## Defining parameters

 Level: $$N$$ = $$164 = 2^{2} \cdot 41$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$3$$ Newform subspaces: $$4$$ Sturm bound: $$1680$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(164))$$.

Total New Old
Modular forms 111 49 62
Cusp forms 11 11 0
Eisenstein series 100 38 62

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 11 0 0 0

## Trace form

 $$11q - 3q^{2} + q^{4} - 2q^{5} - 3q^{8} + q^{9} + O(q^{10})$$ $$11q - 3q^{2} + q^{4} - 2q^{5} - 3q^{8} + q^{9} - 2q^{10} - 2q^{13} + q^{16} - 2q^{17} - 3q^{18} - 2q^{20} - 4q^{21} - 5q^{25} - 2q^{26} - 2q^{29} + 7q^{32} - 4q^{33} + 8q^{34} + q^{36} - 2q^{37} - 2q^{40} + q^{41} + 4q^{42} - 2q^{45} + q^{49} + 9q^{50} + 8q^{52} - 2q^{53} + 4q^{57} - 2q^{58} - 6q^{61} + q^{64} + 6q^{65} + 4q^{66} - 2q^{68} - 3q^{72} - 2q^{73} - 2q^{74} + 4q^{77} - 2q^{80} + 7q^{81} - 3q^{82} - 4q^{84} + 6q^{85} - 2q^{89} - 2q^{90} - 2q^{97} - 3q^{98} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(164))$$

We only show spaces with odd 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
164.1.c $$\chi_{164}(83, \cdot)$$ None 0 1
164.1.d $$\chi_{164}(163, \cdot)$$ 164.1.d.a 1 1
164.1.d.b 2
164.1.e $$\chi_{164}(91, \cdot)$$ None 0 2
164.1.h $$\chi_{164}(85, \cdot)$$ None 0 4
164.1.j $$\chi_{164}(51, \cdot)$$ 164.1.j.a 4 4
164.1.l $$\chi_{164}(23, \cdot)$$ 164.1.l.a 4 4
164.1.n $$\chi_{164}(39, \cdot)$$ None 0 8
164.1.p $$\chi_{164}(13, \cdot)$$ None 0 16