Properties

Label 403.2.cd
Level 403
Weight 2
Character orbit cd
Rep. character \(\chi_{403}(21,\cdot)\)
Character field \(\Q(\zeta_{60})\)
Dimension 576
Newforms 1
Sturm bound 74
Trace bound 0

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Defining parameters

Level: \( N \) = \( 403 = 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 403.cd (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 403 \)
Character field: \(\Q(\zeta_{60})\)
Newforms: \( 1 \)
Sturm bound: \(74\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(403, [\chi])\).

Total New Old
Modular forms 640 640 0
Cusp forms 576 576 0
Eisenstein series 64 64 0

Trace form

\( 576q - 12q^{2} - 28q^{3} - 8q^{5} + 6q^{6} - 16q^{7} - 46q^{8} - 104q^{9} + O(q^{10}) \) \( 576q - 12q^{2} - 28q^{3} - 8q^{5} + 6q^{6} - 16q^{7} - 46q^{8} - 104q^{9} - 18q^{11} - 24q^{13} - 44q^{14} + 10q^{15} + 120q^{16} - 10q^{18} - 16q^{19} - 32q^{20} - 28q^{21} - 28q^{24} - 72q^{26} - 100q^{27} + 38q^{28} - 40q^{29} - 66q^{31} - 124q^{32} + 52q^{33} + 76q^{34} - 32q^{35} - 36q^{37} + 10q^{39} - 52q^{40} + 2q^{41} + 8q^{42} + 12q^{44} + 30q^{45} + 20q^{46} - 20q^{47} - 40q^{48} + 50q^{52} - 84q^{53} - 80q^{54} - 28q^{55} - 126q^{57} + 70q^{58} - 74q^{59} - 50q^{60} + 212q^{63} + 84q^{65} + 136q^{66} - 20q^{67} - 60q^{68} + 18q^{70} - 62q^{71} - 54q^{72} - 32q^{73} - 112q^{74} - 64q^{76} + 6q^{78} - 56q^{79} + 60q^{80} - 168q^{81} + 238q^{83} - 206q^{84} - 30q^{85} - 158q^{86} + 76q^{87} + 140q^{89} - 50q^{91} + 70q^{93} - 48q^{94} + 8q^{96} - 92q^{97} + 50q^{98} - 156q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(403, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
403.2.cd.a \(576\) \(3.218\) None \(-12\) \(-28\) \(-8\) \(-16\)