# Properties

 Label 164.2 Level 164 Weight 2 Dimension 450 Nonzero newspaces 8 Newform subspaces 10 Sturm bound 3360 Trace bound 3

## Defining parameters

 Level: $$N$$ = $$164 = 2^{2} \cdot 41$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Newform subspaces: $$10$$ Sturm bound: $$3360$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(164))$$.

Total New Old
Modular forms 940 530 410
Cusp forms 741 450 291
Eisenstein series 199 80 119

## Trace form

 $$450q - 20q^{2} - 20q^{4} - 40q^{5} - 20q^{6} - 20q^{8} - 40q^{9} + O(q^{10})$$ $$450q - 20q^{2} - 20q^{4} - 40q^{5} - 20q^{6} - 20q^{8} - 40q^{9} - 20q^{10} - 20q^{12} - 40q^{13} - 20q^{14} - 20q^{16} - 40q^{17} - 20q^{18} - 20q^{20} - 40q^{21} - 20q^{22} - 20q^{24} - 40q^{25} - 20q^{26} - 20q^{28} - 40q^{29} - 20q^{30} - 20q^{31} - 20q^{32} - 100q^{33} - 20q^{34} - 40q^{35} - 20q^{36} - 100q^{37} - 20q^{38} - 80q^{39} - 60q^{41} - 40q^{42} - 20q^{43} - 20q^{44} - 120q^{45} - 20q^{46} - 60q^{47} - 20q^{48} - 80q^{49} - 20q^{50} - 60q^{51} - 20q^{52} - 60q^{53} - 20q^{54} - 20q^{56} - 40q^{57} - 20q^{58} - 20q^{60} - 40q^{61} - 20q^{62} - 20q^{64} - 30q^{65} + 60q^{66} + 60q^{67} + 80q^{68} + 40q^{69} + 180q^{70} + 80q^{71} + 160q^{72} + 40q^{73} + 100q^{74} + 160q^{75} + 280q^{76} + 40q^{77} + 180q^{78} + 80q^{79} + 180q^{80} + 170q^{81} + 220q^{82} + 80q^{83} + 220q^{84} + 130q^{85} + 180q^{86} + 80q^{87} + 180q^{88} + 40q^{89} + 280q^{90} + 160q^{91} + 100q^{92} + 40q^{93} + 160q^{94} + 80q^{95} + 180q^{96} + 40q^{97} + 80q^{98} + 60q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(164))$$

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
164.2.a $$\chi_{164}(1, \cdot)$$ 164.2.a.a 4 1
164.2.b $$\chi_{164}(81, \cdot)$$ 164.2.b.a 4 1
164.2.f $$\chi_{164}(9, \cdot)$$ 164.2.f.a 6 2
164.2.g $$\chi_{164}(37, \cdot)$$ 164.2.g.a 16 4
164.2.i $$\chi_{164}(3, \cdot)$$ 164.2.i.a 4 4
164.2.i.b 72
164.2.k $$\chi_{164}(25, \cdot)$$ 164.2.k.a 16 4
164.2.m $$\chi_{164}(5, \cdot)$$ 164.2.m.a 24 8
164.2.o $$\chi_{164}(7, \cdot)$$ 164.2.o.a 16 16
164.2.o.b 288

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(164))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(164)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(41))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(82))$$$$^{\oplus 2}$$