# Properties

 Label 33.5.c Level $33$ Weight $5$ Character orbit 33.c Rep. character $\chi_{33}(10,\cdot)$ Character field $\Q$ Dimension $8$ Newform subspaces $1$ Sturm bound $20$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$33 = 3 \cdot 11$$ Weight: $$k$$ $$=$$ $$5$$ Character orbit: $$[\chi]$$ $$=$$ 33.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$11$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$20$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{5}(33, [\chi])$$.

Total New Old
Modular forms 18 8 10
Cusp forms 14 8 6
Eisenstein series 4 0 4

## Trace form

 $$8q - 76q^{4} - 36q^{5} + 216q^{9} + O(q^{10})$$ $$8q - 76q^{4} - 36q^{5} + 216q^{9} + 36q^{11} - 360q^{12} - 1140q^{14} + 108q^{15} + 1412q^{16} + 2532q^{20} - 780q^{22} + 516q^{23} - 2280q^{25} - 1524q^{26} + 2752q^{31} + 1008q^{33} - 4920q^{34} - 2052q^{36} + 5296q^{37} + 696q^{38} - 4356q^{42} - 6540q^{44} - 972q^{45} + 420q^{47} + 9936q^{48} - 6832q^{49} + 3540q^{53} + 3784q^{55} + 17964q^{56} + 21624q^{58} - 16632q^{59} - 612q^{60} - 27508q^{64} + 360q^{66} - 3656q^{67} + 9036q^{69} + 3312q^{70} - 13212q^{71} - 9288q^{75} + 23268q^{77} - 13140q^{78} - 4476q^{80} + 5832q^{81} + 17088q^{82} + 19896q^{86} - 12516q^{88} + 15528q^{89} - 19752q^{91} - 81180q^{92} - 21384q^{93} + 7624q^{97} + 972q^{99} + O(q^{100})$$

## Decomposition of $$S_{5}^{\mathrm{new}}(33, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
33.5.c.a $$8$$ $$3.411$$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$0$$ $$-36$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-10-\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{5}^{\mathrm{old}}(33, [\chi])$$ into lower level spaces

$$S_{5}^{\mathrm{old}}(33, [\chi]) \cong$$ $$S_{5}^{\mathrm{new}}(11, [\chi])$$$$^{\oplus 2}$$