Properties

Label 403.2.i
Level 403
Weight 2
Character orbit i
Rep. character \(\chi_{403}(216,\cdot)\)
Character field \(\Q(\zeta_{4})\)
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.i (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 403 \)
Character field: \(\Q(i)\)
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 76 76 0
Cusp forms 68 68 0
Eisenstein series 8 8 0

Trace form

\( 68q - 4q^{2} - 4q^{5} + 8q^{7} + 16q^{8} - 60q^{9} + O(q^{10}) \) \( 68q - 4q^{2} - 4q^{5} + 8q^{7} + 16q^{8} - 60q^{9} - 48q^{14} - 40q^{16} + 4q^{18} - 24q^{19} - 16q^{20} + 44q^{28} + 24q^{31} + 28q^{32} - 40q^{35} - 24q^{39} + 24q^{40} + 20q^{41} - 24q^{45} - 36q^{47} + 80q^{50} + 28q^{59} - 76q^{63} + 152q^{66} - 32q^{67} - 48q^{70} + 20q^{71} - 32q^{72} + 72q^{76} + 84q^{78} - 20q^{80} + 52q^{81} - 112q^{87} - 8q^{93} - 16q^{94} - 4q^{97} - 92q^{98} + O(q^{100}) \)

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.i.a \(68\) \(3.218\) None \(-4\) \(0\) \(-4\) \(8\)