# Properties

 Label 576.8 Level 576 Weight 8 Dimension 28629 Nonzero newspaces 16 Sturm bound 147456 Trace bound 25

## Defining parameters

 Level: $$N$$ = $$576 = 2^{6} \cdot 3^{2}$$ Weight: $$k$$ = $$8$$ Nonzero newspaces: $$16$$ Sturm bound: $$147456$$ Trace bound: $$25$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{8}(\Gamma_1(576))$$.

Total New Old
Modular forms 65088 28827 36261
Cusp forms 63936 28629 35307
Eisenstein series 1152 198 954

## Trace form

 $$28629q - 24q^{2} - 24q^{3} - 24q^{4} - 24q^{5} - 32q^{6} - 20q^{7} - 24q^{8} - 40q^{9} + O(q^{10})$$ $$28629q - 24q^{2} - 24q^{3} - 24q^{4} - 24q^{5} - 32q^{6} - 20q^{7} - 24q^{8} - 40q^{9} - 72q^{10} - 1222q^{11} - 32q^{12} - 7088q^{13} - 24q^{14} - 24q^{15} - 24q^{16} - 5858q^{17} - 32q^{18} - 60638q^{19} - 24q^{20} - 32q^{21} + 274432q^{22} - 12q^{23} - 32q^{24} - 13659q^{25} + 727936q^{26} - 24q^{27} + 390848q^{28} - 103400q^{29} - 32q^{30} - 357500q^{31} - 1071344q^{32} + 8724q^{33} + 403136q^{34} + 876984q^{35} - 32q^{36} - 1070992q^{37} + 1244896q^{38} - 283968q^{39} - 2686384q^{40} + 1842082q^{41} - 32q^{42} + 2441618q^{43} + 3370448q^{44} - 2210960q^{45} - 72q^{46} - 6229404q^{47} - 32q^{48} - 2242787q^{49} - 2317440q^{50} + 2234416q^{51} + 10204920q^{52} + 11597952q^{53} - 32q^{54} + 16763976q^{55} - 10737296q^{56} - 2745416q^{57} - 10358160q^{58} - 7251694q^{59} - 32q^{60} - 922320q^{61} + 10344408q^{62} + 3294148q^{63} + 22837080q^{64} - 291580q^{65} - 32q^{66} + 9445798q^{67} - 8750088q^{68} - 17528q^{69} - 35990328q^{70} + 24697384q^{71} - 32q^{72} - 2836570q^{73} + 4214368q^{74} - 303776q^{75} + 38942888q^{76} - 2194548q^{77} - 78695216q^{78} + 9598892q^{79} + 108869520q^{80} + 54057480q^{81} + 147943848q^{82} + 14600542q^{83} - 34113664q^{84} - 55819968q^{85} - 208606656q^{86} - 40789136q^{87} - 157553544q^{88} - 100935502q^{89} - 63468032q^{90} + 4226276q^{91} + 163322304q^{92} + 57999040q^{93} + 224074632q^{94} + 114644568q^{95} + 225737936q^{96} + 144734470q^{97} + 188307072q^{98} + 9729704q^{99} + O(q^{100})$$

## Decomposition of $$S_{8}^{\mathrm{new}}(\Gamma_1(576))$$

We only show spaces with even 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
576.8.a $$\chi_{576}(1, \cdot)$$ 576.8.a.a 1 1
576.8.a.b 1
576.8.a.c 1
576.8.a.d 1
576.8.a.e 1
576.8.a.f 1
576.8.a.g 1
576.8.a.h 1
576.8.a.i 1
576.8.a.j 1
576.8.a.k 1
576.8.a.l 1
576.8.a.m 1
576.8.a.n 1
576.8.a.o 1
576.8.a.p 1
576.8.a.q 1
576.8.a.r 1
576.8.a.s 1
576.8.a.t 1
576.8.a.u 1
576.8.a.v 1
576.8.a.w 1
576.8.a.x 1
576.8.a.y 1
576.8.a.z 1
576.8.a.ba 1
576.8.a.bb 2
576.8.a.bc 2
576.8.a.bd 2
576.8.a.be 2
576.8.a.bf 2
576.8.a.bg 2
576.8.a.bh 2
576.8.a.bi 2
576.8.a.bj 2
576.8.a.bk 2
576.8.a.bl 2
576.8.a.bm 2
576.8.a.bn 2
576.8.a.bo 2
576.8.a.bp 2
576.8.a.bq 2
576.8.a.br 2
576.8.a.bs 4
576.8.a.bt 4
576.8.c $$\chi_{576}(575, \cdot)$$ 576.8.c.a 2 1
576.8.c.b 2
576.8.c.c 4
576.8.c.d 8
576.8.c.e 12
576.8.c.f 12
576.8.c.g 16
576.8.d $$\chi_{576}(289, \cdot)$$ 576.8.d.a 2 1
576.8.d.b 4
576.8.d.c 4
576.8.d.d 4
576.8.d.e 4
576.8.d.f 8
576.8.d.g 8
576.8.d.h 8
576.8.d.i 12
576.8.d.j 16
576.8.f $$\chi_{576}(287, \cdot)$$ 576.8.f.a 16 1
576.8.f.b 40
576.8.i $$\chi_{576}(193, \cdot)$$ n/a 332 2
576.8.k $$\chi_{576}(145, \cdot)$$ n/a 138 2
576.8.l $$\chi_{576}(143, \cdot)$$ n/a 112 2
576.8.p $$\chi_{576}(95, \cdot)$$ n/a 336 2
576.8.r $$\chi_{576}(97, \cdot)$$ n/a 336 2
576.8.s $$\chi_{576}(191, \cdot)$$ n/a 332 2
576.8.v $$\chi_{576}(73, \cdot)$$ None 0 4
576.8.w $$\chi_{576}(71, \cdot)$$ None 0 4
576.8.y $$\chi_{576}(47, \cdot)$$ n/a 664 4
576.8.bb $$\chi_{576}(49, \cdot)$$ n/a 664 4
576.8.bd $$\chi_{576}(37, \cdot)$$ n/a 2232 8
576.8.be $$\chi_{576}(35, \cdot)$$ n/a 1792 8
576.8.bg $$\chi_{576}(25, \cdot)$$ None 0 8
576.8.bj $$\chi_{576}(23, \cdot)$$ None 0 8
576.8.bl $$\chi_{576}(11, \cdot)$$ n/a 10720 16
576.8.bm $$\chi_{576}(13, \cdot)$$ n/a 10720 16

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{8}^{\mathrm{old}}(\Gamma_1(576))$$ into lower level spaces

$$S_{8}^{\mathrm{old}}(\Gamma_1(576)) \cong$$ $$S_{8}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 18}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 14}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 12}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 12}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 7}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 10}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 9}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 6}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 8}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 6}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 5}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 6}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 3}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 4}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(96))$$$$^{\oplus 4}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(144))$$$$^{\oplus 3}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(192))$$$$^{\oplus 2}$$$$\oplus$$$$S_{8}^{\mathrm{new}}(\Gamma_1(288))$$$$^{\oplus 2}$$