# Properties

 Label 1280.2 Level 1280 Weight 2 Dimension 25032 Nonzero newspaces 22 Sturm bound 196608 Trace bound 50

## Defining parameters

 Level: $$N$$ = $$1280 = 2^{8} \cdot 5$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$22$$ Sturm bound: $$196608$$ Trace bound: $$50$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1280))$$.

Total New Old
Modular forms 50560 25656 24904
Cusp forms 47745 25032 22713
Eisenstein series 2815 624 2191

## Trace form

 $$25032 q - 64 q^{2} - 48 q^{3} - 64 q^{4} - 96 q^{5} - 192 q^{6} - 48 q^{7} - 64 q^{8} - 80 q^{9} + O(q^{10})$$ $$25032 q - 64 q^{2} - 48 q^{3} - 64 q^{4} - 96 q^{5} - 192 q^{6} - 48 q^{7} - 64 q^{8} - 80 q^{9} - 96 q^{10} - 144 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 72 q^{15} - 192 q^{16} - 96 q^{17} - 64 q^{18} - 48 q^{19} - 96 q^{20} - 192 q^{21} - 64 q^{22} - 48 q^{23} - 64 q^{24} - 120 q^{25} - 192 q^{26} - 48 q^{27} - 64 q^{28} - 64 q^{29} - 96 q^{30} - 128 q^{31} - 64 q^{32} - 112 q^{33} - 64 q^{34} - 72 q^{35} - 192 q^{36} - 64 q^{37} - 64 q^{38} - 48 q^{39} - 96 q^{40} - 240 q^{41} - 64 q^{42} - 48 q^{43} - 64 q^{44} - 72 q^{45} - 192 q^{46} - 48 q^{47} - 64 q^{48} - 40 q^{49} - 96 q^{50} - 80 q^{51} - 64 q^{52} - 64 q^{54} - 8 q^{55} - 192 q^{56} + 48 q^{57} - 64 q^{58} + 80 q^{59} - 96 q^{60} - 64 q^{61} - 64 q^{62} + 96 q^{63} - 64 q^{64} - 152 q^{65} - 192 q^{66} + 112 q^{67} - 64 q^{68} + 64 q^{69} - 96 q^{70} - 16 q^{71} - 64 q^{72} + 48 q^{73} - 64 q^{74} - 8 q^{75} - 192 q^{76} - 64 q^{78} + 16 q^{79} - 96 q^{80} - 216 q^{81} - 64 q^{82} - 48 q^{83} - 64 q^{84} - 56 q^{85} - 192 q^{86} - 48 q^{87} - 64 q^{88} - 80 q^{89} - 96 q^{90} - 144 q^{91} - 64 q^{92} - 160 q^{93} - 64 q^{94} - 64 q^{95} - 192 q^{96} - 112 q^{97} - 64 q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1280))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
1280.2.a $$\chi_{1280}(1, \cdot)$$ 1280.2.a.a 2 1
1280.2.a.b 2
1280.2.a.c 2
1280.2.a.d 2
1280.2.a.e 2
1280.2.a.f 2
1280.2.a.g 2
1280.2.a.h 2
1280.2.a.i 2
1280.2.a.j 2
1280.2.a.k 2
1280.2.a.l 2
1280.2.a.m 2
1280.2.a.n 2
1280.2.a.o 2
1280.2.a.p 2
1280.2.c $$\chi_{1280}(769, \cdot)$$ 1280.2.c.a 2 1
1280.2.c.b 2
1280.2.c.c 2
1280.2.c.d 2
1280.2.c.e 4
1280.2.c.f 4
1280.2.c.g 4
1280.2.c.h 4
1280.2.c.i 4
1280.2.c.j 4
1280.2.c.k 4
1280.2.c.l 4
1280.2.c.m 4
1280.2.d $$\chi_{1280}(641, \cdot)$$ 1280.2.d.a 2 1
1280.2.d.b 2
1280.2.d.c 2
1280.2.d.d 2
1280.2.d.e 2
1280.2.d.f 2
1280.2.d.g 2
1280.2.d.h 2
1280.2.d.i 2
1280.2.d.j 2
1280.2.d.k 4
1280.2.d.l 4
1280.2.d.m 4
1280.2.f $$\chi_{1280}(129, \cdot)$$ 1280.2.f.a 2 1
1280.2.f.b 2
1280.2.f.c 2
1280.2.f.d 2
1280.2.f.e 2
1280.2.f.f 2
1280.2.f.g 4
1280.2.f.h 4
1280.2.f.i 6
1280.2.f.j 6
1280.2.f.k 6
1280.2.f.l 6
1280.2.j $$\chi_{1280}(63, \cdot)$$ 1280.2.j.a 16 2
1280.2.j.b 16
1280.2.j.c 32
1280.2.j.d 32
1280.2.l $$\chi_{1280}(321, \cdot)$$ 1280.2.l.a 8 2
1280.2.l.b 8
1280.2.l.c 8
1280.2.l.d 8
1280.2.l.e 8
1280.2.l.f 8
1280.2.l.g 8
1280.2.l.h 8
1280.2.n $$\chi_{1280}(767, \cdot)$$ 1280.2.n.a 2 2
1280.2.n.b 2
1280.2.n.c 2
1280.2.n.d 2
1280.2.n.e 2
1280.2.n.f 2
1280.2.n.g 2
1280.2.n.h 2
1280.2.n.i 2
1280.2.n.j 2
1280.2.n.k 2
1280.2.n.l 2
1280.2.n.m 8
1280.2.n.n 8
1280.2.n.o 8
1280.2.n.p 8
1280.2.n.q 8
1280.2.n.r 12
1280.2.n.s 12
1280.2.o $$\chi_{1280}(127, \cdot)$$ 1280.2.o.a 2 2
1280.2.o.b 2
1280.2.o.c 2
1280.2.o.d 2
1280.2.o.e 2
1280.2.o.f 2
1280.2.o.g 2
1280.2.o.h 2
1280.2.o.i 2
1280.2.o.j 2
1280.2.o.k 2
1280.2.o.l 2
1280.2.o.m 2
1280.2.o.n 2
1280.2.o.o 2
1280.2.o.p 2
1280.2.o.q 4
1280.2.o.r 4
1280.2.o.s 12
1280.2.o.t 12
1280.2.o.u 12
1280.2.o.v 12
1280.2.q $$\chi_{1280}(449, \cdot)$$ 1280.2.q.a 16 2
1280.2.q.b 16
1280.2.q.c 32
1280.2.q.d 32
1280.2.s $$\chi_{1280}(703, \cdot)$$ 1280.2.s.a 16 2
1280.2.s.b 16
1280.2.s.c 32
1280.2.s.d 32
1280.2.u $$\chi_{1280}(543, \cdot)$$ n/a 176 4
1280.2.x $$\chi_{1280}(161, \cdot)$$ n/a 128 4
1280.2.z $$\chi_{1280}(289, \cdot)$$ n/a 176 4
1280.2.ba $$\chi_{1280}(223, \cdot)$$ n/a 176 4
1280.2.bd $$\chi_{1280}(47, \cdot)$$ n/a 368 8
1280.2.be $$\chi_{1280}(81, \cdot)$$ n/a 256 8
1280.2.bf $$\chi_{1280}(49, \cdot)$$ n/a 368 8
1280.2.bj $$\chi_{1280}(207, \cdot)$$ n/a 368 8
1280.2.bl $$\chi_{1280}(7, \cdot)$$ None 0 16
1280.2.bm $$\chi_{1280}(41, \cdot)$$ None 0 16
1280.2.bo $$\chi_{1280}(9, \cdot)$$ None 0 16
1280.2.br $$\chi_{1280}(87, \cdot)$$ None 0 16
1280.2.bt $$\chi_{1280}(3, \cdot)$$ n/a 6080 32
1280.2.bv $$\chi_{1280}(21, \cdot)$$ n/a 4096 32
1280.2.bw $$\chi_{1280}(29, \cdot)$$ n/a 6080 32
1280.2.by $$\chi_{1280}(43, \cdot)$$ n/a 6080 32

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1280))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1280)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(128))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(160))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(256))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(320))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(640))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1280))$$$$^{\oplus 1}$$