# Properties

 Label 1120.2 Level 1120 Weight 2 Dimension 17916 Nonzero newspaces 40 Sturm bound 147456 Trace bound 21

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## Defining parameters

 Level: $$N$$ = $$1120 = 2^{5} \cdot 5 \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$40$$ Sturm bound: $$147456$$ Trace bound: $$21$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1120))$$.

Total New Old
Modular forms 38400 18516 19884
Cusp forms 35329 17916 17413
Eisenstein series 3071 600 2471

## Trace form

 $$17916q - 32q^{2} - 28q^{3} - 32q^{4} - 52q^{5} - 96q^{6} - 32q^{7} - 80q^{8} - 52q^{9} + O(q^{10})$$ $$17916q - 32q^{2} - 28q^{3} - 32q^{4} - 52q^{5} - 96q^{6} - 32q^{7} - 80q^{8} - 52q^{9} - 32q^{10} - 76q^{11} + 32q^{12} - 8q^{13} - 8q^{14} - 84q^{15} - 16q^{16} + 48q^{18} - 20q^{19} - 16q^{20} - 120q^{21} - 32q^{22} + 4q^{23} - 80q^{24} - 80q^{25} - 176q^{26} + 104q^{27} - 80q^{28} - 104q^{29} - 112q^{30} + 36q^{31} - 112q^{32} - 8q^{33} - 80q^{34} + 2q^{35} - 352q^{36} + 40q^{37} + 160q^{39} - 24q^{40} - 32q^{41} + 56q^{43} + 128q^{44} + 116q^{45} + 32q^{46} + 108q^{47} + 176q^{48} + 84q^{49} - 40q^{50} + 60q^{51} + 200q^{53} + 16q^{54} - 20q^{55} - 96q^{56} + 32q^{57} - 48q^{58} - 52q^{59} - 184q^{60} + 88q^{61} - 112q^{62} - 16q^{63} - 320q^{64} - 156q^{65} - 448q^{66} - 164q^{67} - 176q^{68} - 216q^{70} - 352q^{71} - 416q^{72} - 192q^{73} - 320q^{74} - 214q^{75} - 352q^{76} - 104q^{77} - 528q^{78} - 132q^{79} - 376q^{80} - 332q^{81} - 352q^{82} + 64q^{83} - 304q^{84} - 280q^{85} - 432q^{86} + 144q^{87} - 368q^{88} - 128q^{89} - 648q^{90} - 112q^{91} - 560q^{92} - 368q^{93} - 496q^{94} + 38q^{95} - 816q^{96} - 256q^{97} - 464q^{98} + 32q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1120))$$

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
1120.2.a $$\chi_{1120}(1, \cdot)$$ 1120.2.a.a 1 1
1120.2.a.b 1
1120.2.a.c 1
1120.2.a.d 1
1120.2.a.e 1
1120.2.a.f 1
1120.2.a.g 1
1120.2.a.h 1
1120.2.a.i 1
1120.2.a.j 1
1120.2.a.k 1
1120.2.a.l 1
1120.2.a.m 1
1120.2.a.n 1
1120.2.a.o 1
1120.2.a.p 1
1120.2.a.q 2
1120.2.a.r 2
1120.2.a.s 2
1120.2.a.t 2
1120.2.b $$\chi_{1120}(561, \cdot)$$ 1120.2.b.a 2 1
1120.2.b.b 2
1120.2.b.c 8
1120.2.b.d 12
1120.2.e $$\chi_{1120}(1119, \cdot)$$ 1120.2.e.a 48 1
1120.2.g $$\chi_{1120}(449, \cdot)$$ 1120.2.g.a 4 1
1120.2.g.b 10
1120.2.g.c 10
1120.2.g.d 12
1120.2.h $$\chi_{1120}(111, \cdot)$$ 1120.2.h.a 16 1
1120.2.h.b 16
1120.2.k $$\chi_{1120}(671, \cdot)$$ 1120.2.k.a 16 1
1120.2.k.b 16
1120.2.l $$\chi_{1120}(1009, \cdot)$$ 1120.2.l.a 36 1
1120.2.n $$\chi_{1120}(559, \cdot)$$ 1120.2.n.a 4 1
1120.2.n.b 40
1120.2.q $$\chi_{1120}(641, \cdot)$$ 1120.2.q.a 2 2
1120.2.q.b 2
1120.2.q.c 2
1120.2.q.d 2
1120.2.q.e 4
1120.2.q.f 4
1120.2.q.g 8
1120.2.q.h 8
1120.2.q.i 10
1120.2.q.j 10
1120.2.q.k 12
1120.2.r $$\chi_{1120}(153, \cdot)$$ None 0 2
1120.2.t $$\chi_{1120}(407, \cdot)$$ None 0 2
1120.2.w $$\chi_{1120}(433, \cdot)$$ 1120.2.w.a 8 2
1120.2.w.b 8
1120.2.w.c 72
1120.2.x $$\chi_{1120}(127, \cdot)$$ 1120.2.x.a 4 2
1120.2.x.b 4
1120.2.x.c 12
1120.2.x.d 12
1120.2.x.e 20
1120.2.x.f 20
1120.2.bb $$\chi_{1120}(169, \cdot)$$ None 0 2
1120.2.bc $$\chi_{1120}(391, \cdot)$$ None 0 2
1120.2.bd $$\chi_{1120}(281, \cdot)$$ None 0 2
1120.2.be $$\chi_{1120}(279, \cdot)$$ None 0 2
1120.2.bi $$\chi_{1120}(463, \cdot)$$ 1120.2.bi.a 72 2
1120.2.bj $$\chi_{1120}(97, \cdot)$$ 1120.2.bj.a 8 2
1120.2.bj.b 8
1120.2.bj.c 32
1120.2.bj.d 48
1120.2.bl $$\chi_{1120}(183, \cdot)$$ None 0 2
1120.2.bn $$\chi_{1120}(377, \cdot)$$ None 0 2
1120.2.bq $$\chi_{1120}(719, \cdot)$$ 1120.2.bq.a 8 2
1120.2.bq.b 80
1120.2.bs $$\chi_{1120}(31, \cdot)$$ 1120.2.bs.a 32 2
1120.2.bs.b 32
1120.2.bv $$\chi_{1120}(529, \cdot)$$ 1120.2.bv.a 88 2
1120.2.bw $$\chi_{1120}(289, \cdot)$$ 1120.2.bw.a 4 2
1120.2.bw.b 4
1120.2.bw.c 8
1120.2.bw.d 8
1120.2.bw.e 8
1120.2.bw.f 8
1120.2.bw.g 16
1120.2.bw.h 40
1120.2.bz $$\chi_{1120}(271, \cdot)$$ 1120.2.bz.a 4 2
1120.2.bz.b 4
1120.2.bz.c 4
1120.2.bz.d 4
1120.2.bz.e 24
1120.2.bz.f 24
1120.2.cb $$\chi_{1120}(81, \cdot)$$ 1120.2.cb.a 4 2
1120.2.cb.b 60
1120.2.cc $$\chi_{1120}(159, \cdot)$$ 1120.2.cc.a 8 2
1120.2.cc.b 8
1120.2.cc.c 80
1120.2.cg $$\chi_{1120}(141, \cdot)$$ n/a 384 4
1120.2.ch $$\chi_{1120}(139, \cdot)$$ n/a 752 4
1120.2.ci $$\chi_{1120}(13, \cdot)$$ n/a 752 4
1120.2.cj $$\chi_{1120}(43, \cdot)$$ n/a 576 4
1120.2.cm $$\chi_{1120}(267, \cdot)$$ n/a 576 4
1120.2.cn $$\chi_{1120}(237, \cdot)$$ n/a 752 4
1120.2.cs $$\chi_{1120}(251, \cdot)$$ n/a 512 4
1120.2.ct $$\chi_{1120}(29, \cdot)$$ n/a 576 4
1120.2.cv $$\chi_{1120}(23, \cdot)$$ None 0 4
1120.2.cx $$\chi_{1120}(73, \cdot)$$ None 0 4
1120.2.cy $$\chi_{1120}(33, \cdot)$$ n/a 192 4
1120.2.db $$\chi_{1120}(207, \cdot)$$ n/a 176 4
1120.2.de $$\chi_{1120}(199, \cdot)$$ None 0 4
1120.2.df $$\chi_{1120}(121, \cdot)$$ None 0 4
1120.2.dg $$\chi_{1120}(311, \cdot)$$ None 0 4
1120.2.dh $$\chi_{1120}(9, \cdot)$$ None 0 4
1120.2.dk $$\chi_{1120}(543, \cdot)$$ n/a 192 4
1120.2.dn $$\chi_{1120}(17, \cdot)$$ n/a 176 4
1120.2.dp $$\chi_{1120}(297, \cdot)$$ None 0 4
1120.2.dr $$\chi_{1120}(247, \cdot)$$ None 0 4
1120.2.ds $$\chi_{1120}(109, \cdot)$$ n/a 1504 8
1120.2.dt $$\chi_{1120}(131, \cdot)$$ n/a 1024 8
1120.2.dy $$\chi_{1120}(107, \cdot)$$ n/a 1504 8
1120.2.dz $$\chi_{1120}(157, \cdot)$$ n/a 1504 8
1120.2.ec $$\chi_{1120}(117, \cdot)$$ n/a 1504 8
1120.2.ed $$\chi_{1120}(67, \cdot)$$ n/a 1504 8
1120.2.ee $$\chi_{1120}(19, \cdot)$$ n/a 1504 8
1120.2.ef $$\chi_{1120}(221, \cdot)$$ n/a 1024 8

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1120))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1120)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(70))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(140))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(160))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(224))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(280))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(560))$$$$^{\oplus 2}$$