# Properties

 Label 33.6.e Level $33$ Weight $6$ Character orbit 33.e Rep. character $\chi_{33}(4,\cdot)$ Character field $\Q(\zeta_{5})$ Dimension $40$ Newform subspaces $2$ Sturm bound $24$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$33 = 3 \cdot 11$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 33.e (of order $$5$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$11$$ Character field: $$\Q(\zeta_{5})$$ Newform subspaces: $$2$$ Sturm bound: $$24$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(33, [\chi])$$.

Total New Old
Modular forms 88 40 48
Cusp forms 72 40 32
Eisenstein series 16 0 16

## Trace form

 $$40q + 4q^{2} - 116q^{4} - 44q^{5} - 72q^{6} - 474q^{7} - 548q^{8} - 810q^{9} + O(q^{10})$$ $$40q + 4q^{2} - 116q^{4} - 44q^{5} - 72q^{6} - 474q^{7} - 548q^{8} - 810q^{9} + 1528q^{10} + 1454q^{11} + 792q^{12} - 1806q^{13} - 998q^{14} - 198q^{15} - 8576q^{16} - 662q^{17} - 486q^{18} + 2028q^{19} + 11214q^{20} + 7056q^{21} + 10154q^{22} + 9540q^{23} - 3294q^{24} - 22508q^{25} - 10486q^{26} + 6066q^{28} - 15716q^{29} + 6804q^{30} + 14748q^{31} + 64488q^{32} + 7254q^{33} + 7456q^{34} - 65472q^{35} - 9396q^{36} - 28326q^{37} - 54026q^{38} - 1008q^{39} - 30434q^{40} + 46852q^{41} + 54612q^{42} + 41936q^{43} + 82886q^{44} - 3564q^{45} - 50526q^{46} - 91418q^{47} - 55440q^{48} - 84520q^{49} - 56634q^{50} + 7776q^{51} + 28902q^{52} - 94834q^{53} + 23328q^{54} + 15344q^{55} + 338532q^{56} + 13608q^{57} + 94646q^{58} - 6682q^{59} - 43740q^{60} + 67482q^{61} - 39272q^{62} - 38394q^{63} + 42608q^{64} - 162404q^{65} - 81432q^{66} + 30908q^{67} - 33128q^{68} + 113670q^{69} - 119324q^{70} + 308052q^{71} + 53622q^{72} + 87744q^{73} - 42114q^{74} - 87192q^{75} + 126080q^{76} - 311374q^{77} - 432720q^{78} + 77682q^{79} - 89422q^{80} - 65610q^{81} + 240530q^{82} + 12290q^{83} + 253692q^{84} - 72334q^{85} - 37688q^{86} + 401976q^{87} - 569152q^{88} + 387124q^{89} + 76788q^{90} + 679174q^{91} + 716510q^{92} + 33012q^{93} + 11222q^{94} - 243210q^{95} - 359010q^{96} - 445650q^{97} - 2446744q^{98} - 198936q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(33, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
33.6.e.a $$20$$ $$5.293$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$-2$$ $$-45$$ $$-33$$ $$-335$$ $$q+(-\beta _{1}+\beta _{7})q^{2}-9\beta _{9}q^{3}+(-\beta _{6}+\cdots)q^{4}+\cdots$$
33.6.e.b $$20$$ $$5.293$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$6$$ $$45$$ $$-11$$ $$-139$$ $$q+(-\beta _{5}+\beta _{6})q^{2}+9\beta _{7}q^{3}+(-12+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{6}^{\mathrm{old}}(33, [\chi])$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(33, [\chi]) \cong$$ $$S_{6}^{\mathrm{new}}(11, [\chi])$$$$^{\oplus 2}$$