# Properties

 Label 935.2 Level 935 Weight 2 Dimension 30131 Nonzero newspaces 36 Newforms 57 Sturm bound 138240 Trace bound 10

## Defining parameters

 Level: $$N$$ = $$935 = 5 \cdot 11 \cdot 17$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$36$$ Newforms: $$57$$ Sturm bound: $$138240$$ Trace bound: $$10$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(935))$$.

Total New Old
Modular forms 35840 31747 4093
Cusp forms 33281 30131 3150
Eisenstein series 2559 1616 943

## Trace form

 $$30131q - 99q^{2} - 96q^{3} - 87q^{4} - 159q^{5} - 308q^{6} - 104q^{7} - 103q^{8} - 109q^{9} + O(q^{10})$$ $$30131q - 99q^{2} - 96q^{3} - 87q^{4} - 159q^{5} - 308q^{6} - 104q^{7} - 103q^{8} - 109q^{9} - 191q^{10} - 385q^{11} - 340q^{12} - 118q^{13} - 160q^{14} - 238q^{15} - 495q^{16} - 145q^{17} - 367q^{18} - 140q^{19} - 267q^{20} - 424q^{21} - 207q^{22} - 268q^{23} - 308q^{24} - 275q^{25} - 522q^{26} - 204q^{27} - 352q^{28} - 198q^{29} - 384q^{30} - 436q^{31} - 343q^{32} - 272q^{33} - 499q^{34} - 484q^{35} - 731q^{36} - 242q^{37} - 340q^{38} - 352q^{39} - 319q^{40} - 554q^{41} - 504q^{42} - 236q^{43} - 275q^{44} - 457q^{45} - 400q^{46} - 144q^{47} - 292q^{48} - 85q^{49} - 151q^{50} - 392q^{51} - 218q^{52} - 222q^{53} - 368q^{54} - 187q^{55} - 984q^{56} - 392q^{57} - 210q^{58} - 264q^{59} - 424q^{60} - 414q^{61} - 496q^{62} - 456q^{63} - 119q^{64} - 302q^{65} - 692q^{66} - 344q^{67} - 347q^{68} - 548q^{69} - 296q^{70} - 452q^{71} - 347q^{72} - 226q^{73} - 274q^{74} - 330q^{75} - 412q^{76} - 312q^{77} - 504q^{78} - 208q^{79} - 151q^{80} - 453q^{81} - 38q^{82} - 260q^{83} - 40q^{84} - 47q^{85} - 964q^{86} - 208q^{87} - 355q^{88} - 334q^{89} - 47q^{90} - 432q^{91} - 192q^{92} - 132q^{93} - 144q^{94} - 140q^{95} - 572q^{96} + 26q^{97} - 195q^{98} - 129q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(935))$$

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
935.2.a $$\chi_{935}(1, \cdot)$$ 935.2.a.a 1 1
935.2.a.b 1
935.2.a.c 3
935.2.a.d 3
935.2.a.e 3
935.2.a.f 3
935.2.a.g 4
935.2.a.h 6
935.2.a.i 9
935.2.a.j 11
935.2.a.k 11
935.2.b $$\chi_{935}(749, \cdot)$$ 935.2.b.a 36 1
935.2.b.b 44
935.2.e $$\chi_{935}(254, \cdot)$$ 935.2.e.a 88 1
935.2.f $$\chi_{935}(441, \cdot)$$ 935.2.f.a 26 1
935.2.f.b 34
935.2.i $$\chi_{935}(166, \cdot)$$ 935.2.i.a 52 2
935.2.i.b 68
935.2.l $$\chi_{935}(98, \cdot)$$ 935.2.l.a 208 2
935.2.m $$\chi_{935}(307, \cdot)$$ 935.2.m.a 192 2
935.2.p $$\chi_{935}(373, \cdot)$$ 935.2.p.a 208 2
935.2.q $$\chi_{935}(208, \cdot)$$ 935.2.q.a 208 2
935.2.s $$\chi_{935}(89, \cdot)$$ 935.2.s.a 176 2
935.2.u $$\chi_{935}(86, \cdot)$$ 935.2.u.a 4 4
935.2.u.b 4
935.2.u.c 8
935.2.u.d 52
935.2.u.e 60
935.2.u.f 60
935.2.u.g 68
935.2.w $$\chi_{935}(417, \cdot)$$ 935.2.w.a 416 4
935.2.x $$\chi_{935}(111, \cdot)$$ 935.2.x.a 104 4
935.2.x.b 136
935.2.z $$\chi_{935}(144, \cdot)$$ 935.2.z.a 368 4
935.2.bc $$\chi_{935}(32, \cdot)$$ 935.2.bc.a 416 4
935.2.bf $$\chi_{935}(16, \cdot)$$ 935.2.bf.a 288 4
935.2.bg $$\chi_{935}(169, \cdot)$$ 935.2.bg.a 416 4
935.2.bj $$\chi_{935}(69, \cdot)$$ 935.2.bj.a 384 4
935.2.bl $$\chi_{935}(133, \cdot)$$ 935.2.bl.a 720 8
935.2.bm $$\chi_{935}(131, \cdot)$$ 935.2.bm.a 576 8
935.2.bp $$\chi_{935}(54, \cdot)$$ 935.2.bp.a 64 8
935.2.bp.b 768
935.2.bq $$\chi_{935}(12, \cdot)$$ 935.2.bq.a 720 8
935.2.bt $$\chi_{935}(4, \cdot)$$ 935.2.bt.a 832 8
935.2.bv $$\chi_{935}(123, \cdot)$$ 935.2.bv.a 832 8
935.2.bw $$\chi_{935}(118, \cdot)$$ 935.2.bw.a 832 8
935.2.bz $$\chi_{935}(18, \cdot)$$ 935.2.bz.a 768 8
935.2.ca $$\chi_{935}(13, \cdot)$$ 935.2.ca.a 832 8
935.2.cd $$\chi_{935}(81, \cdot)$$ 935.2.cd.a 576 8
935.2.cf $$\chi_{935}(2, \cdot)$$ 935.2.cf.a 1664 16
935.2.cg $$\chi_{935}(9, \cdot)$$ 935.2.cg.a 1664 16
935.2.ci $$\chi_{935}(26, \cdot)$$ 935.2.ci.a 1152 16
935.2.cl $$\chi_{935}(83, \cdot)$$ 935.2.cl.a 1664 16
935.2.cn $$\chi_{935}(37, \cdot)$$ 935.2.cn.a 3328 32
935.2.cp $$\chi_{935}(24, \cdot)$$ 935.2.cp.a 3328 32
935.2.cq $$\chi_{935}(6, \cdot)$$ 935.2.cq.a 2304 32
935.2.cs $$\chi_{935}(3, \cdot)$$ 935.2.cs.a 3328 32

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(935))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(935)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(85))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(187))$$$$^{\oplus 2}$$