## Defining parameters

 Level: $$N$$ = $$576 = 2^{6} \cdot 3^{2}$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$16$$ Sturm bound: $$73728$$ Trace bound: $$25$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(576))$$.

Total New Old
Modular forms 28224 12411 15813
Cusp forms 27072 12213 14859
Eisenstein series 1152 198 954

## Trace form

 $$12213q - 24q^{2} - 24q^{3} - 24q^{4} - 24q^{5} - 32q^{6} - 20q^{7} - 24q^{8} - 40q^{9} + O(q^{10})$$ $$12213q - 24q^{2} - 24q^{3} - 24q^{4} - 24q^{5} - 32q^{6} - 20q^{7} - 24q^{8} - 40q^{9} - 72q^{10} - 38q^{11} - 32q^{12} + 48q^{13} - 24q^{14} - 24q^{15} - 24q^{16} + 62q^{17} - 32q^{18} - 30q^{19} - 24q^{20} - 32q^{21} + 448q^{22} - 12q^{23} - 32q^{24} + 21q^{25} - 64q^{26} - 24q^{27} - 832q^{28} - 424q^{29} - 32q^{30} - 380q^{31} - 1264q^{32} + 84q^{33} - 1024q^{34} + 504q^{35} - 32q^{36} + 1424q^{37} + 416q^{38} + 576q^{39} + 1616q^{40} + 674q^{41} - 32q^{42} - 910q^{43} + 976q^{44} - 2000q^{45} - 72q^{46} - 2844q^{47} - 32q^{48} - 1859q^{49} - 2880q^{50} - 1424q^{51} - 3336q^{52} - 1248q^{53} - 32q^{54} + 1096q^{55} + 368q^{56} + 1336q^{57} + 2352q^{58} - 398q^{59} - 32q^{60} + 3216q^{61} + 2712q^{62} + 1348q^{63} + 5976q^{64} - 1340q^{65} - 32q^{66} - 6042q^{67} + 2040q^{68} - 248q^{69} + 1992q^{70} - 472q^{71} - 32q^{72} + 934q^{73} - 2656q^{74} - 416q^{75} - 5976q^{76} - 2388q^{77} - 10160q^{78} + 4396q^{79} - 32880q^{80} - 7416q^{81} - 20952q^{82} - 2338q^{83} - 8320q^{84} - 288q^{85} + 1536q^{86} + 1264q^{87} + 9336q^{88} + 9970q^{89} + 18688q^{90} + 3812q^{91} + 37824q^{92} + 8512q^{93} + 26760q^{94} + 5208q^{95} + 25808q^{96} + 14438q^{97} + 36288q^{98} + 5288q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(576))$$

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
576.4.a $$\chi_{576}(1, \cdot)$$ 576.4.a.a 1 1
576.4.a.b 1
576.4.a.c 1
576.4.a.d 1
576.4.a.e 1
576.4.a.f 1
576.4.a.g 1
576.4.a.h 1
576.4.a.i 1
576.4.a.j 1
576.4.a.k 1
576.4.a.l 1
576.4.a.m 1
576.4.a.n 1
576.4.a.o 1
576.4.a.p 1
576.4.a.q 1
576.4.a.r 1
576.4.a.s 1
576.4.a.t 1
576.4.a.u 1
576.4.a.v 1
576.4.a.w 1
576.4.a.x 1
576.4.a.y 1
576.4.a.z 2
576.4.a.ba 2
576.4.c $$\chi_{576}(575, \cdot)$$ 576.4.c.a 2 1
576.4.c.b 2
576.4.c.c 4
576.4.c.d 4
576.4.c.e 4
576.4.c.f 8
576.4.d $$\chi_{576}(289, \cdot)$$ 576.4.d.a 2 1
576.4.d.b 4
576.4.d.c 4
576.4.d.d 4
576.4.d.e 4
576.4.d.f 4
576.4.d.g 4
576.4.d.h 4
576.4.f $$\chi_{576}(287, \cdot)$$ 576.4.f.a 8 1
576.4.f.b 16
576.4.i $$\chi_{576}(193, \cdot)$$ n/a 140 2
576.4.k $$\chi_{576}(145, \cdot)$$ 576.4.k.a 10 2
576.4.k.b 24
576.4.k.c 24
576.4.l $$\chi_{576}(143, \cdot)$$ 576.4.l.a 48 2
576.4.p $$\chi_{576}(95, \cdot)$$ n/a 144 2
576.4.r $$\chi_{576}(97, \cdot)$$ n/a 144 2
576.4.s $$\chi_{576}(191, \cdot)$$ n/a 140 2
576.4.v $$\chi_{576}(73, \cdot)$$ None 0 4
576.4.w $$\chi_{576}(71, \cdot)$$ None 0 4
576.4.y $$\chi_{576}(47, \cdot)$$ n/a 280 4
576.4.bb $$\chi_{576}(49, \cdot)$$ n/a 280 4
576.4.bd $$\chi_{576}(37, \cdot)$$ n/a 952 8
576.4.be $$\chi_{576}(35, \cdot)$$ n/a 768 8
576.4.bg $$\chi_{576}(25, \cdot)$$ None 0 8
576.4.bj $$\chi_{576}(23, \cdot)$$ None 0 8
576.4.bl $$\chi_{576}(11, \cdot)$$ n/a 4576 16
576.4.bm $$\chi_{576}(13, \cdot)$$ n/a 4576 16

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(576))$$ into lower level spaces

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