Properties

Label 731.2.y
Level 731
Weight 2
Character orbit y
Rep. character \(\chi_{731}(4,\cdot)\)
Character field \(\Q(\zeta_{28})\)
Dimension 768
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.y (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 731 \)
Character field: \(\Q(\zeta_{28})\)
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 816 816 0
Cusp forms 768 768 0
Eisenstein series 48 48 0

Trace form

\( 768q - 14q^{3} + 104q^{4} - 6q^{5} - 36q^{6} - 28q^{7} + O(q^{10}) \) \( 768q - 14q^{3} + 104q^{4} - 6q^{5} - 36q^{6} - 28q^{7} - 18q^{10} - 4q^{11} + 34q^{12} + 4q^{13} + 26q^{14} - 152q^{16} - 10q^{17} - 24q^{18} + 22q^{20} - 20q^{21} + 12q^{22} - 24q^{23} - 100q^{24} + 10q^{27} - 42q^{28} - 18q^{29} + 48q^{30} + 4q^{31} + 36q^{33} - 4q^{34} - 60q^{35} + 40q^{37} + 12q^{38} + 34q^{39} + 6q^{40} - 48q^{41} - 104q^{44} - 52q^{45} - 74q^{46} + 20q^{47} + 94q^{48} - 344q^{50} + 80q^{51} + 12q^{52} + 60q^{54} - 32q^{55} - 50q^{56} + 38q^{57} + 112q^{58} - 12q^{61} + 10q^{62} + 52q^{63} + 144q^{64} - 10q^{65} - 20q^{67} - 54q^{68} - 12q^{69} + 14q^{71} - 208q^{72} - 176q^{73} + 46q^{74} - 116q^{75} + 140q^{78} - 168q^{79} + 32q^{80} + 116q^{81} + 186q^{82} - 60q^{84} - 184q^{85} + 176q^{86} + 24q^{88} - 4q^{89} - 58q^{90} - 152q^{91} - 136q^{92} + 70q^{95} - 332q^{96} + 72q^{97} + 104q^{98} - 56q^{99} + O(q^{100}) \)

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.y.a \(768\) \(5.837\) None \(0\) \(-14\) \(-6\) \(-28\)