## Defining parameters

 Level: $$N$$ = $$100 = 2^{2} \cdot 5^{2}$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$600$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(100))$$.

Total New Old
Modular forms 74 25 49
Cusp forms 4 4 0
Eisenstein series 70 21 49

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

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

## Trace form

 $$4q - q^{2} - q^{4} - q^{5} - q^{8} - q^{9} + O(q^{10})$$ $$4q - q^{2} - q^{4} - q^{5} - q^{8} - q^{9} - q^{10} - 2q^{13} - q^{16} - 2q^{17} + 4q^{18} + 4q^{20} - q^{25} - 2q^{26} - 2q^{29} + 4q^{32} + 3q^{34} - q^{36} + 3q^{37} - q^{40} - 2q^{41} - q^{45} + 4q^{49} - q^{50} - 2q^{52} + 3q^{53} - 2q^{58} - 2q^{61} - q^{64} + 3q^{65} - 2q^{68} - q^{72} - 2q^{73} - 2q^{74} - q^{80} - q^{81} - 2q^{82} + 3q^{85} + 3q^{89} - q^{90} - 2q^{97} - q^{98} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(100))$$

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
100.1.b $$\chi_{100}(51, \cdot)$$ None 0 1
100.1.d $$\chi_{100}(99, \cdot)$$ None 0 1
100.1.f $$\chi_{100}(57, \cdot)$$ None 0 2
100.1.h $$\chi_{100}(19, \cdot)$$ None 0 4
100.1.j $$\chi_{100}(11, \cdot)$$ 100.1.j.a 4 4
100.1.k $$\chi_{100}(13, \cdot)$$ None 0 8