## Defining parameters

 Level: $$N$$ = $$12 = 2^{2} \cdot 3$$ Weight: $$k$$ = $$5$$ Nonzero newspaces: $$2$$ Newform subspaces: $$2$$ 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

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

## 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

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