# Properties

 Label 927.2 Level 927 Weight 2 Dimension 24735 Nonzero newspaces 20 Newform subspaces 42 Sturm bound 127296 Trace bound 3

## Defining parameters

 Level: $$N$$ = $$927 = 3^{2} \cdot 103$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$20$$ Newform subspaces: $$42$$ Sturm bound: $$127296$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(927))$$.

Total New Old
Modular forms 32640 25643 6997
Cusp forms 31009 24735 6274
Eisenstein series 1631 908 723

## Trace form

 $$24735 q - 153 q^{2} - 204 q^{3} - 153 q^{4} - 153 q^{5} - 204 q^{6} - 153 q^{7} - 153 q^{8} - 204 q^{9} + O(q^{10})$$ $$24735 q - 153 q^{2} - 204 q^{3} - 153 q^{4} - 153 q^{5} - 204 q^{6} - 153 q^{7} - 153 q^{8} - 204 q^{9} - 459 q^{10} - 153 q^{11} - 204 q^{12} - 153 q^{13} - 153 q^{14} - 204 q^{15} - 153 q^{16} - 153 q^{17} - 204 q^{18} - 459 q^{19} - 153 q^{20} - 204 q^{21} - 153 q^{22} - 153 q^{23} - 204 q^{24} - 153 q^{25} - 153 q^{26} - 204 q^{27} - 459 q^{28} - 153 q^{29} - 204 q^{30} - 153 q^{31} - 153 q^{32} - 204 q^{33} - 153 q^{34} - 153 q^{35} - 204 q^{36} - 459 q^{37} - 153 q^{38} - 204 q^{39} - 153 q^{40} - 153 q^{41} - 204 q^{42} - 153 q^{43} - 153 q^{44} - 204 q^{45} - 459 q^{46} - 153 q^{47} - 204 q^{48} - 153 q^{49} - 153 q^{50} - 204 q^{51} - 153 q^{52} - 153 q^{53} - 204 q^{54} - 459 q^{55} - 153 q^{56} - 204 q^{57} - 153 q^{58} - 153 q^{59} - 204 q^{60} - 153 q^{61} - 153 q^{62} - 204 q^{63} - 459 q^{64} - 153 q^{65} - 204 q^{66} - 153 q^{67} - 153 q^{68} - 204 q^{69} - 153 q^{70} - 153 q^{71} - 204 q^{72} - 459 q^{73} - 153 q^{74} - 204 q^{75} - 153 q^{76} - 153 q^{77} - 204 q^{78} - 153 q^{79} - 153 q^{80} - 204 q^{81} - 459 q^{82} - 153 q^{83} - 204 q^{84} - 255 q^{85} - 255 q^{86} - 204 q^{87} - 561 q^{88} - 255 q^{89} - 204 q^{90} - 680 q^{91} - 357 q^{92} - 204 q^{93} - 357 q^{94} - 306 q^{95} - 204 q^{96} - 374 q^{97} - 561 q^{98} - 204 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(927))$$

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
927.2.a $$\chi_{927}(1, \cdot)$$ 927.2.a.a 1 1
927.2.a.b 2
927.2.a.c 3
927.2.a.d 4
927.2.a.e 5
927.2.a.f 6
927.2.a.g 8
927.2.a.h 14
927.2.c $$\chi_{927}(926, \cdot)$$ 927.2.c.a 16 1
927.2.c.b 20
927.2.e $$\chi_{927}(310, \cdot)$$ 927.2.e.a 102 2
927.2.e.b 102
927.2.f $$\chi_{927}(46, \cdot)$$ 927.2.f.a 2 2
927.2.f.b 2
927.2.f.c 16
927.2.f.d 16
927.2.f.e 16
927.2.f.f 32
927.2.g $$\chi_{927}(355, \cdot)$$ 927.2.g.a 204 2
927.2.h $$\chi_{927}(571, \cdot)$$ 927.2.h.a 204 2
927.2.j $$\chi_{927}(263, \cdot)$$ 927.2.j.a 204 2
927.2.n $$\chi_{927}(308, \cdot)$$ 927.2.n.a 204 2
927.2.o $$\chi_{927}(665, \cdot)$$ 927.2.o.a 16 2
927.2.o.b 52
927.2.p $$\chi_{927}(47, \cdot)$$ 927.2.p.a 204 2
927.2.u $$\chi_{927}(64, \cdot)$$ 927.2.u.a 112 16
927.2.u.b 128
927.2.u.c 160
927.2.u.d 288
927.2.w $$\chi_{927}(80, \cdot)$$ 927.2.w.a 576 16
927.2.y $$\chi_{927}(4, \cdot)$$ 927.2.y.a 3264 32
927.2.z $$\chi_{927}(7, \cdot)$$ 927.2.z.a 3264 32
927.2.ba $$\chi_{927}(19, \cdot)$$ 927.2.ba.a 32 32
927.2.ba.b 256
927.2.ba.c 256
927.2.ba.d 288
927.2.ba.e 512
927.2.bb $$\chi_{927}(13, \cdot)$$ 927.2.bb.a 3264 32
927.2.bg $$\chi_{927}(11, \cdot)$$ 927.2.bg.a 3264 32
927.2.bh $$\chi_{927}(35, \cdot)$$ 927.2.bh.a 1088 32
927.2.bi $$\chi_{927}(95, \cdot)$$ 927.2.bi.a 3264 32
927.2.bm $$\chi_{927}(5, \cdot)$$ 927.2.bm.a 3264 32

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(927))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(927)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(103))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(309))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(927))$$$$^{\oplus 1}$$