# Properties

 Label 64.22 Level 64 Weight 22 Dimension 1501 Nonzero newspaces 4 Sturm bound 5632 Trace bound 1

# Learn more

## Defining parameters

 Level: $$N$$ = $$64 = 2^{6}$$ Weight: $$k$$ = $$22$$ Nonzero newspaces: $$4$$ Sturm bound: $$5632$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{22}(\Gamma_1(64))$$.

Total New Old
Modular forms 2724 1523 1201
Cusp forms 2652 1501 1151
Eisenstein series 72 22 50

## Trace form

 $$1501 q - 8 q^{2} - 6 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 10460353213 q^{9} + O(q^{10})$$ $$1501 q - 8 q^{2} - 6 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 10460353213 q^{9} - 8 q^{10} - 67333320746 q^{11} - 8 q^{12} - 1065395863664 q^{13} - 8 q^{14} - 4613203125004 q^{15} - 8 q^{16} - 6962857988022 q^{17} - 8 q^{18} + 46007763621426 q^{19} - 8 q^{20} + 132781988108764 q^{21} - 207411361090032 q^{22} - 8 q^{23} - 1945658207807008 q^{24} + 637048321772881 q^{25} - 1506625290169968 q^{26} - 1147760716556928 q^{27} + 11978218049315072 q^{28} - 4866346900433208 q^{29} - 16217339993829528 q^{30} + 9835539443769616 q^{31} - 12832721772527328 q^{32} - 42872757726145228 q^{33} + 58324591899126992 q^{34} + 19253478556034876 q^{35} - 296417618048471928 q^{36} - 25075936097793568 q^{37} + 303109027666885872 q^{38} - 8 q^{39} - 363206157537854368 q^{40} + 510309577544344566 q^{41} - 980887809273580528 q^{42} - 215332019803969394 q^{43} - 959490752542847008 q^{44} + 828356648574617748 q^{45} - 8 q^{46} - 1051982644716600984 q^{47} - 8 q^{48} + 1837350517946442953 q^{49} - 4761634387503570032 q^{50} - 6784243964339970860 q^{51} - 8655710943494332664 q^{52} + 4030944480231746368 q^{53} - 4994095300087806152 q^{54} + 15854219360527201336 q^{55} + 13445791338293702016 q^{56} + 2559856001679390352 q^{57} - 24235593818026622336 q^{58} + 21123007083356949214 q^{59} + 34373655846659160856 q^{60} + 2876746575441830032 q^{61} - 9454210277557709848 q^{62} + 96258845731845948860 q^{63} - 28235118983318354024 q^{64} + 2883914131812497576 q^{65} + 111234197313377019992 q^{66} + 85371272536705140882 q^{67} - 104659289810037971960 q^{68} - 39855976718185394420 q^{69} + 279305961159540045016 q^{70} - 135249633480998712264 q^{71} - 215147916304966389392 q^{72} + 48694326242424071158 q^{73} + 149453752937774472816 q^{74} - 612779223988624340910 q^{75} - 235541415539266676552 q^{76} + 132554470675161717596 q^{77} + 226776658842727689328 q^{78} - 234613589151699565416 q^{79} - 860612604870301954912 q^{80} + 994446341328046922677 q^{81} - 708517628372968195928 q^{82} - 317463236552669319686 q^{83} + 1424936216815736264744 q^{84} + 257778402032356066528 q^{85} - 917406725370159511248 q^{86} - 8 q^{87} - 418946962671126792248 q^{88} + 1439609648740966873318 q^{89} + 4037191479561093749992 q^{90} - 144326756239046079756 q^{91} - 6603731275935646802256 q^{92} - 2037517980701178374048 q^{93} + 2424473717652338934808 q^{94} + 1411330138695550130700 q^{95} + 4329988420061566228352 q^{96} - 2359410602208113631422 q^{97} - 11226390629590293575056 q^{98} - 2710306841442932184622 q^{99} + O(q^{100})$$

## Decomposition of $$S_{22}^{\mathrm{new}}(\Gamma_1(64))$$

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
64.22.a $$\chi_{64}(1, \cdot)$$ 64.22.a.a 1 1
64.22.a.b 1
64.22.a.c 1
64.22.a.d 1
64.22.a.e 1
64.22.a.f 1
64.22.a.g 1
64.22.a.h 2
64.22.a.i 2
64.22.a.j 2
64.22.a.k 2
64.22.a.l 3
64.22.a.m 3
64.22.a.n 4
64.22.a.o 5
64.22.a.p 5
64.22.a.q 6
64.22.b $$\chi_{64}(33, \cdot)$$ 64.22.b.a 2 1
64.22.b.b 12
64.22.b.c 28
64.22.e $$\chi_{64}(17, \cdot)$$ 64.22.e.a 82 2
64.22.g $$\chi_{64}(9, \cdot)$$ None 0 4
64.22.i $$\chi_{64}(5, \cdot)$$ n/a 1336 8

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

## Decomposition of $$S_{22}^{\mathrm{old}}(\Gamma_1(64))$$ into lower level spaces

$$S_{22}^{\mathrm{old}}(\Gamma_1(64)) \cong$$ $$S_{22}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 7}$$$$\oplus$$$$S_{22}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 6}$$$$\oplus$$$$S_{22}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 5}$$$$\oplus$$$$S_{22}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 4}$$$$\oplus$$$$S_{22}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 3}$$$$\oplus$$$$S_{22}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 2}$$