## Defining parameters

 Level: $$N$$ = $$64 = 2^{6}$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$4$$ Newform subspaces: $$5$$ Sturm bound: $$768$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(64))$$.

Total New Old
Modular forms 292 155 137
Cusp forms 220 133 87
Eisenstein series 72 22 50

## Trace form

 $$133q - 8q^{2} - 6q^{3} - 8q^{4} - 8q^{5} - 8q^{6} - 4q^{7} - 8q^{8} - q^{9} + O(q^{10})$$ $$133q - 8q^{2} - 6q^{3} - 8q^{4} - 8q^{5} - 8q^{6} - 4q^{7} - 8q^{8} - q^{9} - 8q^{10} + 10q^{11} - 8q^{12} + 8q^{13} - 8q^{14} - 8q^{15} - 8q^{16} - 30q^{17} - 8q^{18} - 38q^{19} - 8q^{20} - 92q^{21} - 80q^{22} - 68q^{23} - 288q^{24} - 131q^{25} - 208q^{26} - 72q^{27} - 128q^{28} - 40q^{29} - 88q^{30} - 16q^{31} + 32q^{32} + 76q^{33} + 112q^{34} + 92q^{35} + 392q^{36} + 168q^{37} + 272q^{38} + 188q^{39} + 352q^{40} + 246q^{41} + 432q^{42} + 106q^{43} + 96q^{44} + 140q^{45} - 8q^{46} - 8q^{47} - 8q^{48} - 95q^{49} + 304q^{50} - 548q^{51} + 520q^{52} - 152q^{53} + 568q^{54} - 772q^{55} + 384q^{56} - 248q^{57} + 352q^{58} - 470q^{59} + 280q^{60} - 120q^{61} + 8q^{62} - 104q^{64} + 72q^{65} - 264q^{66} + 538q^{67} - 248q^{68} + 196q^{69} - 680q^{70} + 764q^{71} - 656q^{72} + 246q^{73} - 624q^{74} + 998q^{75} - 840q^{76} - 156q^{77} - 1136q^{78} + 504q^{79} - 1376q^{80} - 427q^{81} - 1048q^{82} - 326q^{83} - 1240q^{84} - 472q^{85} - 944q^{86} - 452q^{87} - 568q^{88} - 554q^{89} - 728q^{90} - 196q^{91} - 464q^{92} - 368q^{93} - 104q^{94} - 16q^{95} + 128q^{96} + 202q^{97} + 400q^{98} + 290q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(64))$$

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
64.3.c $$\chi_{64}(63, \cdot)$$ 64.3.c.a 1 1
64.3.c.b 2
64.3.d $$\chi_{64}(31, \cdot)$$ 64.3.d.a 4 1
64.3.f $$\chi_{64}(15, \cdot)$$ 64.3.f.a 6 2
64.3.h $$\chi_{64}(7, \cdot)$$ None 0 4
64.3.j $$\chi_{64}(3, \cdot)$$ 64.3.j.a 120 8

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(64))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(64)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 2}$$