Properties

Label 731.2.bd
Level 731
Weight 2
Character orbit bd
Rep. character \(\chi_{731}(7,\cdot)\)
Character field \(\Q(\zeta_{48})\)
Dimension 1024
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.bd (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 731 \)
Character field: \(\Q(\zeta_{48})\)
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 1088 1088 0
Cusp forms 1024 1024 0
Eisenstein series 64 64 0

Trace form

\( 1024q - 24q^{3} - 32q^{4} - 24q^{5} - 8q^{6} - 24q^{7} - 8q^{9} + O(q^{10}) \) \( 1024q - 24q^{3} - 32q^{4} - 24q^{5} - 8q^{6} - 24q^{7} - 8q^{9} - 8q^{10} - 48q^{11} - 24q^{12} - 16q^{13} - 8q^{14} - 8q^{15} - 8q^{17} - 48q^{18} - 24q^{19} - 24q^{20} - 32q^{21} + 40q^{24} - 24q^{25} - 24q^{26} - 24q^{28} - 24q^{29} - 24q^{30} + 24q^{31} - 24q^{34} - 192q^{35} + 8q^{36} - 24q^{37} - 16q^{38} - 8q^{40} - 32q^{41} + 24q^{43} + 32q^{44} + 72q^{46} + 48q^{47} + 48q^{48} - 8q^{49} - 144q^{52} - 8q^{53} + 144q^{54} + 72q^{55} - 8q^{56} - 24q^{57} - 128q^{58} + 96q^{59} - 112q^{60} + 24q^{61} - 192q^{62} - 24q^{63} + 192q^{64} - 136q^{66} - 8q^{68} - 96q^{69} - 24q^{71} - 432q^{72} - 24q^{73} + 88q^{74} + 144q^{76} - 24q^{77} - 496q^{78} - 40q^{79} + 264q^{80} - 120q^{81} - 16q^{83} - 48q^{86} - 32q^{87} - 24q^{89} - 112q^{90} - 24q^{91} + 184q^{92} + 168q^{93} + 72q^{95} + 40q^{96} - 160q^{97} - 432q^{98} + 8q^{99} + O(q^{100}) \)

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.bd.a \(1024\) \(5.837\) None \(0\) \(-24\) \(-24\) \(-24\)