# Properties

 Label 33.3.b Level $33$ Weight $3$ Character orbit 33.b Rep. character $\chi_{33}(23,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $2$ Sturm bound $12$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$33 = 3 \cdot 11$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 33.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$12$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(33, [\chi])$$.

Total New Old
Modular forms 10 6 4
Cusp forms 6 6 0
Eisenstein series 4 0 4

## Trace form

 $$6 q + q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 11 q^{9} + O(q^{10})$$ $$6 q + q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 11 q^{9} + 36 q^{10} - 28 q^{12} + 13 q^{15} - 12 q^{16} + 38 q^{18} - 48 q^{19} - 86 q^{21} + 24 q^{24} + 48 q^{25} + 34 q^{27} + 48 q^{28} + 142 q^{30} - 6 q^{31} - 11 q^{33} + 24 q^{34} - 212 q^{36} - 30 q^{37} - 32 q^{39} - 168 q^{40} - 68 q^{42} + 180 q^{43} + 17 q^{45} - 132 q^{46} + 140 q^{48} - 30 q^{49} + 214 q^{51} - 192 q^{52} - 176 q^{54} + 66 q^{55} + 108 q^{57} + 480 q^{58} + 56 q^{60} + 14 q^{63} + 228 q^{64} - 110 q^{66} - 54 q^{67} - 253 q^{69} - 360 q^{70} + 72 q^{72} - 432 q^{73} - 238 q^{75} + 264 q^{76} - 128 q^{78} - 156 q^{79} + 275 q^{81} - 48 q^{82} + 416 q^{84} + 108 q^{85} - 252 q^{87} + 132 q^{88} + 410 q^{90} + 192 q^{91} - 131 q^{93} - 312 q^{94} + 272 q^{96} + 342 q^{97} - 55 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(33, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
33.3.b.a $2$ $0.899$ $$\Q(\sqrt{-11})$$ None $$0$$ $$6$$ $$0$$ $$-16$$ $$q-\beta q^{2}+3q^{3}-7q^{4}+2\beta q^{5}-3\beta q^{6}+\cdots$$
33.3.b.b $4$ $0.899$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$0$$ $$-5$$ $$0$$ $$4$$ $$q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+(-1+\beta _{1}+\cdots)q^{3}+\cdots$$