# Properties

 Label 171.1 Level 171 Weight 1 Dimension 7 Nonzero newspaces 3 Newform subspaces 3 Sturm bound 2160 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$171 = 3^{2} \cdot 19$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$3$$ Newform subspaces: $$3$$ Sturm bound: $$2160$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(171))$$.

Total New Old
Modular forms 155 84 71
Cusp forms 11 7 4
Eisenstein series 144 77 67

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 3 4 0 0

## Trace form

 $$7 q - 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{9} + O(q^{10})$$ $$7 q - 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{9} + 2 q^{11} - 3 q^{13} + 2 q^{16} - 3 q^{19} + 2 q^{23} + 4 q^{24} - 4 q^{26} - 3 q^{28} + 4 q^{30} + 4 q^{35} - 2 q^{38} - 2 q^{39} - 2 q^{42} + q^{43} + 2 q^{45} - 2 q^{47} + 3 q^{49} + 3 q^{52} + 2 q^{54} - 4 q^{55} - 4 q^{57} - 2 q^{58} - q^{61} + 4 q^{62} + 2 q^{63} - q^{64} + 2 q^{66} + 3 q^{67} + 3 q^{73} + 2 q^{77} - 3 q^{79} - 4 q^{80} + 4 q^{81} - 4 q^{82} + 2 q^{83} + 2 q^{87} - 3 q^{91} + 2 q^{93} - 2 q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(171))$$

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
171.1.b $$\chi_{171}(134, \cdot)$$ None 0 1
171.1.c $$\chi_{171}(37, \cdot)$$ 171.1.c.a 1 1
171.1.i $$\chi_{171}(88, \cdot)$$ None 0 2
171.1.j $$\chi_{171}(68, \cdot)$$ None 0 2
171.1.n $$\chi_{171}(11, \cdot)$$ None 0 2
171.1.o $$\chi_{171}(94, \cdot)$$ 171.1.o.a 4 2
171.1.p $$\chi_{171}(46, \cdot)$$ 171.1.p.a 2 2
171.1.q $$\chi_{171}(20, \cdot)$$ None 0 2
171.1.r $$\chi_{171}(26, \cdot)$$ None 0 2
171.1.s $$\chi_{171}(31, \cdot)$$ None 0 2
171.1.z $$\chi_{171}(5, \cdot)$$ None 0 6
171.1.ba $$\chi_{171}(10, \cdot)$$ None 0 6
171.1.bb $$\chi_{171}(17, \cdot)$$ None 0 6
171.1.bc $$\chi_{171}(22, \cdot)$$ None 0 6
171.1.be $$\chi_{171}(13, \cdot)$$ None 0 6
171.1.bf $$\chi_{171}(23, \cdot)$$ None 0 6

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(171))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(171)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 2}$$