Properties

Label 504.2.w
Level 504
Weight 2
Character orbit w
Rep. character \(\chi_{504}(205,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 184
Newform subspaces 1
Sturm bound 192
Trace bound 0

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Defining parameters

Level: \( N \) = \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 504.w (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 504 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(504, [\chi])\).

Total New Old
Modular forms 200 200 0
Cusp forms 184 184 0
Eisenstein series 16 16 0

Trace form

\( 184q + q^{2} + q^{4} - 2q^{6} - 2q^{7} - 8q^{8} - 2q^{9} + O(q^{10}) \) \( 184q + q^{2} + q^{4} - 2q^{6} - 2q^{7} - 8q^{8} - 2q^{9} + 2q^{10} - 17q^{12} - 7q^{14} - 2q^{15} + q^{16} - 4q^{17} + 13q^{18} + 6q^{20} + 2q^{22} - 4q^{23} + 12q^{24} - 156q^{25} - 4q^{26} - 8q^{28} - 18q^{30} + 2q^{31} + q^{32} + 22q^{33} - 18q^{36} + 10q^{38} - 14q^{39} + 8q^{40} - 4q^{41} + 3q^{42} + 17q^{44} - 6q^{46} + 42q^{47} - 3q^{48} - 2q^{49} - 31q^{50} - 18q^{52} - 58q^{54} + 4q^{55} - 34q^{56} - 20q^{57} - 10q^{58} + 26q^{60} + 32q^{62} + 50q^{63} - 8q^{64} + 22q^{65} + 79q^{66} + 24q^{68} + 8q^{70} - 16q^{71} - 27q^{72} - 4q^{73} - 38q^{74} - 6q^{76} - 47q^{78} + 2q^{79} - 11q^{80} + 6q^{81} + q^{84} + 46q^{86} + 4q^{87} + 14q^{88} + 4q^{89} - 35q^{90} - 48q^{92} + 9q^{94} + 22q^{95} - 16q^{96} - 4q^{97} - 83q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(504, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
504.2.w.a \(184\) \(4.024\) None \(1\) \(0\) \(0\) \(-2\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database