## Defining parameters

 Level: $$N$$ = $$10 = 2 \cdot 5$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$18$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(10))$$.

Total New Old
Modular forms 10 2 8
Cusp forms 2 2 0
Eisenstein series 8 0 8

## Trace form

 $$2 q - 2 q^{2} - 4 q^{3} + 8 q^{6} + 4 q^{7} + 4 q^{8} + O(q^{10})$$ $$2 q - 2 q^{2} - 4 q^{3} + 8 q^{6} + 4 q^{7} + 4 q^{8} - 10 q^{10} - 16 q^{11} - 8 q^{12} + 6 q^{13} + 20 q^{15} - 8 q^{16} + 14 q^{17} + 2 q^{18} + 20 q^{20} - 16 q^{21} + 16 q^{22} - 4 q^{23} - 50 q^{25} - 12 q^{26} - 40 q^{27} - 8 q^{28} + 104 q^{31} + 8 q^{32} + 32 q^{33} + 20 q^{35} - 4 q^{36} - 6 q^{37} - 40 q^{38} - 20 q^{40} - 16 q^{41} + 16 q^{42} - 84 q^{43} + 10 q^{45} + 8 q^{46} - 36 q^{47} + 16 q^{48} + 50 q^{50} - 56 q^{51} + 12 q^{52} + 106 q^{53} + 16 q^{56} + 80 q^{57} + 80 q^{58} - 40 q^{60} - 96 q^{61} - 104 q^{62} - 4 q^{63} - 30 q^{65} - 64 q^{66} + 124 q^{67} - 28 q^{68} - 40 q^{70} - 56 q^{71} + 4 q^{72} - 94 q^{73} + 100 q^{75} + 80 q^{76} - 32 q^{77} + 24 q^{78} + 142 q^{81} + 16 q^{82} + 36 q^{83} + 70 q^{85} + 168 q^{86} - 160 q^{87} - 32 q^{88} - 10 q^{90} + 24 q^{91} - 8 q^{92} - 208 q^{93} - 200 q^{95} - 32 q^{96} - 126 q^{97} - 82 q^{98} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(10))$$

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
10.3.c $$\chi_{10}(3, \cdot)$$ 10.3.c.a 2 2