## Defining parameters

 Level: $$N$$ = $$15 = 3 \cdot 5$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$3$$ Newform subspaces: $$4$$ Sturm bound: $$48$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(15))$$.

Total New Old
Modular forms 24 12 12
Cusp forms 8 8 0
Eisenstein series 16 4 12

## Trace form

 $$8q - 4q^{2} - 4q^{3} - 8q^{4} - 4q^{5} - 8q^{6} - 8q^{7} + 12q^{8} + 16q^{9} + O(q^{10})$$ $$8q - 4q^{2} - 4q^{3} - 8q^{4} - 4q^{5} - 8q^{6} - 8q^{7} + 12q^{8} + 16q^{9} + 24q^{10} + 16q^{11} + 28q^{12} - 16q^{15} - 48q^{16} - 40q^{17} - 52q^{18} - 48q^{19} - 36q^{20} + 40q^{22} + 56q^{23} + 72q^{24} + 56q^{25} + 88q^{26} + 44q^{27} + 56q^{28} - 44q^{30} - 48q^{31} - 76q^{32} - 56q^{33} - 8q^{34} - 40q^{35} - 40q^{36} + 32q^{37} - 96q^{38} - 64q^{39} + 8q^{40} - 56q^{41} - 48q^{42} + 24q^{43} + 76q^{45} - 8q^{46} + 128q^{47} + 124q^{48} + 72q^{49} + 164q^{50} + 136q^{51} - 112q^{52} + 56q^{53} + 16q^{54} - 144q^{55} - 64q^{57} - 152q^{58} + 16q^{60} + 128q^{61} + 88q^{62} + 24q^{63} - 56q^{64} - 112q^{65} - 16q^{66} - 152q^{67} - 104q^{68} - 264q^{69} - 120q^{70} - 272q^{71} - 156q^{72} - 72q^{73} + 44q^{75} + 448q^{76} + 88q^{77} + 280q^{78} + 472q^{79} + 164q^{80} - 32q^{81} + 408q^{82} - 16q^{83} - 24q^{84} + 72q^{85} - 224q^{86} + 56q^{87} + 72q^{88} - 16q^{90} - 208q^{91} + 104q^{92} - 248q^{94} + 144q^{95} - 352q^{96} - 352q^{97} - 188q^{98} + 80q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(15))$$

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
15.3.c $$\chi_{15}(11, \cdot)$$ 15.3.c.a 2 1
15.3.d $$\chi_{15}(14, \cdot)$$ 15.3.d.a 1 1
15.3.d.b 1
15.3.f $$\chi_{15}(7, \cdot)$$ 15.3.f.a 4 2