## Defining parameters

 Level: $$N$$ = $$129 = 3 \cdot 43$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$1232$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(129))$$.

Total New Old
Modular forms 90 46 44
Cusp forms 6 6 0
Eisenstein series 84 40 44

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 6 0 0 0

## Trace form

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

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(129))$$

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
129.1.b $$\chi_{129}(85, \cdot)$$ None 0 1
129.1.c $$\chi_{129}(44, \cdot)$$ None 0 1
129.1.f $$\chi_{129}(92, \cdot)$$ None 0 2
129.1.g $$\chi_{129}(7, \cdot)$$ None 0 2
129.1.k $$\chi_{129}(22, \cdot)$$ None 0 6
129.1.l $$\chi_{129}(11, \cdot)$$ 129.1.l.a 6 6
129.1.o $$\chi_{129}(14, \cdot)$$ None 0 12
129.1.p $$\chi_{129}(19, \cdot)$$ None 0 12