# Properties

 Label 731.2.d Level 731 Weight 2 Character orbit d Rep. character $$\chi_{731}(560,\cdot)$$ Character field $$\Q$$ Dimension 64 Newforms 4 Sturm bound 132 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$731 = 17 \cdot 43$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 731.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$17$$ Character field: $$\Q$$ Newforms: $$4$$ 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 68 64 4
Cusp forms 64 64 0
Eisenstein series 4 0 4

## Trace form

 $$64q - 2q^{2} + 58q^{4} - 6q^{8} - 76q^{9} + O(q^{10})$$ $$64q - 2q^{2} + 58q^{4} - 6q^{8} - 76q^{9} - 10q^{13} + 12q^{15} + 62q^{16} + 7q^{17} - 2q^{18} + 20q^{19} + 8q^{21} - 60q^{25} - 16q^{26} + 16q^{30} + 6q^{32} + 20q^{33} - 36q^{34} + 4q^{35} - 78q^{36} + 4q^{38} + 12q^{42} - 4q^{43} - 12q^{47} - 52q^{49} - 10q^{50} + 26q^{51} - 52q^{52} - 6q^{53} - 24q^{59} + 12q^{60} + 30q^{64} - 20q^{66} - 22q^{67} + 52q^{68} - 12q^{69} + 100q^{70} - 46q^{72} + 16q^{76} + 4q^{77} + 104q^{81} - 18q^{83} + 28q^{84} + 12q^{85} + 10q^{86} + 40q^{87} - 36q^{89} + 24q^{93} - 96q^{94} + 30q^{98} + O(q^{100})$$

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

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
731.2.d.a $$2$$ $$5.837$$ $$\Q(\sqrt{-2})$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}-q^{4}+\beta q^{5}-3q^{8}+3q^{9}+\beta q^{10}+\cdots$$
731.2.d.b $$8$$ $$5.837$$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-2q^{4}-\beta _{3}q^{5}+(\beta _{1}-\beta _{7})q^{7}+\cdots$$
731.2.d.c $$20$$ $$5.837$$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None $$2$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{6}q^{2}+\beta _{13}q^{3}+(2+\beta _{1})q^{4}+\beta _{10}q^{5}+\cdots$$
731.2.d.d $$34$$ $$5.837$$ None $$-6$$ $$0$$ $$0$$ $$0$$