# Properties

 Label 832.2 Level 832 Weight 2 Dimension 11710 Nonzero newspaces 28 Newform subspaces 127 Sturm bound 86016 Trace bound 17

## Defining parameters

 Level: $$N$$ = $$832 = 2^{6} \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$28$$ Newform subspaces: $$127$$ Sturm bound: $$86016$$ Trace bound: $$17$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(832))$$.

Total New Old
Modular forms 22368 12194 10174
Cusp forms 20641 11710 8931
Eisenstein series 1727 484 1243

## Trace form

 $$11710 q - 80 q^{2} - 60 q^{3} - 80 q^{4} - 80 q^{5} - 80 q^{6} - 56 q^{7} - 80 q^{8} - 94 q^{9} + O(q^{10})$$ $$11710 q - 80 q^{2} - 60 q^{3} - 80 q^{4} - 80 q^{5} - 80 q^{6} - 56 q^{7} - 80 q^{8} - 94 q^{9} - 80 q^{10} - 52 q^{11} - 80 q^{12} - 80 q^{13} - 176 q^{14} - 48 q^{15} - 80 q^{16} - 124 q^{17} - 80 q^{18} - 44 q^{19} - 80 q^{20} - 88 q^{21} - 96 q^{22} - 56 q^{23} - 160 q^{24} - 122 q^{25} - 128 q^{26} - 144 q^{27} - 160 q^{28} - 112 q^{29} - 240 q^{30} - 104 q^{31} - 160 q^{32} - 112 q^{33} - 160 q^{34} - 64 q^{35} - 240 q^{36} - 96 q^{37} - 160 q^{38} - 64 q^{39} - 256 q^{40} - 100 q^{41} - 160 q^{42} - 36 q^{43} - 96 q^{44} - 72 q^{45} - 80 q^{46} - 24 q^{47} - 80 q^{48} - 122 q^{49} - 32 q^{50} - 112 q^{51} - 40 q^{52} - 128 q^{53} + 48 q^{54} - 184 q^{55} + 32 q^{56} - 88 q^{57} + 64 q^{58} - 196 q^{59} + 112 q^{60} - 64 q^{61} - 16 q^{62} - 192 q^{63} + 112 q^{64} - 240 q^{65} - 16 q^{66} - 236 q^{67} + 16 q^{68} - 56 q^{69} + 112 q^{70} - 184 q^{71} + 64 q^{72} - 100 q^{73} + 32 q^{74} - 172 q^{75} + 48 q^{76} - 88 q^{77} - 64 q^{78} - 192 q^{79} - 160 q^{80} - 146 q^{81} - 240 q^{82} - 60 q^{83} - 304 q^{84} - 96 q^{85} - 288 q^{86} - 56 q^{87} - 240 q^{88} - 196 q^{89} - 368 q^{90} - 60 q^{91} - 480 q^{92} - 160 q^{93} - 272 q^{94} - 96 q^{95} - 352 q^{96} - 140 q^{97} - 352 q^{98} - 108 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(832))$$

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
832.2.a $$\chi_{832}(1, \cdot)$$ 832.2.a.a 1 1
832.2.a.b 1
832.2.a.c 1
832.2.a.d 1
832.2.a.e 1
832.2.a.f 1
832.2.a.g 1
832.2.a.h 1
832.2.a.i 1
832.2.a.j 1
832.2.a.k 2
832.2.a.l 2
832.2.a.m 2
832.2.a.n 2
832.2.a.o 2
832.2.a.p 4
832.2.b $$\chi_{832}(417, \cdot)$$ 832.2.b.a 4 1
832.2.b.b 4
832.2.b.c 8
832.2.b.d 8
832.2.e $$\chi_{832}(545, \cdot)$$ 832.2.e.a 4 1
832.2.e.b 4
832.2.e.c 8
832.2.e.d 12
832.2.f $$\chi_{832}(129, \cdot)$$ 832.2.f.a 2 1
832.2.f.b 2
832.2.f.c 2
832.2.f.d 2
832.2.f.e 2
832.2.f.f 4
832.2.f.g 4
832.2.f.h 4
832.2.f.i 4
832.2.i $$\chi_{832}(321, \cdot)$$ 832.2.i.a 2 2
832.2.i.b 2
832.2.i.c 2
832.2.i.d 2
832.2.i.e 2
832.2.i.f 2
832.2.i.g 2
832.2.i.h 2
832.2.i.i 2
832.2.i.j 2
832.2.i.k 4
832.2.i.l 4
832.2.i.m 4
832.2.i.n 4
832.2.i.o 4
832.2.i.p 4
832.2.i.q 8
832.2.k $$\chi_{832}(255, \cdot)$$ 832.2.k.a 2 2
832.2.k.b 2
832.2.k.c 2
832.2.k.d 2
832.2.k.e 4
832.2.k.f 4
832.2.k.g 8
832.2.k.h 8
832.2.k.i 8
832.2.k.j 12
832.2.l $$\chi_{832}(239, \cdot)$$ 832.2.l.a 2 2
832.2.l.b 50
832.2.n $$\chi_{832}(209, \cdot)$$ 832.2.n.a 48 2
832.2.p $$\chi_{832}(337, \cdot)$$ 832.2.p.a 8 2
832.2.p.b 44
832.2.s $$\chi_{832}(47, \cdot)$$ 832.2.s.a 2 2
832.2.s.b 50
832.2.u $$\chi_{832}(31, \cdot)$$ 832.2.u.a 6 2
832.2.u.b 6
832.2.u.c 6
832.2.u.d 6
832.2.u.e 16
832.2.u.f 16
832.2.w $$\chi_{832}(257, \cdot)$$ 832.2.w.a 2 2
832.2.w.b 2
832.2.w.c 2
832.2.w.d 2
832.2.w.e 4
832.2.w.f 4
832.2.w.g 8
832.2.w.h 8
832.2.w.i 8
832.2.w.j 12
832.2.z $$\chi_{832}(289, \cdot)$$ 832.2.z.a 16 2
832.2.z.b 20
832.2.z.c 20
832.2.ba $$\chi_{832}(225, \cdot)$$ 832.2.ba.a 4 2
832.2.ba.b 4
832.2.ba.c 4
832.2.ba.d 4
832.2.ba.e 4
832.2.ba.f 4
832.2.ba.g 8
832.2.ba.h 12
832.2.ba.i 12
832.2.bd $$\chi_{832}(343, \cdot)$$ None 0 4
832.2.bf $$\chi_{832}(105, \cdot)$$ None 0 4
832.2.bg $$\chi_{832}(25, \cdot)$$ None 0 4
832.2.bi $$\chi_{832}(135, \cdot)$$ None 0 4
832.2.bk $$\chi_{832}(223, \cdot)$$ 832.2.bk.a 16 4
832.2.bk.b 16
832.2.bk.c 20
832.2.bk.d 20
832.2.bk.e 20
832.2.bk.f 20
832.2.bn $$\chi_{832}(175, \cdot)$$ 832.2.bn.a 104 4
832.2.bp $$\chi_{832}(17, \cdot)$$ 832.2.bp.a 104 4
832.2.br $$\chi_{832}(81, \cdot)$$ 832.2.br.a 104 4
832.2.bs $$\chi_{832}(15, \cdot)$$ 832.2.bs.a 104 4
832.2.bu $$\chi_{832}(63, \cdot)$$ 832.2.bu.a 4 4
832.2.bu.b 4
832.2.bu.c 4
832.2.bu.d 4
832.2.bu.e 4
832.2.bu.f 4
832.2.bu.g 4
832.2.bu.h 4
832.2.bu.i 8
832.2.bu.j 8
832.2.bu.k 8
832.2.bu.l 16
832.2.bu.m 16
832.2.bu.n 16
832.2.bw $$\chi_{832}(99, \cdot)$$ 832.2.bw.a 880 8
832.2.by $$\chi_{832}(53, \cdot)$$ 832.2.by.a 768 8
832.2.cb $$\chi_{832}(77, \cdot)$$ 832.2.cb.a 880 8
832.2.cc $$\chi_{832}(83, \cdot)$$ 832.2.cc.a 880 8
832.2.cf $$\chi_{832}(71, \cdot)$$ None 0 8
832.2.ch $$\chi_{832}(121, \cdot)$$ None 0 8
832.2.ci $$\chi_{832}(9, \cdot)$$ None 0 8
832.2.ck $$\chi_{832}(7, \cdot)$$ None 0 8
832.2.cn $$\chi_{832}(11, \cdot)$$ 832.2.cn.a 1760 16
832.2.cp $$\chi_{832}(29, \cdot)$$ 832.2.cp.a 1760 16
832.2.cq $$\chi_{832}(69, \cdot)$$ 832.2.cq.a 1760 16
832.2.ct $$\chi_{832}(115, \cdot)$$ 832.2.ct.a 1760 16

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(832))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(832)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(104))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(208))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(416))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(832))$$$$^{\oplus 1}$$