# Properties

 Label 731.2.s Level 731 Weight 2 Character orbit s Rep. character $$\chi_{731}(214,\cdot)$$ Character field $$\Q(\zeta_{16})$$ Dimension 512 Newform subspaces 2 Sturm bound 132 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$731 = 17 \cdot 43$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 731.s (of order $$16$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$731$$ Character field: $$\Q(\zeta_{16})$$ Newform subspaces: $$2$$ Sturm bound: $$132$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(731, [\chi])$$.

Total New Old
Modular forms 544 544 0
Cusp forms 512 512 0
Eisenstein series 32 32 0

## Trace form

 $$512q - 16q^{4} - 16q^{6} - 16q^{9} + O(q^{10})$$ $$512q - 16q^{4} - 16q^{6} - 16q^{9} - 16q^{10} - 8q^{13} - 16q^{14} - 16q^{15} - 16q^{17} - 16q^{21} - 24q^{23} - 64q^{24} + 48q^{31} - 96q^{35} + 16q^{36} - 32q^{38} - 16q^{40} - 16q^{41} - 48q^{43} - 80q^{44} - 96q^{47} - 16q^{49} + 96q^{52} - 16q^{53} + 144q^{54} - 16q^{56} - 48q^{57} - 64q^{58} - 48q^{59} - 224q^{60} - 48q^{64} - 272q^{66} - 16q^{68} - 112q^{74} + 64q^{78} + 16q^{79} + 96q^{81} + 16q^{83} + 96q^{86} - 16q^{87} + 64q^{90} + 368q^{92} - 96q^{95} + 80q^{96} - 80q^{97} - 128q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(731, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
731.2.s.a $$16$$ $$5.837$$ 16.0.$$\cdots$$.1 $$\Q(\sqrt{-43})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+2\beta _{4}q^{4}-3\beta _{5}q^{9}+(-\beta _{4}-\beta _{6}-\beta _{7}+\cdots)q^{11}+\cdots$$
731.2.s.b $$496$$ $$5.837$$ None $$0$$ $$0$$ $$0$$ $$0$$