Properties

Label 8.21
Level 8
Weight 21
Dimension 19
Nonzero newspaces 1
Newforms 2
Sturm bound 84
Trace bound 0

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 21 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 2 \)
Sturm bound: \(84\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{21}(\Gamma_1(8))\).

Total New Old
Modular forms 43 21 22
Cusp forms 37 19 18
Eisenstein series 6 2 4

Trace form

\( 19q + 626q^{2} - 2q^{3} + 1773556q^{4} + 25323676q^{6} - 2031549544q^{8} + 19758444937q^{9} + O(q^{10}) \) \( 19q + 626q^{2} - 2q^{3} + 1773556q^{4} + 25323676q^{6} - 2031549544q^{8} + 19758444937q^{9} + 742754160q^{10} - 14520628706q^{11} - 92518091912q^{12} - 431248136928q^{14} + 140976757264q^{16} + 990389375398q^{17} + 5272759222774q^{18} - 1375336086082q^{19} - 32520172742880q^{20} - 109675699217572q^{22} + 144938556063376q^{24} - 300360045368285q^{25} + 154289718058128q^{26} - 514588541331140q^{27} - 394619539621440q^{28} + 223250517248160q^{30} - 1707914682142624q^{32} - 379273727638900q^{33} - 4373483391631324q^{34} + 3615863153468160q^{35} + 11585741011529500q^{36} + 11866377694661788q^{38} + 11813880412973760q^{40} - 8427241614192506q^{41} + 38127588900300480q^{42} - 24717352370364898q^{43} - 11262977142561032q^{44} - 21739818881100192q^{46} + 153956946591726688q^{48} - 173173121721250637q^{49} + 139361869584456530q^{50} - 417243550710750724q^{51} - 44583718369992480q^{52} + 131060624290419256q^{54} - 505574909383001472q^{56} - 638353406270838580q^{57} - 677523738697093680q^{58} - 80800002484130978q^{59} + 1631640690429240000q^{60} + 1780090172849178240q^{62} + 1328363317618417216q^{64} + 1575343920200472960q^{65} + 3043614561170466056q^{66} - 1808783156240800642q^{67} - 2362666796221870232q^{68} - 6151558949299572480q^{70} + 4959295908955144264q^{72} + 3866104143546483398q^{73} - 5642095430673385488q^{74} + 24308156015351409310q^{75} - 9480723535297927816q^{76} - 14599907290310144160q^{78} - 22104885212702947200q^{80} + 13599596957313525631q^{81} - 15707154812006670172q^{82} - 77448386448570160322q^{83} + 17095266896298568320q^{84} + 36403346004507897820q^{86} - 13164074256796170352q^{88} + 33127276190960144518q^{89} - 33204348719592139440q^{90} + 161045136122144660736q^{91} - 932896292396925120q^{92} - 107259275077774974528q^{94} + 197187886676221266496q^{96} + 77267514659308382822q^{97} + 236544665851892453426q^{98} - 342412845288286744966q^{99} + O(q^{100}) \)

Decomposition of \(S_{21}^{\mathrm{new}}(\Gamma_1(8))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
8.21.c \(\chi_{8}(7, \cdot)\) None 0 1
8.21.d \(\chi_{8}(3, \cdot)\) 8.21.d.a 1 1
8.21.d.b 18

Decomposition of \(S_{21}^{\mathrm{old}}(\Gamma_1(8))\) into lower level spaces

\( S_{21}^{\mathrm{old}}(\Gamma_1(8)) \cong \) \(S_{21}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)