Properties

Label 804.2.w
Level 804
Weight 2
Character orbit w
Rep. character \(\chi_{804}(59,\cdot)\)
Character field \(\Q(\zeta_{22})\)
Dimension 1320
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.w (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 804 \)
Character field: \(\Q(\zeta_{22})\)
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 1400 1400 0
Cusp forms 1320 1320 0
Eisenstein series 80 80 0

Trace form

\( 1320q - 18q^{4} - 5q^{6} - 22q^{9} + O(q^{10}) \) \( 1320q - 18q^{4} - 5q^{6} - 22q^{9} - 26q^{10} - 15q^{12} - 44q^{13} - 34q^{16} - 13q^{18} - 66q^{21} + 74q^{22} + 13q^{24} + 80q^{25} - 110q^{28} - 36q^{30} - 22q^{33} - 54q^{34} - 37q^{36} - 72q^{37} - 22q^{40} + q^{42} - 154q^{45} - 82q^{46} + 11q^{48} + 96q^{49} - 14q^{52} - 138q^{54} - 6q^{57} + 74q^{58} + 3q^{60} - 28q^{61} - 6q^{64} - 4q^{66} - 38q^{69} - 18q^{70} - 145q^{72} + 96q^{73} + 14q^{76} - 51q^{78} - 38q^{81} - 74q^{82} - 41q^{84} - 76q^{85} + 6q^{88} - 5q^{90} + 78q^{93} - 22q^{94} + 184q^{96} - 128q^{97} + O(q^{100}) \)

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.w.a \(1320\) \(6.420\) None \(0\) \(0\) \(0\) \(0\)