# Properties

 Label 786.2 Level 786 Weight 2 Dimension 4291 Nonzero newspaces 8 Newform subspaces 41 Sturm bound 68640 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$786 = 2 \cdot 3 \cdot 131$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Newform subspaces: $$41$$ Sturm bound: $$68640$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(786))$$.

Total New Old
Modular forms 17680 4291 13389
Cusp forms 16641 4291 12350
Eisenstein series 1039 0 1039

## Trace form

 $$4291q + q^{2} + q^{3} + q^{4} + 6q^{5} + q^{6} + 8q^{7} + q^{8} + q^{9} + O(q^{10})$$ $$4291q + q^{2} + q^{3} + q^{4} + 6q^{5} + q^{6} + 8q^{7} + q^{8} + q^{9} + 6q^{10} + 12q^{11} + q^{12} + 14q^{13} + 8q^{14} + 6q^{15} + q^{16} + 18q^{17} + q^{18} + 20q^{19} + 6q^{20} + 8q^{21} + 12q^{22} + 24q^{23} + q^{24} + 31q^{25} + 14q^{26} + q^{27} + 8q^{28} + 30q^{29} + 6q^{30} + 32q^{31} + q^{32} + 12q^{33} + 18q^{34} + 48q^{35} + q^{36} + 38q^{37} + 20q^{38} + 14q^{39} + 6q^{40} + 42q^{41} + 8q^{42} + 44q^{43} + 12q^{44} + 6q^{45} + 24q^{46} + 48q^{47} + q^{48} + 57q^{49} + 31q^{50} + 18q^{51} + 14q^{52} + 54q^{53} + q^{54} + 72q^{55} + 8q^{56} + 20q^{57} + 30q^{58} + 60q^{59} + 6q^{60} + 62q^{61} + 32q^{62} + 8q^{63} + q^{64} + 84q^{65} + 12q^{66} + 68q^{67} + 18q^{68} + 24q^{69} + 48q^{70} + 72q^{71} + q^{72} + 74q^{73} + 38q^{74} + 31q^{75} + 20q^{76} + 96q^{77} + 14q^{78} + 80q^{79} + 6q^{80} + q^{81} + 42q^{82} + 84q^{83} + 8q^{84} + 108q^{85} + 44q^{86} + 30q^{87} + 12q^{88} + 90q^{89} + 6q^{90} + 112q^{91} + 24q^{92} + 32q^{93} + 48q^{94} + 120q^{95} + q^{96} + 98q^{97} + 57q^{98} + 12q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(786))$$

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
786.2.a $$\chi_{786}(1, \cdot)$$ 786.2.a.a 1 1
786.2.a.b 1
786.2.a.c 1
786.2.a.d 1
786.2.a.e 1
786.2.a.f 1
786.2.a.g 1
786.2.a.h 1
786.2.a.i 1
786.2.a.j 1
786.2.a.k 1
786.2.a.l 1
786.2.a.m 1
786.2.a.n 3
786.2.a.o 3
786.2.a.p 4
786.2.c $$\chi_{786}(785, \cdot)$$ 786.2.c.a 22 1
786.2.c.b 22
786.2.e $$\chi_{786}(61, \cdot)$$ 786.2.e.a 4 4
786.2.e.b 4
786.2.e.c 4
786.2.e.d 4
786.2.e.e 8
786.2.e.f 12
786.2.e.g 16
786.2.e.h 16
786.2.e.i 20
786.2.g $$\chi_{786}(173, \cdot)$$ 786.2.g.a 88 4
786.2.g.b 88
786.2.i $$\chi_{786}(193, \cdot)$$ 786.2.i.a 60 12
786.2.i.b 60
786.2.i.c 72
786.2.i.d 72
786.2.k $$\chi_{786}(47, \cdot)$$ 786.2.k.a 264 12
786.2.k.b 264
786.2.m $$\chi_{786}(7, \cdot)$$ 786.2.m.a 240 48
786.2.m.b 240
786.2.m.c 288
786.2.m.d 288
786.2.o $$\chi_{786}(17, \cdot)$$ 786.2.o.a 1056 48
786.2.o.b 1056

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(786))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(786)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(131))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(262))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(393))$$$$^{\oplus 2}$$