## Defining parameters

 Level: $$N$$ = $$471 = 3 \cdot 157$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$3$$ Newform subspaces: $$5$$ Sturm bound: $$16432$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(471))$$.

Total New Old
Modular forms 343 185 158
Cusp forms 31 31 0
Eisenstein series 312 154 158

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 31 0 0 0

## Trace form

 $$31q - 3q^{3} + 5q^{4} - 2q^{7} + 5q^{9} + O(q^{10})$$ $$31q - 3q^{3} + 5q^{4} - 2q^{7} + 5q^{9} - 4q^{10} - 3q^{12} - 6q^{13} + q^{16} - 2q^{19} - 2q^{21} + 5q^{25} - 3q^{27} - 2q^{28} - 4q^{30} - 2q^{31} + 5q^{36} - 2q^{37} - 6q^{39} - 8q^{40} - 2q^{43} - 4q^{46} - 7q^{48} + 3q^{49} - 6q^{52} - 2q^{57} - 4q^{58} - 2q^{61} - 2q^{63} + q^{64} - 6q^{67} - 2q^{73} - 3q^{75} - 10q^{76} - 2q^{79} + 5q^{81} - 4q^{82} - 2q^{84} - 4q^{90} - 4q^{91} - 2q^{93} - 2q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(471))$$

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
471.1.c $$\chi_{471}(158, \cdot)$$ None 0 1
471.1.d $$\chi_{471}(470, \cdot)$$ 471.1.d.a 1 1
471.1.d.b 2
471.1.d.c 4
471.1.g $$\chi_{471}(28, \cdot)$$ None 0 2
471.1.i $$\chi_{471}(326, \cdot)$$ None 0 2
471.1.j $$\chi_{471}(170, \cdot)$$ None 0 2
471.1.k $$\chi_{471}(22, \cdot)$$ None 0 4
471.1.n $$\chi_{471}(56, \cdot)$$ 471.1.n.a 12 12
471.1.o $$\chi_{471}(14, \cdot)$$ 471.1.o.a 12 12
471.1.r $$\chi_{471}(7, \cdot)$$ None 0 24
471.1.t $$\chi_{471}(44, \cdot)$$ None 0 24
471.1.u $$\chi_{471}(11, \cdot)$$ None 0 24
471.1.x $$\chi_{471}(34, \cdot)$$ None 0 48