Base field 6.6.485125.1
Generator \(w\), with minimal polynomial \(x^{6} - 2x^{5} - 4x^{4} + 8x^{3} + 2x^{2} - 5x + 1\); narrow class number \(1\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2, 2, 2]$ |
| Level: | $[64, 2, -2]$ |
| Dimension: | $9$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $11$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{9} - 4x^{8} - 50x^{7} + 189x^{6} + 792x^{5} - 2821x^{4} - 4252x^{3} + 15087x^{2} + 4626x - 20934\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -w^{2} + 2]$ | $\phantom{-}e$ |
| 19 | $[19, 19, -w^{3} + 4w]$ | $...$ |
| 19 | $[19, 19, w^{3} - 3w - 1]$ | $-\frac{1449239}{180524109}e^{8} + \frac{2933000}{180524109}e^{7} + \frac{76317421}{180524109}e^{6} - \frac{38605923}{60174703}e^{5} - \frac{434024801}{60174703}e^{4} + \frac{1267733570}{180524109}e^{3} + \frac{7891282658}{180524109}e^{2} - \frac{1364231083}{60174703}e - \frac{4304921925}{60174703}$ |
| 29 | $[29, 29, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 8w - 3]$ | $\phantom{-}\frac{432709}{60174703}e^{8} - \frac{981531}{60174703}e^{7} - \frac{22630899}{60174703}e^{6} + \frac{40065344}{60174703}e^{5} + \frac{382244300}{60174703}e^{4} - \frac{456307749}{60174703}e^{3} - \frac{2309681809}{60174703}e^{2} + \frac{1484771920}{60174703}e + \frac{3996647478}{60174703}$ |
| 29 | $[29, 29, w^{4} - w^{3} - 4w^{2} + 2w + 2]$ | $-\frac{56584}{60174703}e^{8} + \frac{260334}{60174703}e^{7} + \frac{3095425}{60174703}e^{6} - \frac{10111341}{60174703}e^{5} - \frac{56692281}{60174703}e^{4} + \frac{94829544}{60174703}e^{3} + \frac{395952630}{60174703}e^{2} - \frac{104539265}{60174703}e - \frac{856968539}{60174703}$ |
| 31 | $[31, 31, -w^{4} + 4w^{2} + w - 3]$ | $-\frac{171865}{180524109}e^{8} + \frac{375334}{180524109}e^{7} + \frac{6596450}{180524109}e^{6} - \frac{3781037}{60174703}e^{5} - \frac{19692508}{60174703}e^{4} + \frac{57835063}{180524109}e^{3} - \frac{21774794}{180524109}e^{2} + \frac{53605785}{60174703}e + \frac{108838248}{60174703}$ |
| 41 | $[41, 41, 2w^{5} - 2w^{4} - 10w^{3} + 7w^{2} + 11w - 4]$ | $\phantom{-}\frac{248840}{180524109}e^{8} - \frac{78968}{180524109}e^{7} - \frac{13226206}{180524109}e^{6} + \frac{526226}{60174703}e^{5} + \frac{73775403}{60174703}e^{4} + \frac{16974346}{180524109}e^{3} - \frac{1181215646}{180524109}e^{2} - \frac{37909428}{60174703}e + \frac{312835420}{60174703}$ |
| 49 | $[49, 7, -2w^{5} + 3w^{4} + 10w^{3} - 12w^{2} - 11w + 6]$ | $...$ |
| 59 | $[59, 59, w^{5} - 2w^{4} - 5w^{3} + 8w^{2} + 7w - 5]$ | $-\frac{1179646}{180524109}e^{8} + \frac{2467105}{180524109}e^{7} + \frac{64919489}{180524109}e^{6} - \frac{32839239}{60174703}e^{5} - \frac{392337391}{60174703}e^{4} + \frac{1125683176}{180524109}e^{3} + \frac{7694079037}{180524109}e^{2} - \frac{1455554865}{60174703}e - \frac{4409199200}{60174703}$ |
| 59 | $[59, 59, w^{5} - w^{4} - 4w^{3} + 3w^{2} + 3w - 3]$ | $...$ |
| 59 | $[59, 59, 2w^{5} - 3w^{4} - 9w^{3} + 11w^{2} + 9w - 4]$ | $...$ |
| 61 | $[61, 61, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 7w + 1]$ | $-\frac{341617}{180524109}e^{8} + \frac{1156336}{180524109}e^{7} + \frac{15882725}{180524109}e^{6} - \frac{13892378}{60174703}e^{5} - \frac{76384789}{60174703}e^{4} + \frac{342323695}{180524109}e^{3} + \frac{1166083096}{180524109}e^{2} - \frac{50933480}{60174703}e - \frac{748130291}{60174703}$ |
| 64 | $[64, 2, -2]$ | $-1$ |
| 71 | $[71, 71, -2w^{5} + 2w^{4} + 10w^{3} - 8w^{2} - 11w + 6]$ | $...$ |
| 79 | $[79, 79, -3w^{5} + 4w^{4} + 13w^{3} - 14w^{2} - 9w + 5]$ | $...$ |
| 79 | $[79, 79, -w^{4} - w^{3} + 5w^{2} + 4w - 3]$ | $...$ |
| 79 | $[79, 79, -2w^{5} + 2w^{4} + 9w^{3} - 7w^{2} - 8w + 4]$ | $-\frac{1770103}{180524109}e^{8} + \frac{3702409}{180524109}e^{7} + \frac{94028420}{180524109}e^{6} - \frac{47257843}{60174703}e^{5} - \frac{542497583}{60174703}e^{4} + \frac{1451032525}{180524109}e^{3} + \frac{10041377779}{180524109}e^{2} - \frac{1468578917}{60174703}e - \frac{5470164911}{60174703}$ |
| 81 | $[81, 3, 3w^{5} - 5w^{4} - 14w^{3} + 19w^{2} + 13w - 8]$ | $...$ |
| 89 | $[89, 89, 2w^{5} - 2w^{4} - 9w^{3} + 6w^{2} + 8w - 1]$ | $-\frac{1791701}{180524109}e^{8} + \frac{3680165}{180524109}e^{7} + \frac{96211948}{180524109}e^{6} - \frac{50170028}{60174703}e^{5} - \frac{565426824}{60174703}e^{4} + \frac{1677864065}{180524109}e^{3} + \frac{11027738732}{180524109}e^{2} - \frac{1603381620}{60174703}e - \frac{6916085534}{60174703}$ |
| 101 | $[101, 101, -w^{4} - w^{3} + 5w^{2} + 3w - 3]$ | $-\frac{31234}{60174703}e^{8} + \frac{170799}{60174703}e^{7} + \frac{1442149}{60174703}e^{6} - \frac{8632295}{60174703}e^{5} - \frac{32048068}{60174703}e^{4} + \frac{137889264}{60174703}e^{3} + \frac{439793583}{60174703}e^{2} - \frac{637100091}{60174703}e - \frac{1556910468}{60174703}$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $64$ | $[64, 2, -2]$ | $1$ |