# Properties

 Label 880.2 Level 880 Weight 2 Dimension 11438 Nonzero newspaces 28 Newform subspaces 106 Sturm bound 92160 Trace bound 11

## Defining parameters

 Level: $$N$$ = $$880 = 2^{4} \cdot 5 \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$28$$ Newform subspaces: $$106$$ Sturm bound: $$92160$$ Trace bound: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(880))$$.

Total New Old
Modular forms 24160 11926 12234
Cusp forms 21921 11438 10483
Eisenstein series 2239 488 1751

## Trace form

 $$11438 q - 32 q^{2} - 26 q^{3} - 24 q^{4} - 59 q^{5} - 72 q^{6} - 18 q^{7} - 8 q^{8} - 2 q^{9} + O(q^{10})$$ $$11438 q - 32 q^{2} - 26 q^{3} - 24 q^{4} - 59 q^{5} - 72 q^{6} - 18 q^{7} - 8 q^{8} - 2 q^{9} - 44 q^{10} - 74 q^{11} - 80 q^{12} - 30 q^{13} - 40 q^{14} - q^{15} - 120 q^{16} - 54 q^{17} - 16 q^{18} + 26 q^{19} - 36 q^{20} - 52 q^{21} - 32 q^{22} - 24 q^{23} - 24 q^{24} + 5 q^{25} - 72 q^{26} - 38 q^{27} - 56 q^{28} - 10 q^{29} - 116 q^{30} - 146 q^{31} - 72 q^{32} - 66 q^{33} - 176 q^{34} - 35 q^{35} - 232 q^{36} - 46 q^{37} - 184 q^{38} + 50 q^{39} - 220 q^{40} - 6 q^{41} - 184 q^{42} + 40 q^{43} - 96 q^{44} - 126 q^{45} - 168 q^{46} + 106 q^{47} - 120 q^{48} + 22 q^{49} - 156 q^{50} + 102 q^{51} - 104 q^{52} + 2 q^{53} - 120 q^{54} + 5 q^{55} - 240 q^{56} + 110 q^{57} - 72 q^{58} + 26 q^{59} + 20 q^{60} - 150 q^{61} + 40 q^{62} - 112 q^{63} + 24 q^{64} - 30 q^{65} - 32 q^{66} - 160 q^{67} + 88 q^{68} - 44 q^{69} - 24 q^{70} - 198 q^{71} + 32 q^{72} - 126 q^{73} - 48 q^{74} - 297 q^{75} - 232 q^{76} - 202 q^{77} - 288 q^{78} - 306 q^{79} - 88 q^{80} - 394 q^{81} - 296 q^{82} - 302 q^{83} - 232 q^{84} - 215 q^{85} - 280 q^{86} - 432 q^{87} - 568 q^{88} - 132 q^{89} - 132 q^{90} - 234 q^{91} - 360 q^{92} - 258 q^{93} - 456 q^{94} - 199 q^{95} - 424 q^{96} - 254 q^{97} - 552 q^{98} - 202 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(880))$$

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
880.2.a $$\chi_{880}(1, \cdot)$$ 880.2.a.a 1 1
880.2.a.b 1
880.2.a.c 1
880.2.a.d 1
880.2.a.e 1
880.2.a.f 1
880.2.a.g 1
880.2.a.h 1
880.2.a.i 1
880.2.a.j 1
880.2.a.k 2
880.2.a.l 2
880.2.a.m 2
880.2.a.n 2
880.2.a.o 2
880.2.b $$\chi_{880}(529, \cdot)$$ 880.2.b.a 2 1
880.2.b.b 2
880.2.b.c 2
880.2.b.d 2
880.2.b.e 2
880.2.b.f 2
880.2.b.g 2
880.2.b.h 4
880.2.b.i 4
880.2.b.j 8
880.2.c $$\chi_{880}(439, \cdot)$$ None 0 1
880.2.f $$\chi_{880}(351, \cdot)$$ 880.2.f.a 2 1
880.2.f.b 2
880.2.f.c 4
880.2.f.d 8
880.2.f.e 8
880.2.g $$\chi_{880}(441, \cdot)$$ None 0 1
880.2.l $$\chi_{880}(89, \cdot)$$ None 0 1
880.2.m $$\chi_{880}(879, \cdot)$$ 880.2.m.a 2 1
880.2.m.b 2
880.2.m.c 4
880.2.m.d 4
880.2.m.e 8
880.2.m.f 8
880.2.m.g 8
880.2.p $$\chi_{880}(791, \cdot)$$ None 0 1
880.2.s $$\chi_{880}(67, \cdot)$$ 880.2.s.a 4 2
880.2.s.b 236
880.2.t $$\chi_{880}(197, \cdot)$$ 880.2.t.a 8 2
880.2.t.b 272
880.2.v $$\chi_{880}(131, \cdot)$$ 880.2.v.a 192 2
880.2.w $$\chi_{880}(221, \cdot)$$ 880.2.w.a 72 2
880.2.w.b 88
880.2.z $$\chi_{880}(23, \cdot)$$ None 0 2
880.2.bb $$\chi_{880}(153, \cdot)$$ None 0 2
880.2.bd $$\chi_{880}(417, \cdot)$$ 880.2.bd.a 4 2
880.2.bd.b 4
880.2.bd.c 4
880.2.bd.d 4
880.2.bd.e 4
880.2.bd.f 4
880.2.bd.g 4
880.2.bd.h 8
880.2.bd.i 32
880.2.bf $$\chi_{880}(287, \cdot)$$ 880.2.bf.a 2 2
880.2.bf.b 2
880.2.bf.c 2
880.2.bf.d 2
880.2.bf.e 6
880.2.bf.f 6
880.2.bf.g 20
880.2.bf.h 20
880.2.bh $$\chi_{880}(309, \cdot)$$ 880.2.bh.a 240 2
880.2.bi $$\chi_{880}(219, \cdot)$$ 880.2.bi.a 4 2
880.2.bi.b 4
880.2.bi.c 16
880.2.bi.d 256
880.2.bk $$\chi_{880}(243, \cdot)$$ 880.2.bk.a 4 2
880.2.bk.b 236
880.2.bl $$\chi_{880}(373, \cdot)$$ 880.2.bl.a 8 2
880.2.bl.b 272
880.2.bo $$\chi_{880}(81, \cdot)$$ 880.2.bo.a 4 4
880.2.bo.b 4
880.2.bo.c 8
880.2.bo.d 8
880.2.bo.e 8
880.2.bo.f 8
880.2.bo.g 8
880.2.bo.h 8
880.2.bo.i 12
880.2.bo.j 12
880.2.bo.k 16
880.2.bp $$\chi_{880}(151, \cdot)$$ None 0 4
880.2.bs $$\chi_{880}(79, \cdot)$$ 880.2.bs.a 48 4
880.2.bs.b 96
880.2.bt $$\chi_{880}(9, \cdot)$$ None 0 4
880.2.by $$\chi_{880}(201, \cdot)$$ None 0 4
880.2.bz $$\chi_{880}(271, \cdot)$$ 880.2.bz.a 16 4
880.2.bz.b 16
880.2.bz.c 32
880.2.bz.d 32
880.2.cc $$\chi_{880}(39, \cdot)$$ None 0 4
880.2.cd $$\chi_{880}(49, \cdot)$$ 880.2.cd.a 8 4
880.2.cd.b 16
880.2.cd.c 16
880.2.cd.d 24
880.2.cd.e 72
880.2.cg $$\chi_{880}(237, \cdot)$$ 880.2.cg.a 1120 8
880.2.ch $$\chi_{880}(3, \cdot)$$ 880.2.ch.a 1120 8
880.2.ci $$\chi_{880}(19, \cdot)$$ 880.2.ci.a 1120 8
880.2.cl $$\chi_{880}(69, \cdot)$$ 880.2.cl.a 1120 8
880.2.cm $$\chi_{880}(17, \cdot)$$ 880.2.cm.a 32 8
880.2.cm.b 48
880.2.cm.c 48
880.2.cm.d 144
880.2.co $$\chi_{880}(47, \cdot)$$ 880.2.co.a 96 8
880.2.co.b 192
880.2.cq $$\chi_{880}(103, \cdot)$$ None 0 8
880.2.cs $$\chi_{880}(57, \cdot)$$ None 0 8
880.2.cu $$\chi_{880}(141, \cdot)$$ 880.2.cu.a 768 8
880.2.cx $$\chi_{880}(51, \cdot)$$ 880.2.cx.a 768 8
880.2.cy $$\chi_{880}(13, \cdot)$$ 880.2.cy.a 1120 8
880.2.cz $$\chi_{880}(147, \cdot)$$ 880.2.cz.a 1120 8

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(880))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(880)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(88))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(110))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(176))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(220))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(440))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(880))$$$$^{\oplus 1}$$