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: | $[41, 41, 2w^{5} + w^{4} - 10w^{3} - 3w^{2} + 7w + 2]$ |
| Dimension: | $16$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $22$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{16} - 96x^{14} + 3448x^{12} - 58208x^{10} + 479696x^{8} - 1909120x^{6} + 3386368x^{4} - 2088960x^{2} + 65536\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 9 | $[9, 3, -w^{2} + 2]$ | $\phantom{-}e$ |
| 11 | $[11, 11, w^{4} + w^{3} - 4w^{2} - 3w + 2]$ | $...$ |
| 11 | $[11, 11, -w^{5} + 6w^{3} - w^{2} - 7w + 1]$ | $-\frac{3851747}{1667182936064}e^{15} + \frac{42555457}{208397867008}e^{13} - \frac{1329560893}{208397867008}e^{11} + \frac{4320840951}{52099466752}e^{9} - \frac{39190505639}{104198933504}e^{7} + \frac{610694257}{6512433344}e^{5} + \frac{661043363}{814054168}e^{3} + \frac{662219259}{203513542}e$ |
| 19 | $[19, 19, -w^{5} - w^{4} + 5w^{3} + 4w^{2} - 5w - 3]$ | $...$ |
| 29 | $[29, 29, -2w^{4} - w^{3} + 9w^{2} + 2w - 5]$ | $...$ |
| 31 | $[31, 31, -w^{5} + w^{4} + 6w^{3} - 5w^{2} - 7w + 1]$ | $...$ |
| 41 | $[41, 41, 2w^{5} + w^{4} - 10w^{3} - 3w^{2} + 7w + 2]$ | $-1$ |
| 41 | $[41, 41, w^{5} - w^{4} - 6w^{3} + 5w^{2} + 6w - 3]$ | $...$ |
| 41 | $[41, 41, w^{5} - 6w^{3} + w^{2} + 7w - 2]$ | $...$ |
| 59 | $[59, 59, -w^{5} - w^{4} + 4w^{3} + 4w^{2} - 2w - 3]$ | $\phantom{-}\frac{1567145}{208397867008}e^{14} - \frac{19186849}{26049733376}e^{12} + \frac{710995559}{26049733376}e^{10} - \frac{3134685405}{6512433344}e^{8} + \frac{53668413461}{13024866688}e^{6} - \frac{6159171537}{407027084}e^{4} + \frac{2777246541}{203513542}e^{2} + \frac{834233552}{101756771}$ |
| 59 | $[59, 59, w^{5} - w^{4} - 5w^{3} + 6w^{2} + 2w - 4]$ | $-\frac{5453239}{208397867008}e^{14} + \frac{65181609}{26049733376}e^{12} - \frac{2326925689}{26049733376}e^{10} + \frac{9712273771}{6512433344}e^{8} - \frac{155903347931}{13024866688}e^{6} + \frac{35826133615}{814054168}e^{4} - \frac{12074799869}{203513542}e^{2} + \frac{1349835112}{101756771}$ |
| 59 | $[59, 59, -w^{5} + 4w^{3} - w^{2} - w + 1]$ | $-\frac{3755105}{208397867008}e^{14} + \frac{90402565}{52099466752}e^{12} - \frac{1621949835}{26049733376}e^{10} + \frac{844454897}{814054168}e^{8} - \frac{106128284989}{13024866688}e^{6} + \frac{91193743531}{3256216672}e^{4} - \frac{12953833917}{407027084}e^{2} + \frac{149692968}{101756771}$ |
| 61 | $[61, 61, -w^{4} + 4w^{2} - 2w - 2]$ | $...$ |
| 64 | $[64, 2, -2]$ | $-\frac{13960925}{208397867008}e^{14} + \frac{327743827}{52099466752}e^{12} - \frac{5672683531}{26049733376}e^{10} + \frac{11209450669}{3256216672}e^{8} - \frac{325664106641}{13024866688}e^{6} + \frac{254227938521}{3256216672}e^{4} - \frac{34531082593}{407027084}e^{2} + \frac{1133901503}{101756771}$ |
| 71 | $[71, 71, 2w^{5} + w^{4} - 10w^{3} - 3w^{2} + 9w + 3]$ | $-\frac{225207}{13024866688}e^{14} + \frac{85606157}{52099466752}e^{12} - \frac{94523085}{1628108336}e^{10} + \frac{6199877527}{6512433344}e^{8} - \frac{12033428065}{1628108336}e^{6} + \frac{83043500753}{3256216672}e^{4} - \frac{11480118351}{407027084}e^{2} - \frac{53572532}{101756771}$ |
| 81 | $[81, 3, w^{5} + 2w^{4} - 4w^{3} - 8w^{2} + 2w + 3]$ | $...$ |
| 89 | $[89, 89, -w^{5} + 6w^{3} - 7w]$ | $-\frac{450417}{52099466752}e^{14} + \frac{10933565}{13024866688}e^{12} - \frac{197123557}{6512433344}e^{10} + \frac{101884215}{203513542}e^{8} - \frac{12220984041}{3256216672}e^{6} + \frac{8643441751}{814054168}e^{4} - \frac{341181508}{101756771}e^{2} + \frac{76399034}{101756771}$ |
| 89 | $[89, 89, w^{5} + w^{4} - 5w^{3} - 4w^{2} + 6w + 2]$ | $...$ |
| 101 | $[101, 101, w^{5} - 4w^{3} + 2w^{2} + w - 3]$ | $\phantom{-}\frac{48259}{208397867008}e^{14} - \frac{1022801}{52099466752}e^{12} + \frac{26062101}{26049733376}e^{10} - \frac{63025341}{1628108336}e^{8} + \frac{10751987247}{13024866688}e^{6} - \frac{25687266703}{3256216672}e^{4} + \frac{11304755355}{407027084}e^{2} - \frac{1327008610}{101756771}$ |
| 101 | $[101, 101, w^{5} + 2w^{4} - 4w^{3} - 8w^{2} + 3w + 4]$ | $...$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $41$ | $[41, 41, 2w^{5} + w^{4} - 10w^{3} - 3w^{2} + 7w + 2]$ | $1$ |