# Properties

 Label 33.8.d Level $33$ Weight $8$ Character orbit 33.d Rep. character $\chi_{33}(32,\cdot)$ Character field $\Q$ Dimension $26$ Newform subspaces $2$ Sturm bound $32$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$33 = 3 \cdot 11$$ Weight: $$k$$ $$=$$ $$8$$ 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: $$32$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{8}(33, [\chi])$$.

Total New Old
Modular forms 30 30 0
Cusp forms 26 26 0
Eisenstein series 4 4 0

## Trace form

 $$26 q + 37 q^{3} + 1532 q^{4} - 3425 q^{9} + O(q^{10})$$ $$26 q + 37 q^{3} + 1532 q^{4} - 3425 q^{9} + 3688 q^{12} + 13007 q^{15} + 38612 q^{16} - 17556 q^{22} + 10644 q^{25} - 19664 q^{27} + 209458 q^{31} + 218977 q^{33} - 436080 q^{34} - 624752 q^{36} - 52454 q^{37} - 100296 q^{42} - 1011553 q^{45} + 1812676 q^{48} + 477782 q^{49} - 2322914 q^{55} - 2920440 q^{58} + 3281036 q^{60} + 10384292 q^{64} + 2895156 q^{66} + 9098542 q^{67} - 1489129 q^{69} - 6924504 q^{70} - 6257742 q^{75} - 26237448 q^{78} + 19126627 q^{81} - 23600232 q^{82} - 25179660 q^{88} + 9380640 q^{91} + 22154513 q^{93} + 42583402 q^{97} + 37852441 q^{99} + O(q^{100})$$

## Decomposition of $$S_{8}^{\mathrm{new}}(33, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
33.8.d.a $2$ $10.309$ $$\Q(\sqrt{-11})$$ $$\Q(\sqrt{-11})$$ $$0$$ $$-83$$ $$0$$ $$0$$ $$q+(-35-13\beta )q^{3}-2^{7}q^{4}+(71-142\beta )q^{5}+\cdots$$
33.8.d.b $24$ $10.309$ None $$0$$ $$120$$ $$0$$ $$0$$