# Properties

 Label 33.6 Level 33 Weight 6 Dimension 138 Nonzero newspaces 4 Newform subspaces 10 Sturm bound 480 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$33 = 3 \cdot 11$$ Weight: $$k$$ = $$6$$ Nonzero newspaces: $$4$$ Newform subspaces: $$10$$ Sturm bound: $$480$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_1(33))$$.

Total New Old
Modular forms 220 158 62
Cusp forms 180 138 42
Eisenstein series 40 20 20

## Trace form

 $$138q + 12q^{2} - 23q^{3} - 18q^{4} - 12q^{5} + 123q^{6} - 520q^{7} - 656q^{8} + 383q^{9} + O(q^{10})$$ $$138q + 12q^{2} - 23q^{3} - 18q^{4} - 12q^{5} + 123q^{6} - 520q^{7} - 656q^{8} + 383q^{9} + 2072q^{10} + 1454q^{11} + 238q^{12} - 2296q^{13} + 510q^{14} - 3853q^{15} - 14018q^{16} - 5274q^{17} + 4977q^{18} + 5572q^{19} + 17002q^{20} + 9540q^{21} + 21746q^{22} + 7060q^{23} - 3559q^{24} - 6592q^{25} - 24794q^{26} + 8602q^{27} - 46240q^{28} - 21896q^{29} - 11402q^{30} + 24410q^{31} + 78100q^{32} - 1869q^{33} - 11236q^{34} - 55480q^{35} - 58293q^{36} - 48430q^{37} - 45722q^{38} + 11876q^{39} + 50284q^{40} + 86040q^{41} + 145940q^{42} + 72292q^{43} + 78046q^{44} + 35213q^{45} - 47720q^{46} - 23266q^{47} - 84942q^{48} - 97746q^{49} - 194258q^{50} - 168726q^{51} - 5984q^{52} - 111610q^{53} + 37908q^{54} + 117854q^{55} + 344040q^{56} + 312018q^{57} + 270916q^{58} + 26598q^{59} + 9958q^{60} - 61616q^{61} + 10320q^{62} - 161640q^{63} - 576714q^{64} - 291396q^{65} - 586956q^{66} - 86074q^{67} - 144976q^{68} - 38285q^{69} + 416860q^{70} + 343116q^{71} + 388834q^{72} + 234640q^{73} - 18810q^{74} + 270702q^{75} + 8368q^{76} - 281850q^{77} + 141964q^{78} - 401280q^{79} - 30258q^{80} - 365017q^{81} - 274510q^{82} + 63866q^{83} + 74340q^{84} + 680436q^{85} + 182608q^{86} + 370656q^{87} + 1238902q^{88} + 427492q^{89} + 414292q^{90} + 1133540q^{91} + 926650q^{92} + 113295q^{93} - 638944q^{94} - 477378q^{95} - 1649900q^{96} - 1950194q^{97} - 2674864q^{98} - 1074091q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_1(33))$$

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
33.6.a $$\chi_{33}(1, \cdot)$$ 33.6.a.a 1 1
33.6.a.b 1
33.6.a.c 2
33.6.a.d 2
33.6.a.e 2
33.6.d $$\chi_{33}(32, \cdot)$$ 33.6.d.a 2 1
33.6.d.b 16
33.6.e $$\chi_{33}(4, \cdot)$$ 33.6.e.a 20 4
33.6.e.b 20
33.6.f $$\chi_{33}(2, \cdot)$$ 33.6.f.a 72 4

## Decomposition of $$S_{6}^{\mathrm{old}}(\Gamma_1(33))$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(\Gamma_1(33)) \cong$$ $$S_{6}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 2}$$