# Properties

 Label 280.3 Level 280 Weight 3 Dimension 2216 Nonzero newspaces 18 Newform subspaces 29 Sturm bound 13824 Trace bound 6

## Defining parameters

 Level: $$N$$ = $$280 = 2^{3} \cdot 5 \cdot 7$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$18$$ Newform subspaces: $$29$$ Sturm bound: $$13824$$ Trace bound: $$6$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(280))$$.

Total New Old
Modular forms 4896 2336 2560
Cusp forms 4320 2216 2104
Eisenstein series 576 120 456

## Trace form

 $$2216q - 12q^{2} - 12q^{3} + 12q^{4} - 8q^{5} - 4q^{6} - 16q^{7} - 48q^{8} - 76q^{9} + O(q^{10})$$ $$2216q - 12q^{2} - 12q^{3} + 12q^{4} - 8q^{5} - 4q^{6} - 16q^{7} - 48q^{8} - 76q^{9} - 10q^{10} + 28q^{11} + 36q^{12} + 76q^{13} + 52q^{14} + 140q^{15} + 140q^{16} + 76q^{17} + 200q^{18} + 36q^{19} + 76q^{20} + 112q^{21} + 52q^{22} - 52q^{23} - 4q^{24} + 16q^{25} - 184q^{26} - 48q^{27} - 276q^{28} - 642q^{30} - 44q^{31} - 712q^{32} - 288q^{33} - 844q^{34} - 98q^{35} - 868q^{36} - 52q^{37} - 152q^{38} - 120q^{39} - 80q^{40} - 336q^{41} - 300q^{42} + 24q^{43} + 100q^{44} - 32q^{45} + 96q^{46} + 660q^{47} + 220q^{48} + 588q^{49} + 872q^{50} + 900q^{51} + 648q^{52} + 492q^{53} + 460q^{54} + 296q^{55} + 224q^{56} + 688q^{57} + 296q^{58} - 468q^{59} + 216q^{60} + 120q^{61} + 392q^{62} - 1040q^{63} + 156q^{64} - 28q^{65} + 340q^{66} - 1356q^{67} + 156q^{68} + 206q^{70} - 680q^{71} + 568q^{72} - 500q^{73} + 228q^{74} - 1186q^{75} + 236q^{76} + 72q^{77} + 352q^{78} - 156q^{79} + 212q^{80} - 648q^{81} + 1324q^{82} + 656q^{83} + 572q^{84} - 540q^{85} + 916q^{86} + 368q^{87} + 676q^{88} - 632q^{89} + 1376q^{90} - 696q^{91} - 388q^{92} - 1032q^{93} - 1332q^{94} - 106q^{95} - 2132q^{96} + 596q^{97} - 3188q^{98} - 1392q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(280))$$

We only show spaces with odd 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
280.3.c $$\chi_{280}(69, \cdot)$$ 280.3.c.a 1 1
280.3.c.b 1
280.3.c.c 1
280.3.c.d 1
280.3.c.e 4
280.3.c.f 4
280.3.c.g 80
280.3.d $$\chi_{280}(71, \cdot)$$ None 0 1
280.3.f $$\chi_{280}(41, \cdot)$$ 280.3.f.a 16 1
280.3.i $$\chi_{280}(99, \cdot)$$ 280.3.i.a 72 1
280.3.j $$\chi_{280}(239, \cdot)$$ None 0 1
280.3.m $$\chi_{280}(181, \cdot)$$ 280.3.m.a 64 1
280.3.o $$\chi_{280}(211, \cdot)$$ 280.3.o.a 48 1
280.3.p $$\chi_{280}(209, \cdot)$$ 280.3.p.a 24 1
280.3.r $$\chi_{280}(167, \cdot)$$ None 0 2
280.3.u $$\chi_{280}(197, \cdot)$$ 280.3.u.a 144 2
280.3.v $$\chi_{280}(57, \cdot)$$ 280.3.v.a 16 2
280.3.v.b 20
280.3.y $$\chi_{280}(27, \cdot)$$ 280.3.y.a 184 2
280.3.z $$\chi_{280}(11, \cdot)$$ 280.3.z.a 128 2
280.3.bb $$\chi_{280}(89, \cdot)$$ 280.3.bb.a 48 2
280.3.bd $$\chi_{280}(39, \cdot)$$ None 0 2
280.3.be $$\chi_{280}(61, \cdot)$$ 280.3.be.a 4 2
280.3.be.b 124
280.3.bh $$\chi_{280}(201, \cdot)$$ 280.3.bh.a 32 2
280.3.bi $$\chi_{280}(179, \cdot)$$ 280.3.bi.a 4 2
280.3.bi.b 4
280.3.bi.c 176
280.3.bk $$\chi_{280}(229, \cdot)$$ 280.3.bk.a 184 2
280.3.bn $$\chi_{280}(151, \cdot)$$ None 0 2
280.3.bp $$\chi_{280}(3, \cdot)$$ 280.3.bp.a 368 4
280.3.bq $$\chi_{280}(137, \cdot)$$ 280.3.bq.a 48 4
280.3.bq.b 48
280.3.bt $$\chi_{280}(37, \cdot)$$ 280.3.bt.a 368 4
280.3.bu $$\chi_{280}(47, \cdot)$$ None 0 4

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(280))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(280)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(70))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(140))$$$$^{\oplus 2}$$