Properties

Label 403.2.cc
Level 403
Weight 2
Character orbit cc
Rep. character \(\chi_{403}(24,\cdot)\)
Character field \(\Q(\zeta_{60})\)
Dimension 560
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.cc (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 624 624 0
Cusp forms 560 560 0
Eisenstein series 64 64 0

Trace form

\( 560q - 12q^{2} - 4q^{3} - 18q^{4} - 8q^{5} - 42q^{6} - 8q^{7} - 40q^{8} - 72q^{9} + O(q^{10}) \) \( 560q - 12q^{2} - 4q^{3} - 18q^{4} - 8q^{5} - 42q^{6} - 8q^{7} - 40q^{8} - 72q^{9} - 30q^{10} - 18q^{11} + 26q^{12} - 24q^{13} + 4q^{14} - 62q^{15} - 58q^{16} - 30q^{17} - 70q^{18} - 24q^{19} - 8q^{20} + 114q^{21} + 78q^{22} - 30q^{23} - 82q^{24} - 24q^{26} - 100q^{27} - 62q^{28} - 10q^{29} - 4q^{31} + 20q^{32} - 110q^{33} + 70q^{34} - 2q^{35} - 40q^{37} - 108q^{38} + 48q^{39} - 28q^{40} - 22q^{41} - 10q^{42} + 78q^{43} - 24q^{44} + 36q^{45} + 44q^{46} - 32q^{47} - 10q^{48} - 30q^{49} - 30q^{50} + 36q^{51} - 252q^{52} - 84q^{53} + 82q^{54} - 4q^{55} + 164q^{57} + 28q^{58} - 2q^{59} - 8q^{60} + 36q^{61} - 12q^{62} + 78q^{63} + 270q^{64} - 72q^{65} - 56q^{66} - 46q^{67} - 12q^{68} + 150q^{69} + 90q^{70} - 74q^{71} + 72q^{72} + 30q^{73} - 10q^{74} - 16q^{75} - 228q^{76} + 72q^{77} + 96q^{78} - 32q^{79} + 108q^{80} - 104q^{81} - 84q^{82} + 4q^{83} + 26q^{84} + 12q^{85} + 34q^{86} + 112q^{87} - 108q^{88} - 154q^{89} - 90q^{90} - 4q^{91} + 64q^{93} - 24q^{94} - 78q^{95} - 4q^{96} - 196q^{97} + 50q^{98} + 96q^{99} + O(q^{100}) \)

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.cc.a \(560\) \(3.218\) None \(-12\) \(-4\) \(-8\) \(-8\)