Base field 6.6.980125.1
Generator \(w\), with minimal polynomial \(x^{6} - x^{5} - 6x^{4} + 6x^{3} + 7x^{2} - 5x - 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[59, 59, -w^{5} - w^{4} + 4w^{3} + 4w^{2} - 2w - 3]$ |
| Dimension: | $8$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{8} - 42x^{6} + 452x^{4} - 972x^{2} + 32\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -w^{2} + 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w^{4} + w^{3} - 4w^{2} - 3w + 2]$ | $-\frac{305}{15956}e^{7} + \frac{6359}{7978}e^{5} - \frac{67365}{7978}e^{3} + \frac{68271}{3989}e$ |
| 11 | $[11, 11, -w^{5} + 6w^{3} - w^{2} - 7w + 1]$ | $\phantom{-}\frac{91}{7978}e^{7} - \frac{3703}{7978}e^{5} + \frac{37517}{7978}e^{3} - \frac{37953}{3989}e$ |
| 19 | $[19, 19, -w^{5} - w^{4} + 5w^{3} + 4w^{2} - 5w - 3]$ | $-\frac{65}{7978}e^{7} + \frac{2645}{7978}e^{5} - \frac{13114}{3989}e^{3} + \frac{20271}{3989}e$ |
| 29 | $[29, 29, -2w^{4} - w^{3} + 9w^{2} + 2w - 5]$ | $-\frac{111}{15956}e^{6} + \frac{2105}{7978}e^{4} - \frac{9479}{3989}e^{2} - \frac{2606}{3989}$ |
| 31 | $[31, 31, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 7w + 1]$ | $\phantom{-}\frac{85}{15956}e^{7} - \frac{788}{3989}e^{5} + \frac{11319}{7978}e^{3} + \frac{3469}{3989}e$ |
| 41 | $[41, 41, 2w^{5} + w^{4} - 10w^{3} - 3w^{2} + 7w + 2]$ | $\phantom{-}\frac{177}{15956}e^{6} - \frac{3141}{7978}e^{4} + \frac{13498}{3989}e^{2} - \frac{42850}{3989}$ |
| 41 | $[41, 41, w^{5} - w^{4} - 6w^{3} + 5w^{2} + 6w - 3]$ | $\phantom{-}\frac{279}{15956}e^{7} - \frac{2915}{3989}e^{5} + \frac{29863}{3989}e^{3} - \frac{43474}{3989}e$ |
| 41 | $[41, 41, w^{5} - 6w^{3} + w^{2} + 7w - 2]$ | $\phantom{-}\frac{84}{3989}e^{7} - \frac{3725}{3989}e^{5} + \frac{44757}{3989}e^{3} - \frac{128061}{3989}e$ |
| 59 | $[59, 59, -w^{5} - w^{4} + 4w^{3} + 4w^{2} - 2w - 3]$ | $\phantom{-}1$ |
| 59 | $[59, 59, w^{5} - w^{4} - 5w^{3} + 6w^{2} + 2w - 4]$ | $\phantom{-}\frac{33}{7978}e^{6} - \frac{518}{3989}e^{4} + \frac{4019}{3989}e^{2} - \frac{29500}{3989}$ |
| 59 | $[59, 59, -w^{5} + 4w^{3} - w^{2} - w + 1]$ | $-\frac{16}{3989}e^{6} + \frac{1609}{7978}e^{4} - \frac{9095}{3989}e^{2} - \frac{21196}{3989}$ |
| 61 | $[61, 61, -w^{4} + 4w^{2} - 2w - 2]$ | $-\frac{1395}{15956}e^{7} + \frac{14575}{3989}e^{5} - \frac{310597}{7978}e^{3} + \frac{321084}{3989}e$ |
| 64 | $[64, 2, -2]$ | $\phantom{-}\frac{94}{3989}e^{6} - \frac{7957}{7978}e^{4} + \frac{38973}{3989}e^{2} - \frac{33039}{3989}$ |
| 71 | $[71, 71, 2w^{5} + w^{4} - 10w^{3} - 3w^{2} + 9w + 3]$ | $-\frac{85}{3989}e^{6} + \frac{3152}{3989}e^{4} - \frac{26627}{3989}e^{2} + \frac{2080}{3989}$ |
| 81 | $[81, 3, w^{5} + 2w^{4} - 4w^{3} - 8w^{2} + 2w + 3]$ | $\phantom{-}\frac{461}{15956}e^{7} - \frac{9533}{7978}e^{5} + \frac{50616}{3989}e^{3} - \frac{113339}{3989}e$ |
| 89 | $[89, 89, -w^{5} + 6w^{3} - 7w]$ | $-\frac{205}{15956}e^{6} + \frac{3097}{7978}e^{4} - \frac{6258}{3989}e^{2} - \frac{29250}{3989}$ |
| 89 | $[89, 89, w^{5} + w^{4} - 5w^{3} - 4w^{2} + 6w + 2]$ | $\phantom{-}\frac{1357}{15956}e^{7} - \frac{14035}{3989}e^{5} + \frac{146034}{3989}e^{3} - \frac{279319}{3989}e$ |
| 101 | $[101, 101, w^{5} - 4w^{3} + 2w^{2} + w - 3]$ | $\phantom{-}\frac{19}{15956}e^{6} - \frac{270}{3989}e^{4} + \frac{3635}{3989}e^{2} - \frac{10910}{3989}$ |
| 101 | $[101, 101, w^{5} + 2w^{4} - 4w^{3} - 8w^{2} + 3w + 4]$ | $-\frac{137}{7978}e^{7} + \frac{2634}{3989}e^{5} - \frac{22608}{3989}e^{3} + \frac{16459}{3989}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $59$ | $[59, 59, -w^{5} - w^{4} + 4w^{3} + 4w^{2} - 2w - 3]$ | $-1$ |