Properties

Label 403.2.bk
Level 403
Weight 2
Character orbit bk
Rep. character \(\chi_{403}(9,\cdot)\)
Character field \(\Q(\zeta_{15})\)
Dimension 280
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.bk (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 403 \)
Character field: \(\Q(\zeta_{15})\)
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 312 312 0
Cusp forms 280 280 0
Eisenstein series 32 32 0

Trace form

\( 280q - 3q^{2} - 9q^{3} + 29q^{4} - 8q^{5} - 10q^{6} - 13q^{7} - 29q^{8} + 24q^{9} + O(q^{10}) \) \( 280q - 3q^{2} - 9q^{3} + 29q^{4} - 8q^{5} - 10q^{6} - 13q^{7} - 29q^{8} + 24q^{9} - 9q^{10} - 6q^{11} - 50q^{12} - 6q^{13} - 21q^{15} + 23q^{16} + 3q^{17} - 15q^{18} - 9q^{19} + 60q^{20} - 34q^{21} + 41q^{22} - 12q^{23} - 89q^{24} - 112q^{25} + 39q^{26} + 48q^{27} + 66q^{28} - 11q^{29} + 24q^{30} - 22q^{31} + q^{32} - 37q^{33} - 49q^{34} + 41q^{35} + 134q^{36} + 17q^{37} - 23q^{38} + 10q^{39} + 31q^{40} + q^{41} - 71q^{42} - 7q^{43} - 42q^{44} - 13q^{45} + 21q^{46} - 20q^{47} - 3q^{48} - 69q^{49} - 42q^{50} - 71q^{51} - 140q^{52} - 8q^{53} - 149q^{54} + 5q^{55} - 126q^{56} + 21q^{57} + 79q^{58} + 77q^{59} + 2q^{60} + 53q^{61} + 72q^{62} + 17q^{63} - 91q^{64} - 25q^{65} - 62q^{66} - 14q^{67} + 83q^{68} - 31q^{69} + 134q^{70} + 32q^{71} - 70q^{72} - 31q^{73} + 51q^{74} + 79q^{75} + 98q^{76} - 80q^{77} - 141q^{78} - 142q^{79} + 6q^{80} + 66q^{81} - 48q^{82} + 94q^{83} + 130q^{84} + 90q^{85} - 34q^{86} + 22q^{87} - 122q^{88} - 15q^{89} + 43q^{90} + 56q^{91} - 294q^{92} - 52q^{93} - 57q^{94} + 94q^{95} + 24q^{96} + 46q^{97} + 73q^{98} + 12q^{99} + O(q^{100}) \)

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.bk.a \(280\) \(3.218\) None \(-3\) \(-9\) \(-8\) \(-13\)