## Defining parameters

 Level: $$N$$ = $$576 = 2^{6} \cdot 3^{2}$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$16$$ Sturm bound: $$55296$$ Trace bound: $$25$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(576))$$.

Total New Old
Modular forms 19008 8307 10701
Cusp forms 17856 8109 9747
Eisenstein series 1152 198 954

## Trace form

 $$8109 q - 24 q^{2} - 24 q^{3} - 24 q^{4} - 24 q^{5} - 32 q^{6} - 16 q^{7} - 24 q^{8} - 40 q^{9} + O(q^{10})$$ $$8109 q - 24 q^{2} - 24 q^{3} - 24 q^{4} - 24 q^{5} - 32 q^{6} - 16 q^{7} - 24 q^{8} - 40 q^{9} - 72 q^{10} - 2 q^{11} - 32 q^{12} - 8 q^{13} - 24 q^{14} - 24 q^{15} - 24 q^{16} - 58 q^{17} - 32 q^{18} - 86 q^{19} - 24 q^{20} - 32 q^{21} - 96 q^{22} - 88 q^{23} - 32 q^{24} - 151 q^{25} - 224 q^{26} - 24 q^{27} - 192 q^{28} - 56 q^{29} - 32 q^{30} - 28 q^{31} + 16 q^{32} - 60 q^{33} + 96 q^{34} - 120 q^{35} - 32 q^{36} - 216 q^{37} + 256 q^{38} - 216 q^{39} + 336 q^{40} - 158 q^{41} - 32 q^{42} - 162 q^{43} + 80 q^{44} - 128 q^{45} - 72 q^{46} - 12 q^{47} - 32 q^{48} + 5 q^{49} + 288 q^{50} + 136 q^{51} + 504 q^{52} + 408 q^{53} - 32 q^{54} - 308 q^{55} + 368 q^{56} + 280 q^{57} + 336 q^{58} + 94 q^{59} - 32 q^{60} + 312 q^{61} + 120 q^{62} + 172 q^{63} - 168 q^{64} + 228 q^{65} - 32 q^{66} + 526 q^{67} - 264 q^{68} + 40 q^{69} - 696 q^{70} + 756 q^{71} - 32 q^{72} + 166 q^{73} - 640 q^{74} + 112 q^{75} - 856 q^{76} + 612 q^{77} + 784 q^{78} + 1004 q^{79} + 2448 q^{80} + 840 q^{81} + 3048 q^{82} + 622 q^{83} + 2432 q^{84} + 792 q^{85} + 2784 q^{86} + 424 q^{87} + 1656 q^{88} + 962 q^{89} + 1408 q^{90} + 140 q^{91} + 1344 q^{92} + 160 q^{93} + 264 q^{94} + 12 q^{95} - 304 q^{96} - 322 q^{97} - 1248 q^{98} - 280 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(576))$$

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
576.3.b $$\chi_{576}(415, \cdot)$$ 576.3.b.a 4 1
576.3.b.b 4
576.3.b.c 4
576.3.b.d 4
576.3.b.e 4
576.3.e $$\chi_{576}(449, \cdot)$$ 576.3.e.a 2 1
576.3.e.b 2
576.3.e.c 2
576.3.e.d 2
576.3.e.e 2
576.3.e.f 2
576.3.e.g 2
576.3.e.h 2
576.3.g $$\chi_{576}(127, \cdot)$$ 576.3.g.a 1 1
576.3.g.b 1
576.3.g.c 1
576.3.g.d 2
576.3.g.e 2
576.3.g.f 2
576.3.g.g 2
576.3.g.h 2
576.3.g.i 2
576.3.g.j 4
576.3.h $$\chi_{576}(161, \cdot)$$ 576.3.h.a 8 1
576.3.h.b 8
576.3.j $$\chi_{576}(17, \cdot)$$ 576.3.j.a 32 2
576.3.m $$\chi_{576}(271, \cdot)$$ 576.3.m.a 6 2
576.3.m.b 16
576.3.m.c 16
576.3.n $$\chi_{576}(353, \cdot)$$ 576.3.n.a 8 2
576.3.n.b 24
576.3.n.c 32
576.3.n.d 32
576.3.o $$\chi_{576}(319, \cdot)$$ 576.3.o.a 2 2
576.3.o.b 2
576.3.o.c 4
576.3.o.d 8
576.3.o.e 8
576.3.o.f 8
576.3.o.g 16
576.3.o.h 20
576.3.o.i 24
576.3.q $$\chi_{576}(65, \cdot)$$ 576.3.q.a 2 2
576.3.q.b 2
576.3.q.c 4
576.3.q.d 4
576.3.q.e 4
576.3.q.f 4
576.3.q.g 4
576.3.q.h 4
576.3.q.i 8
576.3.q.j 8
576.3.q.k 24
576.3.q.l 24
576.3.t $$\chi_{576}(31, \cdot)$$ 576.3.t.a 32 2
576.3.t.b 32
576.3.t.c 32
576.3.u $$\chi_{576}(55, \cdot)$$ None 0 4
576.3.x $$\chi_{576}(89, \cdot)$$ None 0 4
576.3.z $$\chi_{576}(79, \cdot)$$ n/a 184 4
576.3.ba $$\chi_{576}(113, \cdot)$$ n/a 184 4
576.3.bc $$\chi_{576}(53, \cdot)$$ n/a 512 8
576.3.bf $$\chi_{576}(19, \cdot)$$ n/a 632 8
576.3.bh $$\chi_{576}(7, \cdot)$$ None 0 8
576.3.bi $$\chi_{576}(41, \cdot)$$ None 0 8
576.3.bk $$\chi_{576}(43, \cdot)$$ n/a 3040 16
576.3.bn $$\chi_{576}(5, \cdot)$$ n/a 3040 16

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

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(576))$$ into lower level spaces

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