# Properties

 Label 731.2.bl Level 731 Weight 2 Character orbit bl Rep. character $$\chi_{731}(9,\cdot)$$ Character field $$\Q(\zeta_{168})$$ Dimension 3072 Newforms 1 Sturm bound 132 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$731 = 17 \cdot 43$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 731.bl (of order $$168$$ and degree $$48$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$731$$ Character field: $$\Q(\zeta_{168})$$ Newforms: $$1$$ Sturm bound: $$132$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 3264 3264 0
Cusp forms 3072 3072 0
Eisenstein series 192 192 0

## Trace form

 $$3072q - 40q^{2} - 52q^{3} - 44q^{5} - 24q^{6} - 24q^{7} - 72q^{8} - 28q^{9} + O(q^{10})$$ $$3072q - 40q^{2} - 52q^{3} - 44q^{5} - 24q^{6} - 24q^{7} - 72q^{8} - 28q^{9} - 52q^{10} - 40q^{11} - 88q^{12} - 68q^{14} - 52q^{15} + 384q^{16} - 52q^{17} - 80q^{18} - 52q^{19} - 68q^{20} - 40q^{22} - 56q^{23} - 120q^{24} - 60q^{25} - 92q^{26} + 56q^{27} - 196q^{28} - 52q^{29} - 44q^{31} - 72q^{32} - 32q^{33} - 68q^{34} - 16q^{35} + 24q^{36} - 56q^{37} - 16q^{39} - 96q^{40} - 24q^{41} - 144q^{42} - 44q^{43} + 40q^{45} - 260q^{46} + 48q^{48} - 44q^{49} + 464q^{50} - 40q^{51} - 200q^{52} - 48q^{53} + 48q^{54} - 208q^{56} - 16q^{57} - 24q^{58} - 16q^{59} - 24q^{60} - 76q^{61} - 72q^{62} - 64q^{63} + 44q^{66} - 264q^{67} - 68q^{68} - 32q^{69} - 8q^{70} - 100q^{71} - 80q^{73} + 180q^{74} + 240q^{75} - 440q^{76} - 92q^{77} - 264q^{78} + 136q^{79} - 104q^{80} + 80q^{82} + 108q^{83} - 208q^{84} - 336q^{85} - 72q^{86} - 56q^{87} - 284q^{88} - 152q^{90} - 320q^{91} + 296q^{92} - 248q^{93} + 80q^{94} - 36q^{95} + 800q^{96} + 96q^{97} - 52q^{99} + O(q^{100})$$

## 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.bl.a $$3072$$ $$5.837$$ None $$-40$$ $$-52$$ $$-44$$ $$-24$$