## Defining parameters

 Level: $$N$$ = $$576 = 2^{6} \cdot 3^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$16$$ Newform subspaces: $$63$$ Sturm bound: $$36864$$ Trace bound: $$25$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(576))$$.

Total New Old
Modular forms 9792 4203 5589
Cusp forms 8641 4005 4636
Eisenstein series 1151 198 953

## Trace form

 $$4005q - 24q^{2} - 24q^{3} - 24q^{4} - 24q^{5} - 32q^{6} - 20q^{7} - 24q^{8} - 40q^{9} + O(q^{10})$$ $$4005q - 24q^{2} - 24q^{3} - 24q^{4} - 24q^{5} - 32q^{6} - 20q^{7} - 24q^{8} - 40q^{9} - 72q^{10} - 22q^{11} - 32q^{12} - 32q^{13} - 24q^{14} - 24q^{15} - 24q^{16} - 50q^{17} - 32q^{18} - 62q^{19} - 24q^{20} - 32q^{21} - 16q^{22} - 12q^{23} - 32q^{24} - 19q^{25} + 16q^{26} - 24q^{27} - 32q^{28} - 8q^{29} - 32q^{30} + 4q^{31} + 16q^{32} - 12q^{33} + 16q^{34} + 24q^{35} - 32q^{36} - 32q^{37} + 16q^{38} + 16q^{40} + 34q^{41} - 32q^{42} + 34q^{43} - 16q^{44} + 16q^{45} - 72q^{46} + 36q^{47} - 32q^{48} + 13q^{49} - 48q^{50} + 16q^{51} - 72q^{52} + 48q^{53} - 32q^{54} + 72q^{55} - 80q^{56} - 8q^{57} - 96q^{58} + 98q^{59} - 32q^{60} - 120q^{62} + 4q^{63} - 168q^{64} - 28q^{65} - 32q^{66} + 70q^{67} - 72q^{68} - 56q^{69} - 120q^{70} + 40q^{71} - 32q^{72} - 90q^{73} - 80q^{74} - 32q^{75} - 88q^{76} - 132q^{77} - 80q^{78} - 20q^{79} - 240q^{80} - 120q^{81} - 312q^{82} - 98q^{83} - 256q^{84} - 144q^{85} - 336q^{86} - 80q^{87} - 264q^{88} - 238q^{89} - 320q^{90} - 156q^{91} - 480q^{92} - 128q^{93} - 312q^{94} - 168q^{95} - 304q^{96} - 234q^{97} - 432q^{98} - 88q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(576))$$

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
576.2.a $$\chi_{576}(1, \cdot)$$ 576.2.a.a 1 1
576.2.a.b 1
576.2.a.c 1
576.2.a.d 1
576.2.a.e 1
576.2.a.f 1
576.2.a.g 1
576.2.a.h 1
576.2.a.i 1
576.2.c $$\chi_{576}(575, \cdot)$$ 576.2.c.a 2 1
576.2.c.b 2
576.2.c.c 4
576.2.d $$\chi_{576}(289, \cdot)$$ 576.2.d.a 2 1
576.2.d.b 4
576.2.d.c 4
576.2.f $$\chi_{576}(287, \cdot)$$ 576.2.f.a 8 1
576.2.i $$\chi_{576}(193, \cdot)$$ 576.2.i.a 2 2
576.2.i.b 2
576.2.i.c 2
576.2.i.d 2
576.2.i.e 2
576.2.i.f 2
576.2.i.g 2
576.2.i.h 2
576.2.i.i 4
576.2.i.j 4
576.2.i.k 4
576.2.i.l 4
576.2.i.m 4
576.2.i.n 8
576.2.k $$\chi_{576}(145, \cdot)$$ 576.2.k.a 2 2
576.2.k.b 8
576.2.k.c 8
576.2.l $$\chi_{576}(143, \cdot)$$ 576.2.l.a 16 2
576.2.p $$\chi_{576}(95, \cdot)$$ 576.2.p.a 16 2
576.2.p.b 16
576.2.p.c 16
576.2.r $$\chi_{576}(97, \cdot)$$ 576.2.r.a 4 2
576.2.r.b 4
576.2.r.c 8
576.2.r.d 8
576.2.r.e 12
576.2.r.f 12
576.2.s $$\chi_{576}(191, \cdot)$$ 576.2.s.a 2 2
576.2.s.b 2
576.2.s.c 2
576.2.s.d 2
576.2.s.e 4
576.2.s.f 8
576.2.s.g 24
576.2.v $$\chi_{576}(73, \cdot)$$ None 0 4
576.2.w $$\chi_{576}(71, \cdot)$$ None 0 4
576.2.y $$\chi_{576}(47, \cdot)$$ 576.2.y.a 88 4
576.2.bb $$\chi_{576}(49, \cdot)$$ 576.2.bb.a 4 4
576.2.bb.b 4
576.2.bb.c 4
576.2.bb.d 4
576.2.bb.e 72
576.2.bd $$\chi_{576}(37, \cdot)$$ 576.2.bd.a 56 8
576.2.bd.b 128
576.2.bd.c 128
576.2.be $$\chi_{576}(35, \cdot)$$ 576.2.be.a 128 8
576.2.be.b 128
576.2.bg $$\chi_{576}(25, \cdot)$$ None 0 8
576.2.bj $$\chi_{576}(23, \cdot)$$ None 0 8
576.2.bl $$\chi_{576}(11, \cdot)$$ 576.2.bl.a 1504 16
576.2.bm $$\chi_{576}(13, \cdot)$$ 576.2.bm.a 1504 16

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(576))$$ into lower level spaces

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