## Defining parameters

 Level: $$N$$ = $$12 = 2^{2} \cdot 3$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$2$$ Newform subspaces: $$2$$ Sturm bound: $$24$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(12))$$.

Total New Old
Modular forms 13 3 10
Cusp forms 3 3 0
Eisenstein series 10 0 10

## Trace form

 $$3q - 2q^{2} - 3q^{3} - 4q^{4} - 4q^{5} + 6q^{6} + 2q^{7} + 16q^{8} + 3q^{9} + O(q^{10})$$ $$3q - 2q^{2} - 3q^{3} - 4q^{4} - 4q^{5} + 6q^{6} + 2q^{7} + 16q^{8} + 3q^{9} + 4q^{10} - 12q^{12} - 18q^{13} - 24q^{14} - 16q^{16} + 20q^{17} + 6q^{18} + 26q^{19} + 8q^{20} + 18q^{21} + 24q^{22} - 17q^{25} - 4q^{26} - 27q^{27} + 48q^{28} - 52q^{29} - 12q^{30} - 46q^{31} - 32q^{32} - 24q^{33} - 20q^{34} + 12q^{36} + 78q^{37} + 72q^{38} + 66q^{39} - 32q^{40} + 116q^{41} - 24q^{42} - 22q^{43} - 48q^{44} + 12q^{45} - 96q^{46} + 48q^{48} - 43q^{49} + 42q^{50} - 8q^{52} - 148q^{53} - 18q^{54} - 150q^{57} + 52q^{58} + 24q^{60} + 126q^{61} + 24q^{62} + 18q^{63} + 128q^{64} - 8q^{65} + 24q^{66} + 122q^{67} - 40q^{68} + 96q^{69} + 48q^{70} - 48q^{72} - 138q^{73} - 52q^{74} - 75q^{75} - 144q^{76} + 96q^{77} + 12q^{78} - 142q^{79} + 32q^{80} + 99q^{81} - 116q^{82} - 48q^{84} - 40q^{85} - 168q^{86} + 164q^{89} - 12q^{90} - 44q^{91} + 192q^{92} + 114q^{93} + 240q^{94} - 96q^{96} + 6q^{97} - 2q^{98} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(12))$$

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
12.3.c $$\chi_{12}(5, \cdot)$$ 12.3.c.a 1 1
12.3.d $$\chi_{12}(7, \cdot)$$ 12.3.d.a 2 1