Properties

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

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

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

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

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