# Properties

 Label 1280.4 Level 1280 Weight 4 Dimension 75720 Nonzero newspaces 22 Sturm bound 393216 Trace bound 50

## Defining parameters

 Level: $$N$$ = $$1280 = 2^{8} \cdot 5$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$22$$ Sturm bound: $$393216$$ Trace bound: $$50$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(1280))$$.

Total New Old
Modular forms 148864 76344 72520
Cusp forms 146048 75720 70328
Eisenstein series 2816 624 2192

## Trace form

 $$75720 q - 64 q^{2} - 48 q^{3} - 64 q^{4} - 96 q^{5} - 192 q^{6} - 48 q^{7} - 64 q^{8} - 80 q^{9} + O(q^{10})$$ $$75720 q - 64 q^{2} - 48 q^{3} - 64 q^{4} - 96 q^{5} - 192 q^{6} - 48 q^{7} - 64 q^{8} - 80 q^{9} - 96 q^{10} - 144 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 72 q^{15} - 192 q^{16} - 96 q^{17} - 64 q^{18} - 48 q^{19} - 96 q^{20} - 192 q^{21} - 64 q^{22} - 48 q^{23} - 64 q^{24} - 120 q^{25} - 192 q^{26} - 48 q^{27} - 64 q^{28} - 64 q^{29} - 96 q^{30} - 128 q^{31} - 64 q^{32} - 112 q^{33} - 64 q^{34} - 72 q^{35} - 192 q^{36} - 64 q^{37} - 64 q^{38} - 48 q^{39} - 96 q^{40} - 240 q^{41} - 64 q^{42} - 48 q^{43} - 64 q^{44} + 120 q^{45} - 192 q^{46} - 48 q^{47} - 64 q^{48} + 2648 q^{49} - 96 q^{50} + 5808 q^{51} - 64 q^{52} + 2944 q^{53} - 64 q^{54} + 504 q^{55} - 192 q^{56} - 2768 q^{57} - 64 q^{58} - 5552 q^{59} - 96 q^{60} - 7488 q^{61} - 64 q^{62} - 10144 q^{63} - 64 q^{64} - 4120 q^{65} - 192 q^{66} - 8208 q^{67} - 64 q^{68} - 4288 q^{69} - 96 q^{70} - 1040 q^{71} - 64 q^{72} + 3376 q^{73} - 64 q^{74} + 4344 q^{75} - 192 q^{76} + 7552 q^{77} - 64 q^{78} + 11280 q^{79} - 96 q^{80} + 5544 q^{81} - 64 q^{82} - 48 q^{83} - 64 q^{84} + 904 q^{85} - 192 q^{86} - 48 q^{87} - 64 q^{88} - 80 q^{89} - 96 q^{90} - 144 q^{91} - 64 q^{92} - 928 q^{93} - 64 q^{94} - 64 q^{95} - 192 q^{96} - 112 q^{97} - 64 q^{98} + 384 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(1280))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
1280.4.a $$\chi_{1280}(1, \cdot)$$ 1280.4.a.a 2 1
1280.4.a.b 2
1280.4.a.c 2
1280.4.a.d 2
1280.4.a.e 2
1280.4.a.f 2
1280.4.a.g 2
1280.4.a.h 2
1280.4.a.i 2
1280.4.a.j 2
1280.4.a.k 2
1280.4.a.l 2
1280.4.a.m 2
1280.4.a.n 2
1280.4.a.o 2
1280.4.a.p 2
1280.4.a.q 4
1280.4.a.r 4
1280.4.a.s 4
1280.4.a.t 4
1280.4.a.u 4
1280.4.a.v 4
1280.4.a.w 4
1280.4.a.x 4
1280.4.a.y 4
1280.4.a.z 4
1280.4.a.ba 6
1280.4.a.bb 6
1280.4.a.bc 6
1280.4.a.bd 6
1280.4.c $$\chi_{1280}(769, \cdot)$$ n/a 140 1
1280.4.d $$\chi_{1280}(641, \cdot)$$ 1280.4.d.a 2 1
1280.4.d.b 2
1280.4.d.c 2
1280.4.d.d 2
1280.4.d.e 2
1280.4.d.f 2
1280.4.d.g 2
1280.4.d.h 2
1280.4.d.i 2
1280.4.d.j 2
1280.4.d.k 2
1280.4.d.l 2
1280.4.d.m 2
1280.4.d.n 2
1280.4.d.o 2
1280.4.d.p 2
1280.4.d.q 4
1280.4.d.r 4
1280.4.d.s 4
1280.4.d.t 4
1280.4.d.u 4
1280.4.d.v 4
1280.4.d.w 4
1280.4.d.x 4
1280.4.d.y 4
1280.4.d.z 6
1280.4.d.ba 6
1280.4.d.bb 8
1280.4.d.bc 8
1280.4.f $$\chi_{1280}(129, \cdot)$$ n/a 140 1
1280.4.j $$\chi_{1280}(63, \cdot)$$ n/a 288 2
1280.4.l $$\chi_{1280}(321, \cdot)$$ n/a 192 2
1280.4.n $$\chi_{1280}(767, \cdot)$$ n/a 280 2
1280.4.o $$\chi_{1280}(127, \cdot)$$ n/a 280 2
1280.4.q $$\chi_{1280}(449, \cdot)$$ n/a 288 2
1280.4.s $$\chi_{1280}(703, \cdot)$$ n/a 288 2
1280.4.u $$\chi_{1280}(543, \cdot)$$ n/a 560 4
1280.4.x $$\chi_{1280}(161, \cdot)$$ n/a 384 4
1280.4.z $$\chi_{1280}(289, \cdot)$$ n/a 560 4
1280.4.ba $$\chi_{1280}(223, \cdot)$$ n/a 560 4
1280.4.bd $$\chi_{1280}(47, \cdot)$$ n/a 1136 8
1280.4.be $$\chi_{1280}(81, \cdot)$$ n/a 768 8
1280.4.bf $$\chi_{1280}(49, \cdot)$$ n/a 1136 8
1280.4.bj $$\chi_{1280}(207, \cdot)$$ n/a 1136 8
1280.4.bl $$\chi_{1280}(7, \cdot)$$ None 0 16
1280.4.bm $$\chi_{1280}(41, \cdot)$$ None 0 16
1280.4.bo $$\chi_{1280}(9, \cdot)$$ None 0 16
1280.4.br $$\chi_{1280}(87, \cdot)$$ None 0 16
1280.4.bt $$\chi_{1280}(3, \cdot)$$ n/a 18368 32
1280.4.bv $$\chi_{1280}(21, \cdot)$$ n/a 12288 32
1280.4.bw $$\chi_{1280}(29, \cdot)$$ n/a 18368 32
1280.4.by $$\chi_{1280}(43, \cdot)$$ n/a 18368 32

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(1280))$$ into lower level spaces

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