## 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

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

## 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

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