Base field 6.6.1292517.1
Generator \(w\), with minimal polynomial \(x^{6} - 6x^{4} - x^{3} + 6x^{2} - 1\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2, 2, 2, 2]$ |
Level: | $[37, 37, w^{5} - 5w^{3} - 2w^{2} + 2w + 3]$ |
Dimension: | $7$ |
CM: | no |
Base change: | no |
Newspace dimension: | $30$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{7} + 3x^{6} - 37x^{5} - 65x^{4} + 507x^{3} + 185x^{2} - 2531x + 2137\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
9 | $[9, 3, -w^{5} + 6w^{3} + w^{2} - 5w - 1]$ | $\phantom{-}e$ |
17 | $[17, 17, w^{5} + w^{4} - 6w^{3} - 6w^{2} + 5w + 1]$ | $-\frac{22}{1975}e^{6} - \frac{61}{3950}e^{5} + \frac{751}{1975}e^{4} + \frac{1071}{1975}e^{3} - \frac{6643}{1975}e^{2} - \frac{18391}{3950}e + \frac{14704}{1975}$ |
17 | $[17, 17, w^{5} - 5w^{3} - 2w^{2} + w + 2]$ | $\phantom{-}\frac{223}{7900}e^{6} + \frac{581}{3950}e^{5} - \frac{5009}{7900}e^{4} - \frac{11757}{3950}e^{3} + \frac{43187}{7900}e^{2} + \frac{29418}{1975}e - \frac{158561}{7900}$ |
17 | $[17, 17, w^{4} - 5w^{2} - 2w + 1]$ | $-\frac{69}{3950}e^{6} + \frac{39}{3950}e^{5} + \frac{1727}{3950}e^{4} - \frac{2854}{1975}e^{3} - \frac{6561}{3950}e^{2} + \frac{68159}{3950}e - \frac{94467}{3950}$ |
17 | $[17, 17, -w^{5} - w^{4} + 5w^{3} + 7w^{2} - 3]$ | $\phantom{-}\frac{3}{1975}e^{6} - \frac{261}{3950}e^{5} - \frac{923}{3950}e^{4} + \frac{2996}{1975}e^{3} + \frac{4407}{1975}e^{2} - \frac{41391}{3950}e + \frac{14483}{3950}$ |
19 | $[19, 19, 2w^{5} - 11w^{3} - 2w^{2} + 7w]$ | $\phantom{-}\frac{101}{7900}e^{6} + \frac{136}{1975}e^{5} - \frac{1383}{7900}e^{4} - \frac{4209}{3950}e^{3} + \frac{6169}{7900}e^{2} + \frac{16507}{3950}e - \frac{50807}{7900}$ |
19 | $[19, 19, w^{5} - 5w^{3} - w^{2} + 2w - 1]$ | $\phantom{-}\frac{21}{1580}e^{6} + \frac{37}{790}e^{5} - \frac{663}{1580}e^{4} - \frac{969}{790}e^{3} + \frac{5569}{1580}e^{2} + \frac{2641}{395}e - \frac{12707}{1580}$ |
37 | $[37, 37, w^{5} - 5w^{3} - 2w^{2} + 2w + 3]$ | $\phantom{-}1$ |
37 | $[37, 37, -2w^{5} - w^{4} + 11w^{3} + 8w^{2} - 6w - 2]$ | $\phantom{-}\frac{31}{1580}e^{6} + \frac{17}{790}e^{5} - \frac{753}{1580}e^{4} + \frac{601}{790}e^{3} + \frac{6039}{1580}e^{2} - \frac{4829}{395}e + \frac{2083}{1580}$ |
53 | $[53, 53, -w^{5} - w^{4} + 6w^{3} + 5w^{2} - 4w - 1]$ | $-\frac{291}{7900}e^{6} - \frac{1077}{3950}e^{5} + \frac{6253}{7900}e^{4} + \frac{26519}{3950}e^{3} - \frac{64079}{7900}e^{2} - \frac{84956}{1975}e + \frac{382837}{7900}$ |
53 | $[53, 53, w^{3} - 4w + 1]$ | $\phantom{-}\frac{67}{7900}e^{6} + \frac{12}{1975}e^{5} - \frac{761}{7900}e^{4} + \frac{1197}{3950}e^{3} - \frac{12177}{7900}e^{2} - \frac{19281}{3950}e + \frac{108731}{7900}$ |
64 | $[64, 2, -2]$ | $-\frac{3}{79}e^{6} - \frac{55}{158}e^{5} + \frac{133}{158}e^{4} + \frac{717}{79}e^{3} - \frac{852}{79}e^{2} - \frac{9959}{158}e + \frac{13799}{158}$ |
73 | $[73, 73, -3w^{5} + 17w^{3} + 3w^{2} - 12w + 1]$ | $-\frac{651}{7900}e^{6} - \frac{1147}{3950}e^{5} + \frac{14233}{7900}e^{4} + \frac{16609}{3950}e^{3} - \frac{87319}{7900}e^{2} - \frac{15116}{1975}e + \frac{27357}{7900}$ |
73 | $[73, 73, w^{3} - w^{2} - 4w + 1]$ | $-\frac{42}{395}e^{6} - \frac{148}{395}e^{5} + \frac{2257}{790}e^{4} + \frac{2691}{395}e^{3} - \frac{10348}{395}e^{2} - \frac{10463}{395}e + \frac{54383}{790}$ |
73 | $[73, 73, 2w^{5} + w^{4} - 11w^{3} - 7w^{2} + 5w + 3]$ | $\phantom{-}\frac{101}{7900}e^{6} + \frac{136}{1975}e^{5} - \frac{1383}{7900}e^{4} - \frac{4209}{3950}e^{3} - \frac{1731}{7900}e^{2} + \frac{8607}{3950}e - \frac{3407}{7900}$ |
73 | $[73, 73, 2w^{5} + w^{4} - 11w^{3} - 8w^{2} + 5w + 4]$ | $-\frac{51}{1975}e^{6} + \frac{487}{3950}e^{5} + \frac{2908}{1975}e^{4} - \frac{5507}{1975}e^{3} - \frac{29494}{1975}e^{2} + \frac{83497}{3950}e + \frac{8232}{1975}$ |
107 | $[107, 107, -w^{4} + w^{3} + 5w^{2} - 2w - 3]$ | $\phantom{-}\frac{823}{7900}e^{6} + \frac{678}{1975}e^{5} - \frac{22259}{7900}e^{4} - \frac{24207}{3950}e^{3} + \frac{189887}{7900}e^{2} + \frac{76861}{3950}e - \frac{420611}{7900}$ |
107 | $[107, 107, -3w^{5} - w^{4} + 17w^{3} + 8w^{2} - 11w - 2]$ | $-\frac{49}{3950}e^{6} - \frac{831}{3950}e^{5} - \frac{33}{3950}e^{4} + \frac{9766}{1975}e^{3} - \frac{881}{3950}e^{2} - \frac{117211}{3950}e + \frac{94693}{3950}$ |
109 | $[109, 109, w^{4} - 6w^{2} + 5]$ | $\phantom{-}\frac{317}{7900}e^{6} + \frac{1499}{3950}e^{5} - \frac{6961}{7900}e^{4} - \frac{38553}{3950}e^{3} + \frac{86473}{7900}e^{2} + \frac{128497}{1975}e - \frac{631469}{7900}$ |
109 | $[109, 109, -w^{5} + 6w^{3} + w^{2} - 7w + 1]$ | $-\frac{329}{7900}e^{6} - \frac{619}{1975}e^{5} + \frac{907}{7900}e^{4} + \frac{16761}{3950}e^{3} + \frac{38099}{7900}e^{2} - \frac{29953}{3950}e - \frac{132197}{7900}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$37$ | $[37, 37, w^{5} - 5w^{3} - 2w^{2} + 2w + 3]$ | $-1$ |