# Properties

 Label 560.2 Level 560 Weight 2 Dimension 4418 Nonzero newspaces 28 Newform subspaces 89 Sturm bound 36864 Trace bound 11

## Defining parameters

 Level: $$N$$ = $$560 = 2^{4} \cdot 5 \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$28$$ Newform subspaces: $$89$$ Sturm bound: $$36864$$ Trace bound: $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(560))$$.

Total New Old
Modular forms 9888 4690 5198
Cusp forms 8545 4418 4127
Eisenstein series 1343 272 1071

## Trace form

 $$4418 q - 16 q^{2} - 14 q^{3} - 8 q^{4} - 29 q^{5} - 24 q^{6} - 12 q^{7} - 16 q^{8} + 2 q^{9} + O(q^{10})$$ $$4418 q - 16 q^{2} - 14 q^{3} - 8 q^{4} - 29 q^{5} - 24 q^{6} - 12 q^{7} - 16 q^{8} + 2 q^{9} - 20 q^{10} - 22 q^{11} - 24 q^{12} - 4 q^{13} - 24 q^{14} - 10 q^{15} - 72 q^{16} - 18 q^{17} + 50 q^{19} - 12 q^{20} - 22 q^{21} - 32 q^{22} + 54 q^{23} - 8 q^{24} + 35 q^{25} - 24 q^{26} + 16 q^{27} - 32 q^{28} + 4 q^{29} - 92 q^{30} - 62 q^{31} - 56 q^{32} - 38 q^{33} - 120 q^{34} - 19 q^{35} - 256 q^{36} - 42 q^{37} - 168 q^{38} - 64 q^{39} - 196 q^{40} - 68 q^{41} - 240 q^{42} - 28 q^{43} - 232 q^{44} - 120 q^{45} - 240 q^{46} + 22 q^{47} - 344 q^{48} - 106 q^{49} - 192 q^{50} - 42 q^{51} - 304 q^{52} - 114 q^{53} - 440 q^{54} - 26 q^{55} - 240 q^{56} - 124 q^{57} - 224 q^{58} - 10 q^{59} - 124 q^{60} - 186 q^{61} - 160 q^{62} - 104 q^{63} - 152 q^{64} - 14 q^{65} - 136 q^{66} - 142 q^{67} - 16 q^{68} - 108 q^{69} + 4 q^{70} - 136 q^{71} + 56 q^{72} + 86 q^{73} + 168 q^{74} - 185 q^{75} + 136 q^{76} + 74 q^{77} + 224 q^{78} - 110 q^{79} + 156 q^{80} + 68 q^{81} + 120 q^{82} - 88 q^{83} + 120 q^{84} - 22 q^{85} + 88 q^{86} - 160 q^{87} + 200 q^{88} + 138 q^{89} + 284 q^{90} - 192 q^{91} - 24 q^{92} + 154 q^{93} + 184 q^{94} - 167 q^{95} + 264 q^{96} + 76 q^{97} + 136 q^{98} - 408 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(560))$$

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
560.2.a $$\chi_{560}(1, \cdot)$$ 560.2.a.a 1 1
560.2.a.b 1
560.2.a.c 1
560.2.a.d 1
560.2.a.e 1
560.2.a.f 1
560.2.a.g 2
560.2.a.h 2
560.2.a.i 2
560.2.b $$\chi_{560}(281, \cdot)$$ None 0 1
560.2.e $$\chi_{560}(559, \cdot)$$ 560.2.e.a 4 1
560.2.e.b 4
560.2.e.c 8
560.2.e.d 8
560.2.g $$\chi_{560}(449, \cdot)$$ 560.2.g.a 2 1
560.2.g.b 2
560.2.g.c 2
560.2.g.d 2
560.2.g.e 4
560.2.g.f 6
560.2.h $$\chi_{560}(391, \cdot)$$ None 0 1
560.2.k $$\chi_{560}(111, \cdot)$$ 560.2.k.a 8 1
560.2.k.b 8
560.2.l $$\chi_{560}(169, \cdot)$$ None 0 1
560.2.n $$\chi_{560}(279, \cdot)$$ None 0 1
560.2.q $$\chi_{560}(81, \cdot)$$ 560.2.q.a 2 2
560.2.q.b 2
560.2.q.c 2
560.2.q.d 2
560.2.q.e 2
560.2.q.f 2
560.2.q.g 2
560.2.q.h 2
560.2.q.i 2
560.2.q.j 4
560.2.q.k 4
560.2.q.l 6
560.2.r $$\chi_{560}(237, \cdot)$$ 560.2.r.a 184 2
560.2.t $$\chi_{560}(43, \cdot)$$ 560.2.t.a 144 2
560.2.w $$\chi_{560}(153, \cdot)$$ None 0 2
560.2.x $$\chi_{560}(127, \cdot)$$ 560.2.x.a 12 2
560.2.x.b 24
560.2.bb $$\chi_{560}(29, \cdot)$$ 560.2.bb.a 2 2
560.2.bb.b 2
560.2.bb.c 70
560.2.bb.d 70
560.2.bc $$\chi_{560}(251, \cdot)$$ 560.2.bc.a 128 2
560.2.bd $$\chi_{560}(141, \cdot)$$ 560.2.bd.a 44 2
560.2.bd.b 52
560.2.be $$\chi_{560}(139, \cdot)$$ 560.2.be.a 184 2
560.2.bi $$\chi_{560}(183, \cdot)$$ None 0 2
560.2.bj $$\chi_{560}(97, \cdot)$$ 560.2.bj.a 4 2
560.2.bj.b 8
560.2.bj.c 8
560.2.bj.d 24
560.2.bl $$\chi_{560}(267, \cdot)$$ 560.2.bl.a 144 2
560.2.bn $$\chi_{560}(13, \cdot)$$ 560.2.bn.a 184 2
560.2.bq $$\chi_{560}(199, \cdot)$$ None 0 2
560.2.bs $$\chi_{560}(31, \cdot)$$ 560.2.bs.a 8 2
560.2.bs.b 12
560.2.bs.c 12
560.2.bv $$\chi_{560}(9, \cdot)$$ None 0 2
560.2.bw $$\chi_{560}(289, \cdot)$$ 560.2.bw.a 4 2
560.2.bw.b 4
560.2.bw.c 4
560.2.bw.d 4
560.2.bw.e 4
560.2.bw.f 24
560.2.bz $$\chi_{560}(311, \cdot)$$ None 0 2
560.2.cb $$\chi_{560}(121, \cdot)$$ None 0 2
560.2.cc $$\chi_{560}(159, \cdot)$$ 560.2.cc.a 4 2
560.2.cc.b 4
560.2.cc.c 4
560.2.cc.d 4
560.2.cc.e 8
560.2.cc.f 8
560.2.cc.g 8
560.2.cc.h 8
560.2.cf $$\chi_{560}(107, \cdot)$$ 560.2.cf.a 368 4
560.2.ch $$\chi_{560}(117, \cdot)$$ 560.2.ch.a 4 4
560.2.ch.b 4
560.2.ch.c 360
560.2.ci $$\chi_{560}(17, \cdot)$$ 560.2.ci.a 4 4
560.2.ci.b 4
560.2.ci.c 16
560.2.ci.d 16
560.2.ci.e 48
560.2.cl $$\chi_{560}(23, \cdot)$$ None 0 4
560.2.co $$\chi_{560}(19, \cdot)$$ 560.2.co.a 368 4
560.2.cp $$\chi_{560}(221, \cdot)$$ 560.2.cp.a 256 4
560.2.cq $$\chi_{560}(131, \cdot)$$ 560.2.cq.a 256 4
560.2.cr $$\chi_{560}(109, \cdot)$$ 560.2.cr.a 368 4
560.2.cu $$\chi_{560}(207, \cdot)$$ 560.2.cu.a 8 4
560.2.cu.b 24
560.2.cu.c 32
560.2.cu.d 32
560.2.cx $$\chi_{560}(73, \cdot)$$ None 0 4
560.2.cz $$\chi_{560}(157, \cdot)$$ 560.2.cz.a 4 4
560.2.cz.b 4
560.2.cz.c 360
560.2.db $$\chi_{560}(67, \cdot)$$ 560.2.db.a 368 4

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(560))$$ into lower level spaces

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