## Defining parameters

 Level: $$N$$ = $$147 = 3 \cdot 7^{2}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$1568$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(147))$$.

Total New Old
Modular forms 126 55 71
Cusp forms 6 6 0
Eisenstein series 120 49 71

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

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

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(147))$$

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
147.1.b $$\chi_{147}(50, \cdot)$$ None 0 1
147.1.d $$\chi_{147}(97, \cdot)$$ None 0 1
147.1.f $$\chi_{147}(19, \cdot)$$ None 0 2
147.1.h $$\chi_{147}(116, \cdot)$$ None 0 2
147.1.j $$\chi_{147}(13, \cdot)$$ None 0 6
147.1.l $$\chi_{147}(8, \cdot)$$ 147.1.l.a 6 6
147.1.n $$\chi_{147}(2, \cdot)$$ None 0 12
147.1.p $$\chi_{147}(10, \cdot)$$ None 0 12