Properties

Label 403.2.e
Level 403
Weight 2
Character orbit e
Rep. character \(\chi_{403}(191,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 70
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.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 403 \)
Character field: \(\Q(\zeta_{3})\)
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 78 78 0
Cusp forms 70 70 0
Eisenstein series 8 8 0

Trace form

\( 70q - 2q^{2} + 4q^{3} - 34q^{4} - 2q^{5} + 8q^{7} - 6q^{8} - 29q^{9} + O(q^{10}) \) \( 70q - 2q^{2} + 4q^{3} - 34q^{4} - 2q^{5} + 8q^{7} - 6q^{8} - 29q^{9} - 6q^{10} - 4q^{11} + 5q^{12} + q^{13} - 10q^{14} + q^{15} - 28q^{16} - 28q^{17} - 20q^{18} + 4q^{19} + 25q^{20} - 21q^{21} + 4q^{22} + 2q^{23} + 4q^{24} - 23q^{25} - 24q^{26} - 38q^{27} - 21q^{28} + 6q^{29} + 31q^{30} + 22q^{31} + 14q^{32} + 2q^{33} - 11q^{34} + 4q^{35} + 56q^{36} - 12q^{37} - 7q^{38} + 10q^{39} - q^{40} + 4q^{41} - 54q^{42} + 2q^{43} + 2q^{44} + 58q^{45} + 14q^{46} - 2q^{48} + 74q^{49} + 7q^{50} - 9q^{51} + 5q^{52} - 2q^{53} + 24q^{54} + 5q^{55} + 26q^{56} - q^{57} + 6q^{58} - 42q^{59} + 18q^{60} - 3q^{61} + 13q^{62} - 32q^{63} - 14q^{64} + 20q^{65} - 28q^{66} + 4q^{67} + 42q^{68} - 64q^{69} - 14q^{70} + 43q^{71} - 5q^{72} + 11q^{73} + 14q^{74} - 74q^{75} - 28q^{76} - 10q^{77} - 64q^{78} + 2q^{79} - 76q^{80} - 11q^{81} - 17q^{82} + 56q^{83} - 45q^{84} - 5q^{85} + 54q^{86} + 48q^{87} - 8q^{88} + 30q^{89} - 23q^{90} - 36q^{91} + 74q^{92} + 22q^{93} + 47q^{94} - 9q^{95} + 26q^{96} + 29q^{97} + 12q^{98} + 3q^{99} + O(q^{100}) \)

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.e.a \(70\) \(3.218\) None \(-2\) \(4\) \(-2\) \(8\)