Properties

Label 403.2.bn
Level 403
Weight 2
Character orbit bn
Rep. character \(\chi_{403}(60,\cdot)\)
Character field \(\Q(\zeta_{20})\)
Dimension 272
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.bn (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 403 \)
Character field: \(\Q(\zeta_{20})\)
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 304 304 0
Cusp forms 272 272 0
Eisenstein series 32 32 0

Trace form

\( 272q - 6q^{2} - 20q^{3} - 16q^{5} - 18q^{7} + 4q^{8} + 40q^{9} + O(q^{10}) \) \( 272q - 6q^{2} - 20q^{3} - 16q^{5} - 18q^{7} + 4q^{8} + 40q^{9} + 8q^{14} - 40q^{15} + 20q^{16} + 16q^{18} + 14q^{19} - 4q^{20} + 50q^{21} - 120q^{22} - 50q^{24} + 40q^{27} + 46q^{28} - 20q^{29} - 14q^{31} + 52q^{32} - 70q^{33} - 10q^{34} + 20q^{35} - 46q^{39} - 44q^{40} - 20q^{41} - 20q^{42} + 30q^{44} - 36q^{45} - 50q^{46} + 26q^{47} - 20q^{48} + 30q^{50} - 50q^{52} + 50q^{54} - 20q^{55} - 100q^{58} + 2q^{59} - 40q^{60} - 4q^{63} - 172q^{66} + 12q^{67} - 102q^{70} + 50q^{71} - 18q^{72} - 10q^{73} - 20q^{74} + 148q^{76} + 66q^{78} - 100q^{79} - 120q^{80} + 88q^{81} - 40q^{83} - 70q^{84} - 10q^{86} - 88q^{87} - 20q^{89} + 150q^{91} + 48q^{93} - 24q^{94} + 40q^{96} - 76q^{97} - 8q^{98} + O(q^{100}) \)

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.bn.a \(272\) \(3.218\) None \(-6\) \(-20\) \(-16\) \(-18\)