Properties

Base field 6.6.485125.1
Weight [2, 2, 2, 2, 2, 2]
Level norm 61
Level $[61, 61, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 7w + 1]$
Label 6.6.485125.1-61.1-b
Dimension 8
CM no
Base change no

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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 $[61, 61, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 7w + 1]$
Label 6.6.485125.1-61.1-b
Dimension 8
Is CM no
Is base change no
Parent newspace dimension 12

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} - 6x^{7} - 32x^{6} + 246x^{5} - 117x^{4} - 1204x^{3} + 1284x^{2} - 368x + 16\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, -w^{2} + 2]$ $\phantom{-}e$
19 $[19, 19, -w^{3} + 4w]$ $-\frac{5}{15438}e^{7} - \frac{793}{30876}e^{6} + \frac{730}{7719}e^{5} + \frac{7621}{7719}e^{4} - \frac{53185}{15438}e^{3} - \frac{122719}{30876}e^{2} + \frac{99404}{7719}e - \frac{40151}{7719}$
19 $[19, 19, w^{3} - 3w - 1]$ $-\frac{2093}{30876}e^{7} + \frac{6167}{15438}e^{6} + \frac{35413}{15438}e^{5} - \frac{255611}{15438}e^{4} + \frac{90983}{30876}e^{3} + \frac{674998}{7719}e^{2} - \frac{459044}{7719}e + \frac{54104}{7719}$
29 $[29, 29, w^{5} - w^{4} - 6w^{3} + 4w^{2} + 8w - 3]$ $-\frac{33}{20584}e^{7} + \frac{91}{2573}e^{6} - \frac{82}{2573}e^{5} - \frac{14541}{10292}e^{4} + \frac{76097}{20584}e^{3} + \frac{70123}{10292}e^{2} - \frac{47484}{2573}e + \frac{14929}{2573}$
29 $[29, 29, w^{4} - w^{3} - 4w^{2} + 2w + 2]$ $\phantom{-}\frac{1823}{15438}e^{7} - \frac{5294}{7719}e^{6} - \frac{61457}{15438}e^{5} + \frac{219443}{7719}e^{4} - \frac{41893}{7719}e^{3} - \frac{1150283}{7719}e^{2} + \frac{805414}{7719}e - \frac{68728}{7719}$
31 $[31, 31, -w^{4} + 4w^{2} + w - 3]$ $\phantom{-}\frac{4}{93}e^{7} - \frac{89}{372}e^{6} - \frac{145}{93}e^{5} + \frac{938}{93}e^{4} + \frac{233}{93}e^{3} - \frac{21623}{372}e^{2} + \frac{1174}{93}e + \frac{890}{93}$
41 $[41, 41, 2w^{5} - 2w^{4} - 10w^{3} + 7w^{2} + 11w - 4]$ $-\frac{1685}{15438}e^{7} + \frac{9181}{15438}e^{6} + \frac{29878}{7719}e^{5} - \frac{382531}{15438}e^{4} - \frac{46141}{15438}e^{3} + \frac{1025222}{7719}e^{2} - \frac{394981}{7719}e - \frac{30356}{7719}$
49 $[49, 7, -2w^{5} + 3w^{4} + 10w^{3} - 12w^{2} - 11w + 6]$ $\phantom{-}\frac{470}{2573}e^{7} - \frac{5221}{5146}e^{6} - \frac{16309}{2573}e^{5} + \frac{108479}{2573}e^{4} - \frac{2522}{2573}e^{3} - \frac{1146731}{5146}e^{2} + \frac{321372}{2573}e - \frac{11086}{2573}$
59 $[59, 59, w^{5} - 2w^{4} - 5w^{3} + 8w^{2} + 7w - 5]$ $-\frac{19927}{61752}e^{7} + \frac{54739}{30876}e^{6} + \frac{173317}{15438}e^{5} - \frac{2275549}{30876}e^{4} + \frac{15679}{61752}e^{3} + \frac{2998978}{7719}e^{2} - \frac{3338779}{15438}e + \frac{104633}{7719}$
59 $[59, 59, w^{5} - w^{4} - 4w^{3} + 3w^{2} + 3w - 3]$ $\phantom{-}\frac{97}{1992}e^{7} - \frac{125}{498}e^{6} - \frac{428}{249}e^{5} + \frac{10417}{996}e^{4} + \frac{2423}{1992}e^{3} - \frac{54541}{996}e^{2} + \frac{6080}{249}e + \frac{973}{249}$
59 $[59, 59, 2w^{5} - 3w^{4} - 9w^{3} + 11w^{2} + 9w - 4]$ $\phantom{-}\frac{16}{249}e^{7} - \frac{353}{996}e^{6} - \frac{1127}{498}e^{5} + \frac{3665}{249}e^{4} + \frac{499}{498}e^{3} - \frac{77483}{996}e^{2} + \frac{8824}{249}e - \frac{151}{249}$
61 $[61, 61, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 7w + 1]$ $-1$
64 $[64, 2, -2]$ $-\frac{2567}{7719}e^{7} + \frac{54907}{30876}e^{6} + \frac{179179}{15438}e^{5} - \frac{1141427}{15438}e^{4} - \frac{10795}{7719}e^{3} + \frac{11913679}{30876}e^{2} - \frac{3478801}{15438}e + \frac{140618}{7719}$
71 $[71, 71, -2w^{5} + 2w^{4} + 10w^{3} - 8w^{2} - 11w + 6]$ $-\frac{3043}{10292}e^{7} + \frac{8381}{5146}e^{6} + \frac{26591}{2573}e^{5} - \frac{174424}{2573}e^{4} - \frac{15489}{10292}e^{3} + \frac{1859429}{5146}e^{2} - \frac{486877}{2573}e + \frac{4058}{2573}$
79 $[79, 79, -3w^{5} + 4w^{4} + 13w^{3} - 14w^{2} - 9w + 5]$ $\phantom{-}\frac{3547}{30876}e^{7} - \frac{4748}{7719}e^{6} - \frac{62441}{15438}e^{5} + \frac{395263}{15438}e^{4} + \frac{60719}{30876}e^{3} - \frac{2090197}{15438}e^{2} + \frac{512791}{7719}e + \frac{20846}{7719}$
79 $[79, 79, -w^{4} - w^{3} + 5w^{2} + 4w - 3]$ $\phantom{-}\frac{20321}{61752}e^{7} - \frac{53783}{30876}e^{6} - \frac{89461}{7719}e^{5} + \frac{2240045}{30876}e^{4} + \frac{346675}{61752}e^{3} - \frac{2949776}{7719}e^{2} + \frac{3115031}{15438}e - \frac{49279}{7719}$
79 $[79, 79, -2w^{5} + 2w^{4} + 9w^{3} - 7w^{2} - 8w + 4]$ $\phantom{-}\frac{3547}{30876}e^{7} - \frac{4748}{7719}e^{6} - \frac{62441}{15438}e^{5} + \frac{395263}{15438}e^{4} + \frac{60719}{30876}e^{3} - \frac{2090197}{15438}e^{2} + \frac{512791}{7719}e + \frac{20846}{7719}$
81 $[81, 3, 3w^{5} - 5w^{4} - 14w^{3} + 19w^{2} + 13w - 8]$ $-\frac{344}{7719}e^{7} + \frac{2053}{7719}e^{6} + \frac{23359}{15438}e^{5} - \frac{170543}{15438}e^{4} + \frac{22513}{15438}e^{3} + \frac{910817}{15438}e^{2} - \frac{220841}{7719}e + \frac{5114}{7719}$
89 $[89, 89, 2w^{5} - 2w^{4} - 9w^{3} + 6w^{2} + 8w - 1]$ $\phantom{-}\frac{4643}{15438}e^{7} - \frac{26251}{15438}e^{6} - \frac{159311}{15438}e^{5} + \frac{544880}{7719}e^{4} - \frac{49459}{7719}e^{3} - \frac{5740759}{15438}e^{2} + \frac{1777249}{7719}e - \frac{101986}{7719}$
101 $[101, 101, -w^{4} - w^{3} + 5w^{2} + 3w - 3]$ $\phantom{-}\frac{7745}{61752}e^{7} - \frac{11449}{15438}e^{6} - \frac{31825}{7719}e^{5} + \frac{946859}{30876}e^{4} - \frac{626561}{61752}e^{3} - \frac{4891007}{30876}e^{2} + \frac{1050238}{7719}e - \frac{123025}{7719}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
61 $[61, 61, -w^{5} + w^{4} + 5w^{3} - 3w^{2} - 7w + 1]$ $1$