## Defining parameters

 Level: $$N$$ = $$12 = 2^{2} \cdot 3$$ Weight: $$k$$ = $$5$$ Nonzero newspaces: $$2$$ Newforms: $$2$$ Sturm bound: $$40$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{5}(\Gamma_1(12))$$.

Total New Old
Modular forms 21 5 16
Cusp forms 11 5 6
Eisenstein series 10 0 10

## Trace form

 $$5q + 6q^{2} + 9q^{3} - 20q^{4} + 24q^{5} - 18q^{6} - 94q^{7} - 27q^{9} + O(q^{10})$$ $$5q + 6q^{2} + 9q^{3} - 20q^{4} + 24q^{5} - 18q^{6} - 94q^{7} - 27q^{9} - 172q^{10} + 180q^{12} + 442q^{13} + 600q^{14} + 112q^{16} - 600q^{17} - 162q^{18} - 46q^{19} - 1368q^{20} - 990q^{21} - 1128q^{22} + 1296q^{24} + 1597q^{25} + 1692q^{26} + 729q^{27} + 1488q^{28} + 888q^{29} - 1980q^{30} + 194q^{31} - 2784q^{32} + 720q^{33} - 484q^{34} + 540q^{36} - 6470q^{37} + 4680q^{38} + 1314q^{39} + 1664q^{40} + 552q^{41} - 2088q^{42} - 3214q^{43} - 3696q^{44} - 648q^{45} - 384q^{46} + 1008q^{48} + 5863q^{49} - 1038q^{50} + 6008q^{52} + 5112q^{53} + 486q^{54} + 1728q^{56} + 5202q^{57} - 124q^{58} - 2664q^{60} + 2266q^{61} - 7224q^{62} - 7614q^{63} - 14720q^{64} - 18192q^{65} + 4824q^{66} + 5906q^{67} + 5496q^{68} - 9792q^{69} + 6096q^{70} + 298q^{73} - 4116q^{74} + 5625q^{75} - 1872q^{76} + 20928q^{77} + 9900q^{78} + 7682q^{79} + 25632q^{80} + 9477q^{81} + 3740q^{82} - 10512q^{84} - 10256q^{85} - 19560q^{86} - 8640q^{88} - 25080q^{89} + 4644q^{90} - 13724q^{91} + 18816q^{92} - 15390q^{93} - 5232q^{94} - 8352q^{96} + 4234q^{97} - 5850q^{98} + O(q^{100})$$

## Decomposition of $$S_{5}^{\mathrm{new}}(\Gamma_1(12))$$

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
12.5.c $$\chi_{12}(5, \cdot)$$ 12.5.c.a 1 1
12.5.d $$\chi_{12}(7, \cdot)$$ 12.5.d.a 4 1

## Decomposition of $$S_{5}^{\mathrm{old}}(\Gamma_1(12))$$ into lower level spaces

$$S_{5}^{\mathrm{old}}(\Gamma_1(12)) \cong$$ $$S_{5}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 2}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 2}$$