↑

Properties

Label 403.2.bz
Level 403
Weight 2
Character orbit bz
Rep. character \(\chi_{403}(38,\cdot)\)
Character field \(\Q(\zeta_{30})\)
Dimension 288
Newforms 1
Sturm bound 74
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 403 = 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 403.bz (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 403 \)
Character field: \(\Q(\zeta_{30})\)
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 320 320 0
Cusp forms 288 288 0
Eisenstein series 32 32 0

Trace form

\( 288q - 16q^{3} + 60q^{4} + 16q^{9} + O(q^{10}) \) \( 288q - 16q^{3} + 60q^{4} + 16q^{9} - 42q^{10} - 58q^{12} - 7q^{13} - 26q^{14} - 84q^{16} - 30q^{17} + 44q^{22} + 44q^{23} + 124q^{25} - 21q^{26} + 2q^{27} - 44q^{29} - 204q^{30} - 34q^{35} + 134q^{36} + 38q^{38} - 11q^{39} - 84q^{40} - 64q^{42} + 60q^{43} - 42q^{48} - 50q^{49} + 14q^{51} - 13q^{52} - 12q^{53} - 92q^{55} - 56q^{56} + 52q^{61} + 18q^{62} + 174q^{64} - 46q^{65} - 128q^{66} - 140q^{68} - 226q^{69} + 82q^{74} + 46q^{75} + 144q^{77} - 95q^{78} + 30q^{79} + 104q^{81} - 2q^{82} + 30q^{87} + 52q^{88} - 328q^{90} + 78q^{91} + 152q^{92} - 60q^{94} - 150q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.bz.a \(288\) \(3.218\) None \(0\) \(-16\) \(0\) \(0\)