## Defining parameters

 Level: $$N$$ = $$6 = 2 \cdot 3$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$8$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(6))$$.

Total New Old
Modular forms 5 1 4
Cusp forms 1 1 0
Eisenstein series 4 0 4

## Trace form

 $$q - 2q^{2} - 3q^{3} + 4q^{4} + 6q^{5} + 6q^{6} - 16q^{7} - 8q^{8} + 9q^{9} + O(q^{10})$$ $$q - 2q^{2} - 3q^{3} + 4q^{4} + 6q^{5} + 6q^{6} - 16q^{7} - 8q^{8} + 9q^{9} - 12q^{10} + 12q^{11} - 12q^{12} + 38q^{13} + 32q^{14} - 18q^{15} + 16q^{16} - 126q^{17} - 18q^{18} + 20q^{19} + 24q^{20} + 48q^{21} - 24q^{22} + 168q^{23} + 24q^{24} - 89q^{25} - 76q^{26} - 27q^{27} - 64q^{28} + 30q^{29} + 36q^{30} - 88q^{31} - 32q^{32} - 36q^{33} + 252q^{34} - 96q^{35} + 36q^{36} + 254q^{37} - 40q^{38} - 114q^{39} - 48q^{40} + 42q^{41} - 96q^{42} - 52q^{43} + 48q^{44} + 54q^{45} - 336q^{46} - 96q^{47} - 48q^{48} - 87q^{49} + 178q^{50} + 378q^{51} + 152q^{52} + 198q^{53} + 54q^{54} + 72q^{55} + 128q^{56} - 60q^{57} - 60q^{58} - 660q^{59} - 72q^{60} - 538q^{61} + 176q^{62} - 144q^{63} + 64q^{64} + 228q^{65} + 72q^{66} + 884q^{67} - 504q^{68} - 504q^{69} + 192q^{70} + 792q^{71} - 72q^{72} + 218q^{73} - 508q^{74} + 267q^{75} + 80q^{76} - 192q^{77} + 228q^{78} - 520q^{79} + 96q^{80} + 81q^{81} - 84q^{82} - 492q^{83} + 192q^{84} - 756q^{85} + 104q^{86} - 90q^{87} - 96q^{88} + 810q^{89} - 108q^{90} - 608q^{91} + 672q^{92} + 264q^{93} + 192q^{94} + 120q^{95} + 96q^{96} + 1154q^{97} + 174q^{98} + 108q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(6))$$

We only show spaces with even 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
6.4.a $$\chi_{6}(1, \cdot)$$ 6.4.a.a 1 1