# Properties

 Label 1280.3 Level 1280 Weight 3 Dimension 50376 Nonzero newspaces 22 Sturm bound 294912 Trace bound 50

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## Defining parameters

 Level: $$N$$ = $$1280 = 2^{8} \cdot 5$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$22$$ Sturm bound: $$294912$$ Trace bound: $$50$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(1280))$$.

Total New Old
Modular forms 99712 51000 48712
Cusp forms 96896 50376 46520
Eisenstein series 2816 624 2192

## Trace form

 $$50376 q - 64 q^{2} - 48 q^{3} - 64 q^{4} - 96 q^{5} - 192 q^{6} - 48 q^{7} - 64 q^{8} - 80 q^{9} + O(q^{10})$$ $$50376 q - 64 q^{2} - 48 q^{3} - 64 q^{4} - 96 q^{5} - 192 q^{6} - 48 q^{7} - 64 q^{8} - 80 q^{9} - 96 q^{10} - 144 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 72 q^{15} - 192 q^{16} - 96 q^{17} - 64 q^{18} - 48 q^{19} - 96 q^{20} - 192 q^{21} - 64 q^{22} - 48 q^{23} - 64 q^{24} - 120 q^{25} - 192 q^{26} - 48 q^{27} - 64 q^{28} - 64 q^{29} - 96 q^{30} - 160 q^{31} - 64 q^{32} - 112 q^{33} - 64 q^{34} - 72 q^{35} - 192 q^{36} - 64 q^{37} - 64 q^{38} - 48 q^{39} - 96 q^{40} - 240 q^{41} - 64 q^{42} - 48 q^{43} - 64 q^{44} - 168 q^{45} - 192 q^{46} - 48 q^{47} - 64 q^{48} - 488 q^{49} - 96 q^{50} - 912 q^{51} - 64 q^{52} - 704 q^{53} - 64 q^{54} - 584 q^{55} - 192 q^{56} - 848 q^{57} - 64 q^{58} - 560 q^{59} - 96 q^{60} - 448 q^{61} - 64 q^{62} - 32 q^{63} - 64 q^{64} - 88 q^{65} - 192 q^{66} + 592 q^{67} - 64 q^{68} + 704 q^{69} - 96 q^{70} + 880 q^{71} - 64 q^{72} + 1200 q^{73} - 64 q^{74} + 696 q^{75} - 192 q^{76} + 832 q^{77} - 64 q^{78} + 976 q^{79} - 96 q^{80} + 360 q^{81} - 64 q^{82} - 48 q^{83} - 64 q^{84} + 104 q^{85} - 192 q^{86} - 48 q^{87} - 64 q^{88} - 80 q^{89} - 96 q^{90} - 144 q^{91} - 64 q^{92} + 224 q^{93} - 64 q^{94} - 80 q^{95} - 192 q^{96} - 112 q^{97} - 64 q^{98} + 96 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(1280))$$

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
1280.3.b $$\chi_{1280}(511, \cdot)$$ 1280.3.b.a 4 1
1280.3.b.b 4
1280.3.b.c 4
1280.3.b.d 4
1280.3.b.e 8
1280.3.b.f 8
1280.3.b.g 8
1280.3.b.h 8
1280.3.b.i 16
1280.3.e $$\chi_{1280}(639, \cdot)$$ 1280.3.e.a 2 1
1280.3.e.b 2
1280.3.e.c 2
1280.3.e.d 2
1280.3.e.e 4
1280.3.e.f 6
1280.3.e.g 6
1280.3.e.h 6
1280.3.e.i 6
1280.3.e.j 8
1280.3.e.k 24
1280.3.e.l 24
1280.3.g $$\chi_{1280}(1151, \cdot)$$ 1280.3.g.a 4 1
1280.3.g.b 4
1280.3.g.c 4
1280.3.g.d 4
1280.3.g.e 8
1280.3.g.f 8
1280.3.g.g 16
1280.3.g.h 16
1280.3.h $$\chi_{1280}(1279, \cdot)$$ 1280.3.h.a 2 1
1280.3.h.b 2
1280.3.h.c 2
1280.3.h.d 2
1280.3.h.e 4
1280.3.h.f 4
1280.3.h.g 4
1280.3.h.h 8
1280.3.h.i 8
1280.3.h.j 8
1280.3.h.k 8
1280.3.h.l 8
1280.3.h.m 16
1280.3.h.n 16
1280.3.i $$\chi_{1280}(833, \cdot)$$ n/a 192 2
1280.3.k $$\chi_{1280}(319, \cdot)$$ n/a 192 2
1280.3.m $$\chi_{1280}(897, \cdot)$$ n/a 184 2
1280.3.p $$\chi_{1280}(257, \cdot)$$ n/a 184 2
1280.3.r $$\chi_{1280}(191, \cdot)$$ n/a 128 2
1280.3.t $$\chi_{1280}(193, \cdot)$$ n/a 192 2
1280.3.v $$\chi_{1280}(33, \cdot)$$ n/a 368 4
1280.3.w $$\chi_{1280}(31, \cdot)$$ n/a 256 4
1280.3.y $$\chi_{1280}(159, \cdot)$$ n/a 368 4
1280.3.bb $$\chi_{1280}(353, \cdot)$$ n/a 368 4
1280.3.bc $$\chi_{1280}(17, \cdot)$$ n/a 752 8
1280.3.bg $$\chi_{1280}(111, \cdot)$$ n/a 512 8
1280.3.bh $$\chi_{1280}(79, \cdot)$$ n/a 752 8
1280.3.bi $$\chi_{1280}(177, \cdot)$$ n/a 752 8
1280.3.bk $$\chi_{1280}(57, \cdot)$$ None 0 16
1280.3.bn $$\chi_{1280}(39, \cdot)$$ None 0 16
1280.3.bp $$\chi_{1280}(71, \cdot)$$ None 0 16
1280.3.bq $$\chi_{1280}(137, \cdot)$$ None 0 16
1280.3.bs $$\chi_{1280}(53, \cdot)$$ n/a 12224 32
1280.3.bu $$\chi_{1280}(19, \cdot)$$ n/a 12224 32
1280.3.bx $$\chi_{1280}(11, \cdot)$$ n/a 8192 32
1280.3.bz $$\chi_{1280}(13, \cdot)$$ n/a 12224 32

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

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(1280))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(1280)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 12}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 10}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 7}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(128))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(160))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(256))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(320))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(640))$$$$^{\oplus 2}$$