# Properties

 Label 33.2.e Level $33$ Weight $2$ Character orbit 33.e Rep. character $\chi_{33}(4,\cdot)$ Character field $\Q(\zeta_{5})$ Dimension $8$ Newform subspaces $2$ Sturm bound $8$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$33 = 3 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ 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: $$8$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(33, [\chi])$$.

Total New Old
Modular forms 24 8 16
Cusp forms 8 8 0
Eisenstein series 16 0 16

## Trace form

 $$8 q - 4 q^{2} - 6 q^{4} - 4 q^{5} - 2 q^{6} - 2 q^{7} + 8 q^{8} - 2 q^{9} + O(q^{10})$$ $$8 q - 4 q^{2} - 6 q^{4} - 4 q^{5} - 2 q^{6} - 2 q^{7} + 8 q^{8} - 2 q^{9} + 4 q^{10} - 2 q^{11} - 8 q^{12} - 2 q^{13} + 2 q^{14} + 2 q^{15} + 10 q^{16} + 14 q^{17} + 6 q^{18} - 20 q^{19} + 6 q^{20} + 16 q^{21} - 4 q^{22} - 12 q^{23} + 12 q^{24} + 10 q^{26} - 12 q^{28} - 4 q^{29} - 4 q^{31} - 48 q^{32} - 10 q^{33} + 8 q^{34} - 6 q^{36} + 6 q^{37} - 10 q^{38} - 16 q^{39} + 4 q^{40} + 20 q^{41} - 10 q^{42} + 16 q^{43} + 34 q^{44} - 4 q^{45} + 10 q^{46} + 14 q^{47} + 8 q^{48} + 4 q^{49} + 18 q^{50} + 10 q^{52} + 10 q^{53} + 8 q^{54} + 16 q^{55} + 12 q^{56} - 24 q^{58} - 26 q^{59} - 18 q^{61} - 28 q^{62} - 2 q^{63} + 6 q^{64} - 28 q^{65} - 12 q^{66} - 4 q^{67} - 28 q^{68} - 6 q^{69} - 6 q^{70} - 12 q^{71} - 2 q^{72} + 20 q^{73} - 30 q^{74} + 8 q^{75} + 40 q^{76} - 2 q^{77} + 16 q^{78} - 6 q^{79} + 22 q^{80} - 2 q^{81} - 14 q^{82} + 34 q^{83} - 2 q^{85} + 8 q^{86} + 24 q^{87} - 62 q^{88} - 4 q^{89} + 4 q^{90} + 6 q^{91} + 10 q^{92} + 20 q^{93} + 18 q^{94} + 30 q^{95} - 8 q^{96} - 30 q^{97} + 40 q^{98} + 8 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(33, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
33.2.e.a $4$ $0.264$ $$\Q(\zeta_{10})$$ None $$-3$$ $$-1$$ $$-1$$ $$-3$$ $$q+(-1-\zeta_{10}^{2})q^{2}-\zeta_{10}^{3}q^{3}+(\zeta_{10}+\cdots)q^{4}+\cdots$$
33.2.e.b $4$ $0.264$ $$\Q(\zeta_{10})$$ None $$-1$$ $$1$$ $$-3$$ $$1$$ $$q+(-1+2\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}^{3}q^{3}+\cdots$$