Defining parameters

 Level: $$N$$ = $$64 = 2^{6}$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$4$$ Newform subspaces: $$9$$ Sturm bound: $$1024$$ Trace bound: $$1$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(64))$$.

Total New Old
Modular forms 420 227 193
Cusp forms 348 205 143
Eisenstein series 72 22 50

Trace form

 $$205 q - 8 q^{2} - 6 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 37 q^{9} + O(q^{10})$$ $$205 q - 8 q^{2} - 6 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 37 q^{9} - 8 q^{10} - 26 q^{11} - 8 q^{12} + 64 q^{13} - 8 q^{14} + 116 q^{15} - 8 q^{16} + 90 q^{17} - 8 q^{18} + 18 q^{19} - 8 q^{20} - 20 q^{21} + 464 q^{22} - 8 q^{23} + 992 q^{24} + 41 q^{25} - 48 q^{26} - 192 q^{27} - 768 q^{28} - 408 q^{29} - 2328 q^{30} - 368 q^{31} - 1248 q^{32} - 988 q^{33} - 1008 q^{34} - 484 q^{35} - 888 q^{36} - 528 q^{37} + 432 q^{38} - 8 q^{39} + 1632 q^{40} + 1014 q^{41} + 3152 q^{42} + 830 q^{43} + 992 q^{44} + 1476 q^{45} - 8 q^{46} + 936 q^{47} - 8 q^{48} + 1049 q^{49} - 2864 q^{50} + 4468 q^{51} - 3320 q^{52} + 400 q^{53} - 1736 q^{54} + 568 q^{55} + 384 q^{56} - 1088 q^{57} + 2368 q^{58} - 4466 q^{59} + 4888 q^{60} - 1088 q^{61} + 2984 q^{62} - 7684 q^{63} + 6040 q^{64} - 2296 q^{65} + 5528 q^{66} - 6030 q^{67} + 2056 q^{68} - 644 q^{69} + 2008 q^{70} - 456 q^{71} - 656 q^{72} + 1014 q^{73} - 2640 q^{74} + 7362 q^{75} - 5960 q^{76} + 3116 q^{77} - 2000 q^{78} + 10072 q^{79} + 4256 q^{80} + 6805 q^{81} + 6952 q^{82} + 2554 q^{83} + 4136 q^{84} + 1648 q^{85} - 528 q^{86} - 8 q^{87} - 3128 q^{88} - 3578 q^{89} - 9368 q^{90} - 3340 q^{91} - 12624 q^{92} - 8384 q^{93} - 8936 q^{94} - 6900 q^{95} - 12928 q^{96} - 9358 q^{97} - 12112 q^{98} - 4750 q^{99} + O(q^{100})$$

Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(64))$$

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
64.4.a $$\chi_{64}(1, \cdot)$$ 64.4.a.a 1 1
64.4.a.b 1
64.4.a.c 1
64.4.a.d 1
64.4.a.e 1
64.4.b $$\chi_{64}(33, \cdot)$$ 64.4.b.a 2 1
64.4.b.b 4
64.4.e $$\chi_{64}(17, \cdot)$$ 64.4.e.a 10 2
64.4.g $$\chi_{64}(9, \cdot)$$ None 0 4
64.4.i $$\chi_{64}(5, \cdot)$$ 64.4.i.a 184 8

Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(64))$$ into lower level spaces

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