Properties

Label 403.2.r
Level 403
Weight 2
Character orbit r
Rep. character \(\chi_{403}(218,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 68
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.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 13 \)
Character field: \(\Q(\zeta_{6})\)
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 80 68 12
Cusp forms 72 68 4
Eisenstein series 8 0 8

Trace form

\( 68q + 32q^{4} - 34q^{9} + O(q^{10}) \) \( 68q + 32q^{4} - 34q^{9} + 8q^{10} - 12q^{11} - 16q^{12} + 6q^{13} - 8q^{14} - 36q^{16} - 6q^{17} + 12q^{19} - 12q^{20} - 20q^{22} - 8q^{23} + 48q^{24} - 72q^{25} - 12q^{27} - 6q^{28} + 32q^{30} + 6q^{33} + 30q^{35} + 40q^{36} - 42q^{37} - 36q^{38} - 14q^{39} + 8q^{40} + 18q^{41} - 16q^{42} + 12q^{43} + 60q^{45} + 30q^{46} - 46q^{48} + 22q^{49} + 56q^{51} + 20q^{53} - 114q^{54} - 6q^{55} - 2q^{56} - 12q^{58} + 6q^{59} + 6q^{61} - 8q^{62} - 30q^{63} + 24q^{64} + 24q^{65} + 8q^{66} - 48q^{67} + 58q^{68} - 28q^{69} - 30q^{71} + 72q^{72} + 8q^{74} - 4q^{75} - 12q^{76} - 20q^{77} + 26q^{78} + 16q^{79} + 42q^{80} - 58q^{81} - 42q^{82} - 72q^{84} + 30q^{85} - 20q^{87} + 64q^{88} + 18q^{89} + 52q^{90} - 22q^{91} + 48q^{92} + 8q^{94} - 32q^{95} - 168q^{98} + O(q^{100}) \)

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.r.a \(68\) \(3.218\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(403, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(403, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 2}\)