Properties

Label 804.2.l
Level 804
Weight 2
Character orbit l
Rep. character \(\chi_{804}(431,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 264
Newforms 1
Sturm bound 272
Trace bound 0

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Defining parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.l (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 804 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 1 \)
Sturm bound: \(272\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(804, [\chi])\).

Total New Old
Modular forms 280 280 0
Cusp forms 264 264 0
Eisenstein series 16 16 0

Trace form

\( 264q - 2q^{4} - 3q^{6} - 12q^{9} + O(q^{10}) \) \( 264q - 2q^{4} - 3q^{6} - 12q^{9} + 2q^{10} + 2q^{12} - 18q^{16} + q^{18} - 4q^{22} - 248q^{25} + 7q^{30} - 38q^{34} + 13q^{36} + 4q^{37} + 48q^{40} - 12q^{42} + 48q^{45} - 2q^{46} - 11q^{48} + 128q^{49} + 32q^{52} - 8q^{54} - 2q^{57} - 32q^{58} + 68q^{60} - 8q^{61} + 4q^{64} + 30q^{66} - 40q^{69} - 140q^{70} + 108q^{72} - 4q^{73} - 120q^{76} + 44q^{78} - 28q^{81} - 64q^{82} + 33q^{84} + 16q^{85} - 14q^{88} + 42q^{90} + 16q^{93} - 12q^{94} - 4q^{96} + 20q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(804, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
804.2.l.a \(264\) \(6.420\) None \(0\) \(0\) \(0\) \(0\)