Properties

Label 403.2.bf
Level 403
Weight 2
Character orbit bf
Rep. character \(\chi_{403}(37,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 140
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.bf (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 403 \)
Character field: \(\Q(\zeta_{12})\)
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 156 156 0
Cusp forms 140 140 0
Eisenstein series 16 16 0

Trace form

\( 140q - 8q^{2} - 6q^{3} - 12q^{4} - 2q^{5} + 12q^{6} - 12q^{7} - 10q^{8} + 62q^{9} + O(q^{10}) \) \( 140q - 8q^{2} - 6q^{3} - 12q^{4} - 2q^{5} + 12q^{6} - 12q^{7} - 10q^{8} + 62q^{9} - 12q^{11} - 26q^{12} - 6q^{13} - 24q^{14} - 18q^{15} + 48q^{16} + 20q^{18} + 4q^{19} - 2q^{20} - 14q^{21} + 12q^{22} - 18q^{24} - 6q^{26} + 42q^{28} - 36q^{31} - 10q^{32} - 30q^{33} + 30q^{34} - 8q^{35} + 10q^{37} - 72q^{38} - 8q^{39} - 12q^{40} - 8q^{41} + 52q^{43} - 36q^{44} - 6q^{45} - 24q^{46} + 12q^{47} + 40q^{50} - 36q^{51} + 2q^{52} + 24q^{53} + 18q^{54} - 6q^{55} - 14q^{57} + 42q^{58} - 58q^{59} + 18q^{60} - 36q^{61} - 18q^{62} - 58q^{63} - 108q^{65} + 16q^{66} + 36q^{67} - 18q^{68} + 30q^{70} - 26q^{71} + 8q^{72} - 50q^{73} - 164q^{75} - 22q^{76} + 48q^{77} - 6q^{78} - 48q^{79} - 148q^{80} - 66q^{81} + 54q^{82} + 6q^{83} + 14q^{84} - 42q^{85} + 6q^{86} + 28q^{87} + 48q^{88} - 36q^{89} + 90q^{90} - 46q^{91} + 16q^{93} + 4q^{94} + 48q^{95} - 66q^{96} + 26q^{97} + 20q^{98} + 24q^{99} + O(q^{100}) \)

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.bf.a \(140\) \(3.218\) None \(-8\) \(-6\) \(-2\) \(-12\)