Properties

Label 731.2.be
Level 731
Weight 2
Character orbit be
Rep. character \(\chi_{731}(59,\cdot)\)
Character field \(\Q(\zeta_{56})\)
Dimension 1536
Newforms 1
Sturm bound 132
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.be (of order \(56\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 731 \)
Character field: \(\Q(\zeta_{56})\)
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 1632 1632 0
Cusp forms 1536 1536 0
Eisenstein series 96 96 0

Trace form

\( 1536q - 20q^{2} - 20q^{3} - 28q^{5} - 48q^{6} - 48q^{7} - 36q^{8} - 44q^{9} + O(q^{10}) \) \( 1536q - 20q^{2} - 20q^{3} - 28q^{5} - 48q^{6} - 48q^{7} - 36q^{8} - 44q^{9} - 20q^{10} - 20q^{11} - 20q^{12} - 52q^{14} - 20q^{15} + 192q^{16} - 20q^{17} - 64q^{18} - 20q^{19} - 52q^{20} - 20q^{22} - 16q^{23} - 12q^{25} - 4q^{26} - 44q^{27} + 28q^{28} - 20q^{29} - 4q^{31} - 36q^{32} + 32q^{33} - 52q^{34} - 8q^{35} - 120q^{36} - 16q^{37} - 44q^{39} - 108q^{40} - 36q^{41} - 48q^{42} - 76q^{43} + 48q^{44} - 100q^{45} - 100q^{46} - 132q^{48} - 88q^{49} - 320q^{50} - 20q^{51} - 40q^{52} - 24q^{53} + 60q^{54} + 88q^{56} + 52q^{57} + 36q^{58} - 44q^{59} + 36q^{60} + 16q^{61} + 84q^{62} - 44q^{63} - 60q^{65} + 76q^{66} + 120q^{67} - 52q^{68} - 88q^{69} - 4q^{70} - 68q^{71} - 40q^{73} - 252q^{74} + 120q^{75} - 208q^{76} - 100q^{77} + 204q^{78} + 80q^{79} + 32q^{80} - 140q^{82} - 96q^{83} - 104q^{84} + 192q^{85} - 24q^{86} - 88q^{87} + 128q^{88} - 52q^{90} + 200q^{91} + 592q^{92} - 400q^{93} - 188q^{94} - 84q^{95} + 88q^{96} - 60q^{97} + 112q^{99} + O(q^{100}) \)

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.be.a \(1536\) \(5.837\) None \(-20\) \(-20\) \(-28\) \(-48\)