Properties

Label 504.2.cq
Level 504
Weight 2
Character orbit cq
Rep. character \(\chi_{504}(277,\cdot)\)
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.cq (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

\( 184q - 2q^{2} - 2q^{4} - 2q^{6} - 2q^{7} - 8q^{8} - 2q^{9} + O(q^{10}) \) \( 184q - 2q^{2} - 2q^{4} - 2q^{6} - 2q^{7} - 8q^{8} - 2q^{9} + 2q^{10} + 16q^{12} - 4q^{14} - 2q^{15} - 2q^{16} - 4q^{17} - 14q^{18} + 6q^{20} + 2q^{22} + 2q^{23} + 12q^{24} + 78q^{25} - 4q^{26} - 8q^{28} - 9q^{30} - 4q^{31} - 2q^{32} - 14q^{33} - 18q^{36} - 5q^{38} + 4q^{39} - 4q^{40} - 4q^{41} - 12q^{42} + 17q^{44} - 6q^{46} - 84q^{47} - 3q^{48} - 2q^{49} - 31q^{50} + 9q^{52} - q^{54} + 4q^{55} - 16q^{56} - 20q^{57} + 5q^{58} + 17q^{60} + 32q^{62} + 8q^{63} - 8q^{64} - 44q^{65} - 56q^{66} - 12q^{68} + 5q^{70} - 16q^{71} + 36q^{72} - 4q^{73} + 19q^{74} - 6q^{76} - 47q^{78} - 4q^{79} - 11q^{80} - 18q^{81} - 65q^{84} - 23q^{86} - 14q^{87} - 7q^{88} + 4q^{89} - 35q^{90} - 48q^{92} - 18q^{94} - 44q^{95} + 95q^{96} - 4q^{97} - 83q^{98} + O(q^{100}) \)

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.cq.a \(184\) \(4.024\) None \(-2\) \(0\) \(0\) \(-2\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database