## 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

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

## 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