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

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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 \(-112\) \(-88\) \(-88\) \(-144\)