## 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

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

## 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