# Properties

 Label 912.2 Level 912 Weight 2 Dimension 9512 Nonzero newspaces 24 Newform subspaces 126 Sturm bound 92160 Trace bound 13

## Defining parameters

 Level: $$N$$ = $$912 = 2^{4} \cdot 3 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$24$$ Newform subspaces: $$126$$ Sturm bound: $$92160$$ Trace bound: $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(912))$$.

Total New Old
Modular forms 24048 9820 14228
Cusp forms 22033 9512 12521
Eisenstein series 2015 308 1707

## Trace form

 $$9512 q - 25 q^{3} - 56 q^{4} + 4 q^{5} - 20 q^{6} - 38 q^{7} + 24 q^{8} + q^{9} + O(q^{10})$$ $$9512 q - 25 q^{3} - 56 q^{4} + 4 q^{5} - 20 q^{6} - 38 q^{7} + 24 q^{8} + q^{9} - 56 q^{10} + 24 q^{11} - 36 q^{12} - 70 q^{13} - 24 q^{14} - 7 q^{15} - 104 q^{16} - 4 q^{17} - 52 q^{18} - 38 q^{19} - 32 q^{20} - 53 q^{21} - 104 q^{22} - 16 q^{23} - 92 q^{24} - 36 q^{25} - 40 q^{26} - 49 q^{27} - 72 q^{28} + 20 q^{29} - 76 q^{30} - 86 q^{31} - 65 q^{33} - 56 q^{34} - 48 q^{35} - 68 q^{36} - 4 q^{37} + 8 q^{38} - 90 q^{39} - 24 q^{40} + 12 q^{41} + 52 q^{42} - 54 q^{43} + 80 q^{44} - 17 q^{45} + 24 q^{46} + 92 q^{48} - 72 q^{49} + 72 q^{50} - 95 q^{51} - 8 q^{52} - 28 q^{53} + 60 q^{54} - 118 q^{55} - q^{57} - 176 q^{58} - 56 q^{59} - 52 q^{60} - 126 q^{61} + 24 q^{62} - 25 q^{63} - 200 q^{64} + 168 q^{65} - 140 q^{66} + 130 q^{67} - 64 q^{68} - 29 q^{69} - 216 q^{70} + 124 q^{71} - 108 q^{72} + 138 q^{73} - 104 q^{74} + 128 q^{75} - 136 q^{76} + 184 q^{77} - 132 q^{78} + 230 q^{79} - 16 q^{80} - 95 q^{81} - 120 q^{82} + 180 q^{83} - 20 q^{84} + 30 q^{85} + 32 q^{86} + 189 q^{87} - 8 q^{88} + 156 q^{89} + 12 q^{90} + 218 q^{91} + 32 q^{92} + 23 q^{93} + 8 q^{94} + 56 q^{95} + 40 q^{96} - 94 q^{97} + 80 q^{98} + 101 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(912))$$

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
912.2.a $$\chi_{912}(1, \cdot)$$ 912.2.a.a 1 1
912.2.a.b 1
912.2.a.c 1
912.2.a.d 1
912.2.a.e 1
912.2.a.f 1
912.2.a.g 1
912.2.a.h 1
912.2.a.i 1
912.2.a.j 1
912.2.a.k 1
912.2.a.l 1
912.2.a.m 2
912.2.a.n 2
912.2.a.o 2
912.2.d $$\chi_{912}(191, \cdot)$$ 912.2.d.a 12 1
912.2.d.b 24
912.2.e $$\chi_{912}(151, \cdot)$$ None 0 1
912.2.f $$\chi_{912}(113, \cdot)$$ 912.2.f.a 2 1
912.2.f.b 2
912.2.f.c 2
912.2.f.d 2
912.2.f.e 2
912.2.f.f 4
912.2.f.g 4
912.2.f.h 10
912.2.f.i 10
912.2.g $$\chi_{912}(457, \cdot)$$ None 0 1
912.2.j $$\chi_{912}(647, \cdot)$$ None 0 1
912.2.k $$\chi_{912}(607, \cdot)$$ 912.2.k.a 2 1
912.2.k.b 2
912.2.k.c 2
912.2.k.d 2
912.2.k.e 2
912.2.k.f 2
912.2.k.g 4
912.2.k.h 4
912.2.p $$\chi_{912}(569, \cdot)$$ None 0 1
912.2.q $$\chi_{912}(49, \cdot)$$ 912.2.q.a 2 2
912.2.q.b 2
912.2.q.c 2
912.2.q.d 2
912.2.q.e 2
912.2.q.f 2
912.2.q.g 4
912.2.q.h 4
912.2.q.i 4
912.2.q.j 4
912.2.q.k 6
912.2.q.l 6
912.2.r $$\chi_{912}(341, \cdot)$$ 912.2.r.a 312 2
912.2.u $$\chi_{912}(229, \cdot)$$ 912.2.u.a 72 2
912.2.u.b 72
912.2.v $$\chi_{912}(419, \cdot)$$ 912.2.v.a 288 2
912.2.y $$\chi_{912}(379, \cdot)$$ 912.2.y.a 160 2
912.2.bb $$\chi_{912}(31, \cdot)$$ 912.2.bb.a 2 2
912.2.bb.b 2
912.2.bb.c 4
912.2.bb.d 4
912.2.bb.e 6
912.2.bb.f 6
912.2.bb.g 8
912.2.bb.h 8
912.2.bc $$\chi_{912}(311, \cdot)$$ None 0 2
912.2.bd $$\chi_{912}(521, \cdot)$$ None 0 2
912.2.bg $$\chi_{912}(103, \cdot)$$ None 0 2
912.2.bh $$\chi_{912}(239, \cdot)$$ 912.2.bh.a 2 2
912.2.bh.b 2
912.2.bh.c 2
912.2.bh.d 2
912.2.bh.e 24
912.2.bh.f 24
912.2.bh.g 24
912.2.bm $$\chi_{912}(121, \cdot)$$ None 0 2
912.2.bn $$\chi_{912}(65, \cdot)$$ 912.2.bn.a 2 2
912.2.bn.b 2
912.2.bn.c 2
912.2.bn.d 2
912.2.bn.e 2
912.2.bn.f 2
912.2.bn.g 4
912.2.bn.h 4
912.2.bn.i 4
912.2.bn.j 4
912.2.bn.k 4
912.2.bn.l 4
912.2.bn.m 8
912.2.bn.n 16
912.2.bn.o 16
912.2.bo $$\chi_{912}(289, \cdot)$$ 912.2.bo.a 6 6
912.2.bo.b 6
912.2.bo.c 6
912.2.bo.d 6
912.2.bo.e 6
912.2.bo.f 6
912.2.bo.g 12
912.2.bo.h 12
912.2.bo.i 12
912.2.bo.j 12
912.2.bo.k 18
912.2.bo.l 18
912.2.bq $$\chi_{912}(277, \cdot)$$ 912.2.bq.a 320 4
912.2.br $$\chi_{912}(221, \cdot)$$ 912.2.br.a 624 4
912.2.bu $$\chi_{912}(259, \cdot)$$ 912.2.bu.a 320 4
912.2.bv $$\chi_{912}(11, \cdot)$$ 912.2.bv.a 8 4
912.2.bv.b 8
912.2.bv.c 608
912.2.bz $$\chi_{912}(41, \cdot)$$ None 0 6
912.2.ca $$\chi_{912}(25, \cdot)$$ None 0 6
912.2.cc $$\chi_{912}(257, \cdot)$$ 912.2.cc.a 6 6
912.2.cc.b 6
912.2.cc.c 18
912.2.cc.d 18
912.2.cc.e 24
912.2.cc.f 36
912.2.cc.g 60
912.2.cc.h 60
912.2.cf $$\chi_{912}(295, \cdot)$$ None 0 6
912.2.ch $$\chi_{912}(47, \cdot)$$ 912.2.ch.a 6 6
912.2.ch.b 6
912.2.ch.c 6
912.2.ch.d 6
912.2.ch.e 72
912.2.ch.f 72
912.2.ch.g 72
912.2.ci $$\chi_{912}(79, \cdot)$$ 912.2.ci.a 6 6
912.2.ci.b 6
912.2.ci.c 12
912.2.ci.d 12
912.2.ci.e 18
912.2.ci.f 18
912.2.ci.g 24
912.2.ci.h 24
912.2.ck $$\chi_{912}(23, \cdot)$$ None 0 6
912.2.cn $$\chi_{912}(67, \cdot)$$ 912.2.cn.a 960 12
912.2.cp $$\chi_{912}(35, \cdot)$$ 912.2.cp.a 1872 12
912.2.cq $$\chi_{912}(61, \cdot)$$ 912.2.cq.a 960 12
912.2.cs $$\chi_{912}(29, \cdot)$$ 912.2.cs.a 1872 12

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(912))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(912)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(114))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(228))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(304))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(456))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(912))$$$$^{\oplus 1}$$