## Defining parameters

 Level: $$N$$ = $$133 = 7 \cdot 19$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$2$$ Newform subspaces: $$2$$ Sturm bound: $$1440$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(133))$$.

Total New Old
Modular forms 114 90 24
Cusp forms 6 6 0
Eisenstein series 108 84 24

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 2 4 0 0

## Trace form

 $$6q - 2q^{2} - q^{4} + q^{5} - q^{7} - 4q^{8} - q^{9} + O(q^{10})$$ $$6q - 2q^{2} - q^{4} + q^{5} - q^{7} - 4q^{8} - q^{9} + q^{11} - 2q^{15} + q^{16} - 2q^{17} - q^{19} - 2q^{20} + 2q^{21} - q^{23} + 2q^{28} + 2q^{29} + 4q^{30} - q^{35} + 2q^{36} - 4q^{39} + 2q^{42} - 4q^{43} + q^{44} + q^{45} + 4q^{46} + q^{47} - 5q^{49} + 2q^{51} + 2q^{53} + 2q^{55} - 2q^{57} - 4q^{58} + q^{61} - q^{63} + 6q^{64} + 4q^{65} - 2q^{67} - 2q^{68} - 2q^{70} + 2q^{71} + q^{73} + 2q^{76} - 2q^{77} + 2q^{78} - 2q^{79} + q^{80} + q^{81} - 2q^{83} - 6q^{85} - 2q^{86} + 2q^{91} - 2q^{92} + 3q^{95} + 2q^{98} - 2q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(133))$$

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
133.1.b $$\chi_{133}(113, \cdot)$$ None 0 1
133.1.d $$\chi_{133}(20, \cdot)$$ None 0 1
133.1.j $$\chi_{133}(46, \cdot)$$ None 0 2
133.1.k $$\chi_{133}(45, \cdot)$$ None 0 2
133.1.l $$\chi_{133}(96, \cdot)$$ None 0 2
133.1.m $$\chi_{133}(83, \cdot)$$ 133.1.m.a 4 2
133.1.n $$\chi_{133}(65, \cdot)$$ None 0 2
133.1.q $$\chi_{133}(8, \cdot)$$ None 0 2
133.1.r $$\chi_{133}(18, \cdot)$$ 133.1.r.a 2 2
133.1.t $$\chi_{133}(26, \cdot)$$ None 0 2
133.1.x $$\chi_{133}(17, \cdot)$$ None 0 6
133.1.y $$\chi_{133}(6, \cdot)$$ None 0 6
133.1.z $$\chi_{133}(5, \cdot)$$ None 0 6
133.1.bc $$\chi_{133}(15, \cdot)$$ None 0 6
133.1.bd $$\chi_{133}(51, \cdot)$$ None 0 6
133.1.be $$\chi_{133}(2, \cdot)$$ None 0 6