# Properties

 Label 33.4.d Level $33$ Weight $4$ Character orbit 33.d Rep. character $\chi_{33}(32,\cdot)$ Character field $\Q$ Dimension $10$ Newform subspaces $2$ Sturm bound $16$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$33 = 3 \cdot 11$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 33.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$33$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$16$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(33, [\chi])$$.

Total New Old
Modular forms 14 14 0
Cusp forms 10 10 0
Eisenstein series 4 4 0

## Trace form

 $$10 q - 2 q^{3} + 28 q^{4} - 20 q^{9} + O(q^{10})$$ $$10 q - 2 q^{3} + 28 q^{4} - 20 q^{9} - 80 q^{12} + 62 q^{15} - 140 q^{16} - 300 q^{22} + 174 q^{25} + 460 q^{27} + 140 q^{31} + 592 q^{33} + 768 q^{34} - 776 q^{36} - 16 q^{37} - 120 q^{42} - 1018 q^{45} - 1244 q^{48} - 1346 q^{49} - 1444 q^{55} + 1992 q^{58} + 3476 q^{60} - 2108 q^{64} + 2076 q^{66} + 1004 q^{67} - 2110 q^{69} + 5016 q^{70} + 2208 q^{75} + 120 q^{78} - 5372 q^{81} - 6408 q^{82} - 3852 q^{88} + 4776 q^{91} + 3866 q^{93} - 3904 q^{97} + 3010 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(33, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
33.4.d.a $2$ $1.947$ $$\Q(\sqrt{-11})$$ $$\Q(\sqrt{-11})$$ $$0$$ $$-8$$ $$0$$ $$0$$ $$q+(-4-\beta )q^{3}-8q^{4}-4\beta q^{5}+(5+8\beta )q^{9}+\cdots$$
33.4.d.b $8$ $1.947$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$0$$ $$6$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+(1-\beta _{3})q^{3}+(5+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$$