## Defining parameters

 Level: $$N$$ = $$6 = 2 \cdot 3$$ Weight: $$k$$ = $$6$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$12$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 7 1 6
Cusp forms 3 1 2
Eisenstein series 4 0 4

## Trace form

 $$q + 4q^{2} - 9q^{3} + 16q^{4} - 66q^{5} - 36q^{6} + 176q^{7} + 64q^{8} + 81q^{9} + O(q^{10})$$ $$q + 4q^{2} - 9q^{3} + 16q^{4} - 66q^{5} - 36q^{6} + 176q^{7} + 64q^{8} + 81q^{9} - 264q^{10} - 60q^{11} - 144q^{12} - 658q^{13} + 704q^{14} + 594q^{15} + 256q^{16} - 414q^{17} + 324q^{18} + 956q^{19} - 1056q^{20} - 1584q^{21} - 240q^{22} + 600q^{23} - 576q^{24} + 1231q^{25} - 2632q^{26} - 729q^{27} + 2816q^{28} + 5574q^{29} + 2376q^{30} - 3592q^{31} + 1024q^{32} + 540q^{33} - 1656q^{34} - 11616q^{35} + 1296q^{36} - 8458q^{37} + 3824q^{38} + 5922q^{39} - 4224q^{40} + 19194q^{41} - 6336q^{42} + 13316q^{43} - 960q^{44} - 5346q^{45} + 2400q^{46} - 19680q^{47} - 2304q^{48} + 14169q^{49} + 4924q^{50} + 3726q^{51} - 10528q^{52} - 31266q^{53} - 2916q^{54} + 3960q^{55} + 11264q^{56} - 8604q^{57} + 22296q^{58} + 26340q^{59} + 9504q^{60} - 31090q^{61} - 14368q^{62} + 14256q^{63} + 4096q^{64} + 43428q^{65} + 2160q^{66} - 16804q^{67} - 6624q^{68} - 5400q^{69} - 46464q^{70} + 6120q^{71} + 5184q^{72} - 25558q^{73} - 33832q^{74} - 11079q^{75} + 15296q^{76} - 10560q^{77} + 23688q^{78} + 74408q^{79} - 16896q^{80} + 6561q^{81} + 76776q^{82} - 6468q^{83} - 25344q^{84} + 27324q^{85} + 53264q^{86} - 50166q^{87} - 3840q^{88} - 32742q^{89} - 21384q^{90} - 115808q^{91} + 9600q^{92} + 32328q^{93} - 78720q^{94} - 63096q^{95} - 9216q^{96} + 166082q^{97} + 56676q^{98} - 4860q^{99} + O(q^{100})$$

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

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
6.6.a $$\chi_{6}(1, \cdot)$$ 6.6.a.a 1 1

## Decomposition of $$S_{6}^{\mathrm{old}}(\Gamma_1(6))$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(\Gamma_1(6)) \cong$$ $$S_{6}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 2}$$