Properties

Label 403.2.bg
Level 403
Weight 2
Character orbit bg
Rep. character \(\chi_{403}(123,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 144
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.bg (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 160 160 0
Cusp forms 144 144 0
Eisenstein series 16 16 0

Trace form

\( 144q - 8q^{2} - 12q^{4} - 8q^{5} - 16q^{7} - 28q^{8} + 64q^{9} + O(q^{10}) \) \( 144q - 8q^{2} - 12q^{4} - 8q^{5} - 16q^{7} - 28q^{8} + 64q^{9} - 12q^{10} + 68q^{16} - 52q^{18} - 4q^{19} - 44q^{20} - 64q^{28} - 4q^{31} - 28q^{32} + 36q^{33} + 28q^{35} - 12q^{36} - 28q^{39} - 48q^{40} - 8q^{41} + 12q^{45} - 24q^{47} + 48q^{49} + 40q^{50} + 48q^{56} + 8q^{59} + 42q^{62} - 84q^{63} - 80q^{66} + 4q^{67} - 24q^{69} - 96q^{70} - 80q^{71} + 104q^{72} - 116q^{76} + 24q^{78} - 112q^{80} + 16q^{81} + 108q^{82} - 92q^{87} + 64q^{93} + 4q^{94} - 132q^{95} + 120q^{97} - 160q^{98} + O(q^{100}) \)

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.bg.a \(144\) \(3.218\) None \(-8\) \(0\) \(-8\) \(-16\)