# Properties

 Label 111.2 Level 111 Weight 2 Dimension 305 Nonzero newspaces 9 Newform subspaces 17 Sturm bound 1824 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$111 = 3 \cdot 37$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$9$$ Newform subspaces: $$17$$ Sturm bound: $$1824$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(111))$$.

Total New Old
Modular forms 528 377 151
Cusp forms 385 305 80
Eisenstein series 143 72 71

## Trace form

 $$305q - 3q^{2} - 19q^{3} - 43q^{4} - 6q^{5} - 21q^{6} - 44q^{7} - 15q^{8} - 19q^{9} + O(q^{10})$$ $$305q - 3q^{2} - 19q^{3} - 43q^{4} - 6q^{5} - 21q^{6} - 44q^{7} - 15q^{8} - 19q^{9} - 54q^{10} - 12q^{11} - 25q^{12} - 50q^{13} - 24q^{14} - 24q^{15} - 67q^{16} - 18q^{17} - 21q^{18} - 56q^{19} - 42q^{20} - 26q^{21} - 72q^{22} - 24q^{23} - 33q^{24} - 67q^{25} - 24q^{26} - 13q^{27} + 28q^{28} + 6q^{29} + 36q^{30} + 40q^{31} + 81q^{32} + 6q^{33} + 54q^{34} + 60q^{35} + 47q^{36} + 11q^{37} + 12q^{38} + 10q^{39} + 144q^{40} + 66q^{41} + 30q^{42} - 8q^{43} + 60q^{44} - 24q^{45} + 36q^{46} - 12q^{47} + 11q^{48} - 45q^{49} - 75q^{50} - 36q^{51} - 134q^{52} - 54q^{53} - 21q^{54} - 108q^{55} - 120q^{56} - 38q^{57} - 90q^{58} + 12q^{59} + 66q^{60} - 8q^{61} + 84q^{62} + 82q^{63} + 89q^{64} + 78q^{65} + 198q^{66} - 32q^{67} + 90q^{68} + 102q^{69} + 216q^{70} + 72q^{71} + 183q^{72} + 70q^{73} + 177q^{74} + 113q^{75} + 184q^{76} + 48q^{77} + 192q^{78} + 28q^{79} + 210q^{80} + 125q^{81} + 54q^{82} - 12q^{83} + 178q^{84} + 18q^{85} + 120q^{86} + 60q^{87} - 36q^{88} + 90q^{90} - 76q^{91} - 132q^{92} - 104q^{93} - 180q^{94} - 120q^{95} - 261q^{96} - 134q^{97} - 171q^{98} - 120q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(111))$$

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
111.2.a $$\chi_{111}(1, \cdot)$$ 111.2.a.a 3 1
111.2.a.b 4
111.2.c $$\chi_{111}(73, \cdot)$$ 111.2.c.a 2 1
111.2.c.b 4
111.2.e $$\chi_{111}(10, \cdot)$$ 111.2.e.a 6 2
111.2.e.b 10
111.2.g $$\chi_{111}(68, \cdot)$$ 111.2.g.a 20 2
111.2.j $$\chi_{111}(64, \cdot)$$ 111.2.j.a 2 2
111.2.j.b 4
111.2.j.c 6
111.2.k $$\chi_{111}(7, \cdot)$$ 111.2.k.a 18 6
111.2.k.b 24
111.2.m $$\chi_{111}(8, \cdot)$$ 111.2.m.a 40 4
111.2.o $$\chi_{111}(4, \cdot)$$ 111.2.o.a 12 6
111.2.o.b 18
111.2.q $$\chi_{111}(2, \cdot)$$ 111.2.q.a 12 12
111.2.q.b 120

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(111))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(111)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(37))$$$$^{\oplus 2}$$