# Properties

 Label 256.6 Level 256 Weight 6 Dimension 5708 Nonzero newspaces 6 Sturm bound 24576 Trace bound 9

## Defining parameters

 Level: $$N$$ = $$256 = 2^{8}$$ Weight: $$k$$ = $$6$$ Nonzero newspaces: $$6$$ Sturm bound: $$24576$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_1(256))$$.

Total New Old
Modular forms 10416 5812 4604
Cusp forms 10064 5708 4356
Eisenstein series 352 104 248

## Trace form

 $$5708q - 32q^{2} - 24q^{3} - 32q^{4} - 32q^{5} - 32q^{6} - 24q^{7} - 32q^{8} - 40q^{9} + O(q^{10})$$ $$5708q - 32q^{2} - 24q^{3} - 32q^{4} - 32q^{5} - 32q^{6} - 24q^{7} - 32q^{8} - 40q^{9} - 32q^{10} - 24q^{11} - 32q^{12} - 32q^{13} - 32q^{14} - 24q^{15} - 32q^{16} - 48q^{17} - 32q^{18} - 24q^{19} - 32q^{20} - 32q^{21} - 32q^{22} - 24q^{23} - 32q^{24} - 40q^{25} - 32q^{26} - 24q^{27} - 32q^{28} - 32q^{29} - 32q^{30} - 32q^{31} - 32q^{32} - 56q^{33} - 32q^{34} - 24q^{35} - 32q^{36} - 32q^{37} - 32q^{38} - 24q^{39} - 32q^{40} - 40q^{41} - 32q^{42} - 24q^{43} - 32q^{44} - 1976q^{45} - 32q^{46} - 24q^{47} - 32q^{48} - 67276q^{49} - 32q^{50} - 41784q^{51} - 32q^{52} + 98880q^{53} - 32q^{54} + 220072q^{55} - 32q^{56} + 103064q^{57} - 32q^{58} - 57944q^{59} - 32q^{60} - 192352q^{61} - 32q^{62} - 317536q^{63} - 32q^{64} - 221576q^{65} - 32q^{66} - 122344q^{67} - 32q^{68} + 89248q^{69} - 32q^{70} + 287656q^{71} - 32q^{72} + 420504q^{73} - 32q^{74} + 386472q^{75} - 32q^{76} + 29760q^{77} - 32q^{78} - 355384q^{79} - 32q^{80} - 236244q^{81} - 32q^{82} - 24q^{83} - 32q^{84} - 25032q^{85} - 32q^{86} - 24q^{87} - 32q^{88} - 40q^{89} - 32q^{90} - 24q^{91} - 32q^{92} + 3856q^{93} - 32q^{94} - 32q^{95} - 32q^{96} - 56q^{97} - 32q^{98} - 1968q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_1(256))$$

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
256.6.a $$\chi_{256}(1, \cdot)$$ 256.6.a.a 1 1
256.6.a.b 1
256.6.a.c 1
256.6.a.d 1
256.6.a.e 2
256.6.a.f 2
256.6.a.g 2
256.6.a.h 2
256.6.a.i 2
256.6.a.j 4
256.6.a.k 4
256.6.a.l 4
256.6.a.m 4
256.6.a.n 4
256.6.a.o 4
256.6.b $$\chi_{256}(129, \cdot)$$ 256.6.b.a 2 1
256.6.b.b 2
256.6.b.c 2
256.6.b.d 2
256.6.b.e 2
256.6.b.f 2
256.6.b.g 2
256.6.b.h 2
256.6.b.i 2
256.6.b.j 4
256.6.b.k 4
256.6.b.l 4
256.6.b.m 4
256.6.b.n 4
256.6.e $$\chi_{256}(65, \cdot)$$ 256.6.e.a 16 2
256.6.e.b 16
256.6.e.c 24
256.6.e.d 24
256.6.g $$\chi_{256}(33, \cdot)$$ n/a 152 4
256.6.i $$\chi_{256}(17, \cdot)$$ n/a 312 8
256.6.k $$\chi_{256}(9, \cdot)$$ None 0 16
256.6.m $$\chi_{256}(5, \cdot)$$ n/a 5088 32

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

## Decomposition of $$S_{6}^{\mathrm{old}}(\Gamma_1(256))$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(\Gamma_1(256)) \cong$$ $$S_{6}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 7}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 5}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 3}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(128))$$$$^{\oplus 2}$$