Properties

Label 804.2.bd
Level 804
Weight 2
Character orbit bd
Rep. character \(\chi_{804}(23,\cdot)\)
Character field \(\Q(\zeta_{66})\)
Dimension 2640
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.bd (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 804 \)
Character field: \(\Q(\zeta_{66})\)
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 2800 2800 0
Cusp forms 2640 2640 0
Eisenstein series 160 160 0

Trace form

\( 2640q - 42q^{4} - 19q^{6} - 32q^{9} + O(q^{10}) \) \( 2640q - 42q^{4} - 19q^{6} - 32q^{9} - 46q^{10} - 24q^{12} - 88q^{13} - 26q^{16} - 23q^{18} - 128q^{22} - 22q^{24} + 160q^{25} + 44q^{28} - 18q^{30} - 44q^{33} - 6q^{34} - 35q^{36} - 48q^{37} - 92q^{40} - 10q^{42} + 40q^{45} + 46q^{46} - 11q^{48} - 216q^{49} - 76q^{52} + 129q^{54} - 42q^{57} - 56q^{58} - 90q^{60} - 80q^{61} - 48q^{64} - 74q^{66} - 4q^{69} + 96q^{70} - 20q^{72} - 216q^{73} + 76q^{76} - 66q^{78} - 16q^{81} + 20q^{82} - 55q^{84} - 104q^{85} - 30q^{88} - 64q^{90} - 192q^{93} - 32q^{94} - 205q^{96} - 64q^{97} + O(q^{100}) \)

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.bd.a \(2640\) \(6.420\) None \(0\) \(0\) \(0\) \(0\)