Properties

Label 403.2.y
Level 403
Weight 2
Character orbit y
Rep. character \(\chi_{403}(64,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 136
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.y (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 403 \)
Character field: \(\Q(\zeta_{10})\)
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 152 152 0
Cusp forms 136 136 0
Eisenstein series 16 16 0

Trace form

\( 136q - 10q^{3} + 22q^{4} - 32q^{9} + O(q^{10}) \) \( 136q - 10q^{3} + 22q^{4} - 32q^{9} + 6q^{10} + 48q^{12} - 16q^{13} - 4q^{14} - 46q^{16} + 12q^{17} - 44q^{22} + 16q^{23} - 92q^{25} - 48q^{26} - 52q^{27} - 10q^{29} + 28q^{35} - 62q^{38} - 31q^{39} + 12q^{40} + 22q^{42} - 66q^{43} + 64q^{48} + 58q^{49} + 28q^{51} + 27q^{52} + 44q^{55} - 208q^{56} + 4q^{61} + 72q^{62} + 10q^{64} + 7q^{65} + 38q^{66} + 44q^{68} + 46q^{69} + 44q^{74} + 34q^{75} + 48q^{77} + 5q^{78} + 48q^{79} - 12q^{81} + 8q^{82} - 60q^{87} - 160q^{88} + 142q^{90} - 80q^{91} + 28q^{92} - 108q^{94} + 60q^{95} + O(q^{100}) \)

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.y.a \(136\) \(3.218\) None \(0\) \(-10\) \(0\) \(0\)