# Properties

 Label 64.10 Level 64 Weight 10 Dimension 637 Nonzero newspaces 4 Newform subspaces 18 Sturm bound 2560 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$64 = 2^{6}$$ Weight: $$k$$ = $$10$$ Nonzero newspaces: $$4$$ Newform subspaces: $$18$$ Sturm bound: $$2560$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{10}(\Gamma_1(64))$$.

Total New Old
Modular forms 1188 659 529
Cusp forms 1116 637 479
Eisenstein series 72 22 50

## Trace form

 $$637 q - 8 q^{2} - 6 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 19693 q^{9} + O(q^{10})$$ $$637 q - 8 q^{2} - 6 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 19693 q^{9} - 8 q^{10} - 65866 q^{11} - 8 q^{12} + 194608 q^{13} - 8 q^{14} - 405004 q^{15} - 8 q^{16} + 407978 q^{17} - 8 q^{18} + 480882 q^{19} - 8 q^{20} - 1959236 q^{21} + 3576336 q^{22} - 8 q^{23} + 12096992 q^{24} + 4933921 q^{25} - 2105968 q^{26} - 6364416 q^{27} - 21791488 q^{28} - 1266808 q^{29} + 44263272 q^{30} + 11082256 q^{31} + 29441312 q^{32} - 190636 q^{33} - 38537008 q^{34} - 23026564 q^{35} - 110500728 q^{36} + 17001152 q^{37} + 66947312 q^{38} - 8 q^{39} + 97089632 q^{40} + 1161206 q^{41} - 224559088 q^{42} + 34881070 q^{43} + 146176992 q^{44} - 14308812 q^{45} - 8 q^{46} - 97593624 q^{47} - 8 q^{48} + 14539433 q^{49} + 182758288 q^{50} - 332675180 q^{51} - 25227512 q^{52} + 161472928 q^{53} - 646232264 q^{54} + 280217656 q^{55} + 203163008 q^{56} - 377672144 q^{57} + 855153280 q^{58} - 670653826 q^{59} + 230939416 q^{60} + 209365552 q^{61} - 597609496 q^{62} + 1413881660 q^{63} - 1364809832 q^{64} + 409307496 q^{65} + 186013784 q^{66} - 1413262638 q^{67} + 1004327944 q^{68} - 607316180 q^{69} + 1869092056 q^{70} - 476202952 q^{71} - 714729104 q^{72} + 927119350 q^{73} - 2182183312 q^{74} + 3347963250 q^{75} - 888710984 q^{76} - 277316164 q^{77} + 5243787376 q^{78} - 4182694632 q^{79} - 5193915232 q^{80} - 721500299 q^{81} + 3136405672 q^{82} + 1637053434 q^{83} + 6148771880 q^{84} + 2166685888 q^{85} - 988828368 q^{86} - 8 q^{87} - 4940685368 q^{88} - 4491535450 q^{89} - 7222410008 q^{90} - 2019528204 q^{91} + 1729489584 q^{92} + 1068636832 q^{93} + 6710490136 q^{94} + 5087413260 q^{95} + 10366581632 q^{96} + 3131588962 q^{97} + 2543861360 q^{98} - 3713593966 q^{99} + O(q^{100})$$

## Decomposition of $$S_{10}^{\mathrm{new}}(\Gamma_1(64))$$

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
64.10.a $$\chi_{64}(1, \cdot)$$ 64.10.a.a 1 1
64.10.a.b 1
64.10.a.c 1
64.10.a.d 1
64.10.a.e 1
64.10.a.f 1
64.10.a.g 1
64.10.a.h 1
64.10.a.i 1
64.10.a.j 2
64.10.a.k 2
64.10.a.l 2
64.10.a.m 2
64.10.b $$\chi_{64}(33, \cdot)$$ 64.10.b.a 2 1
64.10.b.b 4
64.10.b.c 12
64.10.e $$\chi_{64}(17, \cdot)$$ 64.10.e.a 34 2
64.10.g $$\chi_{64}(9, \cdot)$$ None 0 4
64.10.i $$\chi_{64}(5, \cdot)$$ 64.10.i.a 568 8

## Decomposition of $$S_{10}^{\mathrm{old}}(\Gamma_1(64))$$ into lower level spaces

$$S_{10}^{\mathrm{old}}(\Gamma_1(64)) \cong$$ $$S_{10}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 6}$$$$\oplus$$$$S_{10}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 5}$$$$\oplus$$$$S_{10}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 4}$$$$\oplus$$$$S_{10}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 3}$$$$\oplus$$$$S_{10}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 2}$$