## Defining parameters

 Level: $$N$$ = $$201 = 3 \cdot 67$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Newforms: $$18$$ Sturm bound: $$5984$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(201))$$.

Total New Old
Modular forms 1628 1187 441
Cusp forms 1365 1055 310
Eisenstein series 263 132 131

## Trace form

 $$1055q - 3q^{2} - 34q^{3} - 73q^{4} - 6q^{5} - 36q^{6} - 74q^{7} - 15q^{8} - 34q^{9} + O(q^{10})$$ $$1055q - 3q^{2} - 34q^{3} - 73q^{4} - 6q^{5} - 36q^{6} - 74q^{7} - 15q^{8} - 34q^{9} - 84q^{10} - 12q^{11} - 40q^{12} - 80q^{13} - 24q^{14} - 39q^{15} - 97q^{16} - 18q^{17} - 36q^{18} - 86q^{19} - 42q^{20} - 41q^{21} - 102q^{22} - 24q^{23} - 48q^{24} - 97q^{25} - 42q^{26} - 34q^{27} - 122q^{28} - 30q^{29} - 51q^{30} - 98q^{31} - 63q^{32} - 45q^{33} - 120q^{34} - 48q^{35} - 40q^{36} - 104q^{37} - 60q^{38} - 47q^{39} - 156q^{40} - 42q^{41} - 57q^{42} - 110q^{43} - 84q^{44} - 39q^{45} - 138q^{46} - 48q^{47} - 64q^{48} - 123q^{49} - 93q^{50} - 51q^{51} - 76q^{52} + 12q^{53} - 36q^{54} + 60q^{55} + 276q^{56} + 24q^{57} + 108q^{58} + 72q^{59} + 189q^{60} + 136q^{61} + 36q^{62} - 30q^{63} + 467q^{64} + 180q^{65} + 228q^{66} - q^{67} + 138q^{68} + 9q^{69} + 318q^{70} + 192q^{71} + 84q^{72} + 146q^{73} + 18q^{74} + 68q^{75} + 322q^{76} + 36q^{77} + 57q^{78} + 8q^{79} + 210q^{80} - 34q^{81} + 6q^{82} - 18q^{83} - 45q^{84} - 174q^{85} - 132q^{86} - 63q^{87} - 246q^{88} - 90q^{89} - 51q^{90} - 178q^{91} - 168q^{92} - 65q^{93} - 210q^{94} - 120q^{95} - 96q^{96} - 164q^{97} - 171q^{98} - 45q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(201))$$

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
201.2.a $$\chi_{201}(1, \cdot)$$ 201.2.a.a 1 1
201.2.a.b 1
201.2.a.c 1
201.2.a.d 3
201.2.a.e 5
201.2.d $$\chi_{201}(200, \cdot)$$ 201.2.d.a 20 1
201.2.e $$\chi_{201}(37, \cdot)$$ 201.2.e.a 2 2
201.2.e.b 10
201.2.e.c 10
201.2.f $$\chi_{201}(38, \cdot)$$ 201.2.f.a 2 2
201.2.f.b 40
201.2.i $$\chi_{201}(22, \cdot)$$ 201.2.i.a 50 10
201.2.i.b 70
201.2.j $$\chi_{201}(5, \cdot)$$ 201.2.j.a 200 10
201.2.m $$\chi_{201}(4, \cdot)$$ 201.2.m.a 100 20
201.2.m.b 120
201.2.p $$\chi_{201}(2, \cdot)$$ 201.2.p.a 20 20
201.2.p.b 400

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(201))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(201)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(67))$$$$^{\oplus 2}$$