Properties

Label 504.2.bt
Level 504
Weight 2
Character orbit bt
Rep. character \(\chi_{504}(11,\cdot)\)
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.bt (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

\( 184q - 2q^{3} - 2q^{4} - 2q^{6} - 2q^{9} + O(q^{10}) \) \( 184q - 2q^{3} - 2q^{4} - 2q^{6} - 2q^{9} - 6q^{10} - 6q^{11} - 8q^{12} + 12q^{14} - 2q^{16} + 2q^{18} - 4q^{19} - 6q^{20} + 2q^{22} - 8q^{24} - 74q^{25} - 6q^{26} - 8q^{27} + 3q^{30} - 14q^{33} - 4q^{34} + 30q^{35} - 38q^{36} + 39q^{38} + 6q^{40} - 12q^{41} - 20q^{42} - 4q^{43} + 9q^{44} - 6q^{46} - 5q^{48} - 2q^{49} - 21q^{50} - 34q^{51} + 9q^{52} + 47q^{54} - 24q^{56} + 4q^{57} - 3q^{58} - 11q^{60} - 8q^{64} - 26q^{66} - 4q^{67} - 42q^{68} - 3q^{70} + 52q^{72} - 4q^{73} + 27q^{74} + 30q^{75} + 2q^{76} - 29q^{78} + 87q^{80} + 14q^{81} - 4q^{82} - 72q^{83} - 59q^{84} - 27q^{86} - 7q^{88} - 24q^{89} - 49q^{90} - 36q^{91} - 36q^{92} - 18q^{94} + 23q^{96} - 4q^{97} + 57q^{98} + 10q^{99} + O(q^{100}) \)

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database