{3}e^{3} - \frac{62}{3}e^{2} - \frac{158}{3}e + \frac{44}{3}$ |
| 71 | $[71, 71, w^{2} + 3w + 1]$ | $-\frac{13}{6}e^{7} - \frac{5}{6}e^{6} + \frac{181}{6}e^{5} + \frac{23}{3}e^{4} - \frac{370}{3}e^{3} - \frac{53}{6}e^{2} + \frac{407}{3}e - \frac{83}{3}$ |
| 73 | $[73, 73, w^{3} - 5w + 1]$ | $\phantom{-}\frac{4}{3}e^{7} - \frac{1}{3}e^{6} - \frac{55}{3}e^{5} + \frac{14}{3}e^{4} + \frac{227}{3}e^{3} - \frac{61}{3}e^{2} - \frac{268}{3}e + \frac{70}{3}$ |
| 89 | $[89, 89, -4w^{3} + 7w^{2} + 19w - 29]$ | $\phantom{-}\frac{13}{6}e^{7} + \frac{5}{6}e^{6} - \frac{187}{6}e^{5} - \frac{23}{3}e^{4} + \frac{400}{3}e^{3} + \frac{35}{6}e^{2} - \frac{473}{3}e + \frac{113}{3}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $2$ | $[2, 2, w + 1]$ | $1$ |