Properties

Label 731.2.v
Level 731
Weight 2
Character orbit v
Rep. character \(\chi_{731}(36,\cdot)\)
Character field \(\Q(\zeta_{24})\)
Dimension 512
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.v (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 731 \)
Character field: \(\Q(\zeta_{24})\)
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 544 544 0
Cusp forms 512 512 0
Eisenstein series 32 32 0

Trace form

\( 512q - 16q^{2} - 4q^{3} - 12q^{5} - 4q^{6} - 4q^{7} + 16q^{8} - 28q^{9} + O(q^{10}) \) \( 512q - 16q^{2} - 4q^{3} - 12q^{5} - 4q^{6} - 4q^{7} + 16q^{8} - 28q^{9} - 4q^{10} - 16q^{11} + 32q^{12} + 12q^{14} - 4q^{15} - 496q^{16} - 4q^{17} - 32q^{18} - 4q^{19} + 12q^{20} - 16q^{22} + 36q^{24} + 4q^{25} + 36q^{26} - 112q^{27} + 28q^{28} - 4q^{29} - 12q^{31} + 16q^{32} + 32q^{33} + 12q^{34} - 96q^{35} - 52q^{36} + 28q^{37} - 40q^{39} + 40q^{40} - 32q^{41} + 32q^{42} + 44q^{43} + 112q^{44} + 16q^{45} - 20q^{46} - 104q^{48} + 16q^{49} - 16q^{50} - 16q^{51} + 88q^{52} - 8q^{53} - 104q^{54} - 44q^{56} - 40q^{57} - 32q^{58} - 40q^{59} - 32q^{60} - 8q^{61} + 16q^{62} + 8q^{63} - 56q^{65} - 100q^{66} - 72q^{67} + 12q^{68} - 80q^{69} - 48q^{70} + 44q^{71} + 52q^{73} - 68q^{74} + 96q^{75} - 8q^{76} + 36q^{77} + 40q^{78} + 60q^{79} + 76q^{80} - 136q^{82} - 24q^{83} + 96q^{84} - 56q^{85} - 40q^{86} - 56q^{87} - 24q^{88} + 96q^{90} - 44q^{91} - 44q^{92} - 4q^{93} + 88q^{94} - 20q^{95} + 40q^{96} - 152q^{97} - 88q^{99} + O(q^{100}) \)

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.v.a \(512\) \(5.837\) None \(-16\) \(-4\) \(-12\) \(-4\)