# Properties

 Label 256.3 Level 256 Weight 3 Dimension 2252 Nonzero newspaces 6 Newform subspaces 20 Sturm bound 12288 Trace bound 9

# Learn more

## Defining parameters

 Level: $$N$$ = $$256 = 2^{8}$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$6$$ Newform subspaces: $$20$$ Sturm bound: $$12288$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(256))$$.

Total New Old
Modular forms 4272 2356 1916
Cusp forms 3920 2252 1668
Eisenstein series 352 104 248

## Trace form

 $$2252q - 32q^{2} - 24q^{3} - 32q^{4} - 32q^{5} - 32q^{6} - 24q^{7} - 32q^{8} - 40q^{9} + O(q^{10})$$ $$2252q - 32q^{2} - 24q^{3} - 32q^{4} - 32q^{5} - 32q^{6} - 24q^{7} - 32q^{8} - 40q^{9} - 32q^{10} - 24q^{11} - 32q^{12} - 32q^{13} - 32q^{14} - 24q^{15} - 32q^{16} - 48q^{17} - 32q^{18} - 24q^{19} - 32q^{20} - 32q^{21} - 32q^{22} - 24q^{23} - 32q^{24} - 40q^{25} - 32q^{26} - 24q^{27} - 32q^{28} - 32q^{29} - 32q^{30} - 16q^{31} - 32q^{32} - 56q^{33} - 32q^{34} - 24q^{35} - 32q^{36} - 32q^{37} - 32q^{38} - 24q^{39} - 32q^{40} - 40q^{41} - 32q^{42} - 24q^{43} - 32q^{44} + 40q^{45} - 32q^{46} - 24q^{47} - 32q^{48} + 148q^{49} - 32q^{50} + 360q^{51} - 32q^{52} + 288q^{53} - 32q^{54} + 488q^{55} - 32q^{56} + 344q^{57} - 32q^{58} + 232q^{59} - 32q^{60} + 96q^{61} - 32q^{62} - 32q^{63} - 32q^{64} - 200q^{65} - 32q^{66} - 344q^{67} - 32q^{68} - 416q^{69} - 32q^{70} - 536q^{71} - 32q^{72} - 680q^{73} - 32q^{74} - 792q^{75} - 32q^{76} - 480q^{77} - 32q^{78} - 536q^{79} - 32q^{80} - 372q^{81} - 32q^{82} - 24q^{83} - 32q^{84} - 232q^{85} - 32q^{86} - 24q^{87} - 32q^{88} - 40q^{89} - 32q^{90} - 24q^{91} - 32q^{92} - 176q^{93} - 32q^{94} - 16q^{95} - 32q^{96} - 56q^{97} - 32q^{98} - 96q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(256))$$

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
256.3.c $$\chi_{256}(255, \cdot)$$ 256.3.c.a 1 1
256.3.c.b 1
256.3.c.c 2
256.3.c.d 2
256.3.c.e 2
256.3.c.f 2
256.3.c.g 4
256.3.d $$\chi_{256}(127, \cdot)$$ 256.3.d.a 2 1
256.3.d.b 2
256.3.d.c 2
256.3.d.d 4
256.3.d.e 4
256.3.f $$\chi_{256}(63, \cdot)$$ 256.3.f.a 8 2
256.3.f.b 8
256.3.f.c 8
256.3.f.d 8
256.3.h $$\chi_{256}(31, \cdot)$$ 256.3.h.a 28 4
256.3.h.b 28
256.3.j $$\chi_{256}(15, \cdot)$$ 256.3.j.a 120 8
256.3.l $$\chi_{256}(7, \cdot)$$ None 0 16
256.3.n $$\chi_{256}(3, \cdot)$$ 256.3.n.a 2016 32

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(256))$$ into lower level spaces

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