Properties

 Label 731.2.bm Level 731 Weight 2 Character orbit bm Rep. character $$\chi_{731}(3,\cdot)$$ Character field $$\Q(\zeta_{336})$$ Dimension 6144 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.bm (of order $$336$$ and degree $$96$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$731$$ Character field: $$\Q(\zeta_{336})$$ 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 6528 6528 0
Cusp forms 6144 6144 0
Eisenstein series 384 384 0

Trace form

 $$6144q - 112q^{2} - 88q^{3} - 80q^{4} - 88q^{5} - 48q^{6} - 144q^{7} - 112q^{8} - 104q^{9} + O(q^{10})$$ $$6144q - 112q^{2} - 88q^{3} - 80q^{4} - 88q^{5} - 48q^{6} - 144q^{7} - 112q^{8} - 104q^{9} - 104q^{10} - 64q^{11} - 88q^{12} - 96q^{13} - 104q^{14} - 104q^{15} - 104q^{17} - 176q^{18} - 88q^{19} - 88q^{20} - 80q^{21} - 112q^{22} - 112q^{23} + 16q^{24} - 88q^{25} - 88q^{26} - 112q^{27} - 88q^{28} - 88q^{29} - 88q^{30} - 136q^{31} - 112q^{32} - 88q^{34} - 32q^{35} - 64q^{36} - 144q^{37} - 96q^{38} - 112q^{39} - 104q^{40} - 80q^{41} - 24q^{43} - 256q^{44} - 336q^{45} + 264q^{46} - 160q^{47} - 160q^{48} - 48q^{49} - 112q^{51} - 80q^{52} - 104q^{53} - 256q^{54} - 184q^{55} - 104q^{56} - 88q^{57} + 16q^{58} - 208q^{59} - 136q^{61} + 80q^{62} - 88q^{63} - 304q^{64} - 112q^{65} + 24q^{66} - 104q^{68} - 128q^{69} - 112q^{70} - 88q^{71} - 408q^{72} - 368q^{73} + 136q^{74} - 112q^{75} + 528q^{76} - 88q^{77} + 384q^{78} + 208q^{79} - 432q^{80} + 8q^{81} - 112q^{82} - 376q^{83} - 176q^{86} - 192q^{87} - 112q^{88} - 88q^{89} - 88q^{91} - 240q^{92} + 1008q^{93} + 560q^{94} - 184q^{95} - 488q^{96} + 48q^{97} + 320q^{98} - 400q^{99} + O(q^{100})$$

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.bm.a $$6144$$ $$5.837$$ None $$-112$$ $$-88$$ $$-88$$ $$-144$$