## Defining parameters

 Level: $$N$$ = $$280 = 2^{3} \cdot 5 \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$18$$ Newform subspaces: $$44$$ Sturm bound: $$9216$$ Trace bound: $$10$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(280))$$.

Total New Old
Modular forms 2592 1198 1394
Cusp forms 2017 1078 939
Eisenstein series 575 120 455

## Trace form

 $$1078q - 4q^{2} - 4q^{3} - 4q^{4} + 2q^{5} - 20q^{6} - 4q^{7} - 16q^{8} + 14q^{9} + O(q^{10})$$ $$1078q - 4q^{2} - 4q^{3} - 4q^{4} + 2q^{5} - 20q^{6} - 4q^{7} - 16q^{8} + 14q^{9} - 10q^{10} - 28q^{12} + 16q^{13} - 20q^{14} - 32q^{15} - 52q^{16} - 96q^{18} - 36q^{19} - 68q^{20} - 8q^{21} - 116q^{22} - 48q^{23} - 132q^{24} - 28q^{25} - 112q^{26} - 88q^{27} - 100q^{28} + 12q^{29} - 66q^{30} - 72q^{31} - 24q^{32} - 20q^{33} - 12q^{34} - 26q^{35} - 52q^{36} - 40q^{39} + 40q^{40} + 12q^{41} + 84q^{42} - 64q^{43} + 68q^{44} + 8q^{45} + 88q^{46} - 96q^{47} + 124q^{48} - 50q^{49} - 56q^{50} - 136q^{51} + 56q^{52} - 24q^{53} + 84q^{54} - 128q^{55} - 176q^{57} - 40q^{58} - 172q^{59} - 32q^{60} - 28q^{61} - 16q^{62} - 172q^{63} - 4q^{64} - 136q^{65} - 20q^{66} - 104q^{67} - 52q^{68} - 136q^{69} - 42q^{70} - 144q^{71} - 24q^{72} - 136q^{73} - 140q^{74} + 8q^{75} - 180q^{76} - 92q^{77} - 64q^{78} + 16q^{79} - 84q^{80} - 198q^{81} - 84q^{82} - 12q^{83} - 196q^{84} - 52q^{85} - 268q^{86} - 24q^{87} - 156q^{88} - 64q^{89} - 88q^{90} + 4q^{91} - 148q^{92} - 12q^{93} - 148q^{94} + 12q^{95} - 180q^{96} - 92q^{97} - 100q^{98} + 128q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(280))$$

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
280.2.a $$\chi_{280}(1, \cdot)$$ 280.2.a.a 1 1
280.2.a.b 1
280.2.a.c 2
280.2.a.d 2
280.2.b $$\chi_{280}(141, \cdot)$$ 280.2.b.a 2 1
280.2.b.b 2
280.2.b.c 8
280.2.b.d 12
280.2.e $$\chi_{280}(279, \cdot)$$ None 0 1
280.2.g $$\chi_{280}(169, \cdot)$$ 280.2.g.a 2 1
280.2.g.b 6
280.2.h $$\chi_{280}(251, \cdot)$$ 280.2.h.a 16 1
280.2.h.b 16
280.2.k $$\chi_{280}(111, \cdot)$$ None 0 1
280.2.l $$\chi_{280}(29, \cdot)$$ 280.2.l.a 36 1
280.2.n $$\chi_{280}(139, \cdot)$$ 280.2.n.a 4 1
280.2.n.b 40
280.2.q $$\chi_{280}(81, \cdot)$$ 280.2.q.a 2 2
280.2.q.b 2
280.2.q.c 2
280.2.q.d 4
280.2.q.e 6
280.2.s $$\chi_{280}(13, \cdot)$$ 280.2.s.a 8 2
280.2.s.b 8
280.2.s.c 72
280.2.t $$\chi_{280}(127, \cdot)$$ None 0 2
280.2.w $$\chi_{280}(43, \cdot)$$ 280.2.w.a 72 2
280.2.x $$\chi_{280}(97, \cdot)$$ 280.2.x.a 24 2
280.2.ba $$\chi_{280}(19, \cdot)$$ 280.2.ba.a 8 2
280.2.ba.b 80
280.2.bc $$\chi_{280}(31, \cdot)$$ None 0 2
280.2.bf $$\chi_{280}(109, \cdot)$$ 280.2.bf.a 88 2
280.2.bg $$\chi_{280}(9, \cdot)$$ 280.2.bg.a 24 2
280.2.bj $$\chi_{280}(131, \cdot)$$ 280.2.bj.a 4 2
280.2.bj.b 4
280.2.bj.c 4
280.2.bj.d 4
280.2.bj.e 24
280.2.bj.f 24
280.2.bl $$\chi_{280}(221, \cdot)$$ 280.2.bl.a 4 2
280.2.bl.b 60
280.2.bm $$\chi_{280}(159, \cdot)$$ None 0 2
280.2.bo $$\chi_{280}(17, \cdot)$$ 280.2.bo.a 48 4
280.2.br $$\chi_{280}(67, \cdot)$$ 280.2.br.a 176 4
280.2.bs $$\chi_{280}(23, \cdot)$$ None 0 4
280.2.bv $$\chi_{280}(117, \cdot)$$ 280.2.bv.a 4 4
280.2.bv.b 4
280.2.bv.c 4
280.2.bv.d 4
280.2.bv.e 160

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(280))$$ into lower level spaces

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