# Properties

 Label 532.2 Level 532 Weight 2 Dimension 4634 Nonzero newspaces 32 Newform subspaces 57 Sturm bound 34560 Trace bound 10

## Defining parameters

 Level: $$N$$ = $$532 = 2^{2} \cdot 7 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$32$$ Newform subspaces: $$57$$ Sturm bound: $$34560$$ Trace bound: $$10$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(532))$$.

Total New Old
Modular forms 9180 4970 4210
Cusp forms 8101 4634 3467
Eisenstein series 1079 336 743

## Trace form

 $$4634 q - 30 q^{2} + 2 q^{3} - 30 q^{4} - 54 q^{5} - 36 q^{6} + 8 q^{7} - 84 q^{8} - 64 q^{9} + O(q^{10})$$ $$4634 q - 30 q^{2} + 2 q^{3} - 30 q^{4} - 54 q^{5} - 36 q^{6} + 8 q^{7} - 84 q^{8} - 64 q^{9} - 48 q^{10} - 6 q^{11} - 60 q^{12} - 56 q^{13} - 63 q^{14} + 24 q^{15} - 54 q^{16} - 36 q^{17} - 60 q^{18} + 41 q^{19} - 72 q^{20} - 79 q^{21} - 54 q^{22} + 24 q^{23} - 12 q^{24} - 40 q^{25} - 12 q^{26} + 26 q^{27} - 18 q^{28} - 216 q^{29} - 150 q^{30} - 50 q^{31} - 120 q^{32} - 198 q^{33} - 126 q^{34} - 66 q^{35} - 288 q^{36} - 158 q^{37} - 180 q^{38} - 104 q^{39} - 186 q^{40} - 132 q^{41} - 159 q^{42} - 50 q^{43} - 162 q^{44} - 138 q^{45} - 150 q^{46} - 162 q^{48} - 76 q^{49} - 150 q^{50} + 78 q^{51} - 36 q^{52} + 42 q^{53} + 54 q^{54} + 108 q^{55} - 72 q^{56} - 52 q^{57} - 60 q^{58} + 108 q^{59} - 30 q^{60} - 50 q^{61} + 54 q^{62} + 32 q^{63} + 36 q^{64} - 102 q^{65} + 120 q^{66} - 44 q^{67} + 90 q^{68} - 318 q^{69} + 51 q^{70} + 18 q^{71} + 264 q^{72} - 290 q^{73} + 96 q^{74} - 76 q^{75} + 144 q^{76} - 339 q^{77} + 6 q^{78} - 74 q^{79} + 156 q^{80} - 232 q^{81} + 210 q^{82} - 30 q^{83} + 63 q^{84} - 456 q^{85} + 126 q^{86} + 60 q^{87} + 72 q^{88} - 204 q^{89} + 18 q^{90} + 28 q^{91} + 12 q^{92} - 38 q^{93} + 6 q^{94} - 21 q^{95} - 168 q^{96} - 50 q^{97} - 114 q^{98} - 6 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(532))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
532.2.a $$\chi_{532}(1, \cdot)$$ 532.2.a.a 1 1
532.2.a.b 2
532.2.a.c 2
532.2.a.d 2
532.2.a.e 3
532.2.f $$\chi_{532}(419, \cdot)$$ 532.2.f.a 4 1
532.2.f.b 4
532.2.f.c 32
532.2.f.d 32
532.2.g $$\chi_{532}(265, \cdot)$$ 532.2.g.a 4 1
532.2.g.b 8
532.2.h $$\chi_{532}(379, \cdot)$$ 532.2.h.a 4 1
532.2.h.b 4
532.2.h.c 52
532.2.i $$\chi_{532}(305, \cdot)$$ 532.2.i.a 4 2
532.2.i.b 6
532.2.i.c 14
532.2.j $$\chi_{532}(197, \cdot)$$ 532.2.j.a 2 2
532.2.j.b 8
532.2.j.c 10
532.2.k $$\chi_{532}(121, \cdot)$$ 532.2.k.a 4 2
532.2.k.b 24
532.2.l $$\chi_{532}(429, \cdot)$$ 532.2.l.a 4 2
532.2.l.b 24
532.2.q $$\chi_{532}(145, \cdot)$$ 532.2.q.a 28 2
532.2.r $$\chi_{532}(87, \cdot)$$ 532.2.r.a 4 2
532.2.r.b 148
532.2.s $$\chi_{532}(183, \cdot)$$ 532.2.s.a 120 2
532.2.t $$\chi_{532}(151, \cdot)$$ 532.2.t.a 152 2
532.2.u $$\chi_{532}(83, \cdot)$$ 532.2.u.a 16 2
532.2.u.b 136
532.2.v $$\chi_{532}(341, \cdot)$$ 532.2.v.a 2 2
532.2.v.b 2
532.2.v.c 4
532.2.v.d 4
532.2.v.e 16
532.2.w $$\chi_{532}(115, \cdot)$$ 532.2.w.a 72 2
532.2.w.b 72
532.2.x $$\chi_{532}(69, \cdot)$$ 532.2.x.a 24 2
532.2.y $$\chi_{532}(107, \cdot)$$ 532.2.y.a 152 2
532.2.bl $$\chi_{532}(331, \cdot)$$ 532.2.bl.a 152 2
532.2.bm $$\chi_{532}(297, \cdot)$$ 532.2.bm.a 28 2
532.2.bn $$\chi_{532}(311, \cdot)$$ 532.2.bn.a 4 2
532.2.bn.b 148
532.2.bo $$\chi_{532}(85, \cdot)$$ 532.2.bo.a 30 6
532.2.bo.b 30
532.2.bp $$\chi_{532}(9, \cdot)$$ 532.2.bp.a 78 6
532.2.bq $$\chi_{532}(25, \cdot)$$ 532.2.bq.a 78 6
532.2.br $$\chi_{532}(131, \cdot)$$ 532.2.br.a 456 6
532.2.bs $$\chi_{532}(67, \cdot)$$ 532.2.bs.a 456 6
532.2.bv $$\chi_{532}(13, \cdot)$$ 532.2.bv.a 84 6
532.2.bw $$\chi_{532}(89, \cdot)$$ 532.2.bw.a 78 6
532.2.cb $$\chi_{532}(15, \cdot)$$ 532.2.cb.a 360 6
532.2.cc $$\chi_{532}(55, \cdot)$$ 532.2.cc.a 456 6
532.2.cd $$\chi_{532}(47, \cdot)$$ 532.2.cd.a 456 6
532.2.ce $$\chi_{532}(51, \cdot)$$ 532.2.ce.a 456 6
532.2.cj $$\chi_{532}(33, \cdot)$$ 532.2.cj.a 78 6

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(532))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(532)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(133))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(266))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(532))$$$$^{\oplus 1}$$