Properties

Label 504.2.y
Level 504
Weight 2
Character orbit y
Rep. character \(\chi_{504}(173,\cdot)\)
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.y (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

\( 184q - 3q^{2} + q^{4} + 6q^{6} - 2q^{7} - 2q^{9} + O(q^{10}) \) \( 184q - 3q^{2} + q^{4} + 6q^{6} - 2q^{7} - 2q^{9} - 6q^{10} - 3q^{12} - 3q^{14} - 2q^{15} + q^{16} - 15q^{18} - 6q^{22} - 12q^{24} - 156q^{25} + 6q^{26} - 8q^{28} - 14q^{30} - 6q^{31} - 33q^{32} - 6q^{33} - 6q^{34} + 22q^{36} - 66q^{38} + 10q^{39} - 15q^{42} + 9q^{44} + 2q^{46} - 6q^{47} - 9q^{48} - 2q^{49} + 9q^{50} + 24q^{54} + 60q^{56} + 4q^{57} + 6q^{58} + 34q^{60} - 12q^{62} - 30q^{63} - 8q^{64} - 6q^{65} - 21q^{66} - 36q^{68} + 30q^{70} + 9q^{72} - 12q^{73} - 12q^{76} + 19q^{78} + 2q^{79} + 57q^{80} + 6q^{81} + 9q^{84} + 12q^{87} - 18q^{88} + 24q^{89} + 75q^{90} - 36q^{92} - 3q^{94} + 54q^{95} - 54q^{96} + 45q^{98} + O(q^{100}) \)

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.y.a \(184\) \(4.024\) None \(-3\) \(0\) \(0\) \(-2\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database