Properties

Label 731.2.bj
Level 731
Weight 2
Character orbit bj
Rep. character \(\chi_{731}(22,\cdot)\)
Character field \(\Q(\zeta_{112})\)
Dimension 3072
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.bj (of order \(112\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 731 \)
Character field: \(\Q(\zeta_{112})\)
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

\( 3072q - 56q^{2} - 56q^{3} - 40q^{4} - 56q^{5} - 96q^{6} - 56q^{8} - 40q^{9} + O(q^{10}) \) \( 3072q - 56q^{2} - 56q^{3} - 40q^{4} - 56q^{5} - 96q^{6} - 56q^{8} - 40q^{9} - 40q^{10} - 56q^{11} - 56q^{12} - 48q^{13} - 40q^{14} - 40q^{15} - 40q^{17} - 112q^{18} - 56q^{19} - 56q^{20} - 40q^{21} - 56q^{22} - 32q^{23} - 160q^{24} - 56q^{25} - 56q^{26} - 56q^{27} - 56q^{28} - 56q^{29} - 56q^{30} - 104q^{31} - 56q^{32} - 56q^{34} - 16q^{35} - 128q^{36} - 24q^{38} - 56q^{39} - 40q^{40} - 40q^{41} - 120q^{43} - 32q^{44} + 168q^{45} + 168q^{46} + 40q^{47} - 56q^{48} - 96q^{49} - 56q^{51} - 208q^{52} - 40q^{53} - 200q^{54} - 56q^{55} - 40q^{56} - 8q^{57} + 8q^{58} - 8q^{59} + 168q^{60} - 56q^{61} - 56q^{62} - 56q^{63} - 8q^{64} - 56q^{65} + 216q^{66} - 40q^{68} - 112q^{69} - 56q^{70} - 56q^{71} + 672q^{72} + 224q^{73} - 280q^{74} - 56q^{75} + 336q^{76} - 56q^{77} - 120q^{78} - 352q^{79} - 152q^{81} - 56q^{82} + 208q^{83} - 208q^{86} - 96q^{87} - 56q^{88} - 56q^{89} - 120q^{90} - 56q^{91} - 480q^{92} - 728q^{94} + 40q^{95} + 200q^{96} + 24q^{97} - 56q^{98} + 352q^{99} + O(q^{100}) \)

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.bj.a \(3072\) \(5.837\) None \(-56\) \(-56\) \(-56\) \(0\)