Properties

Label 504.2.be
Level 504
Weight 2
Character orbit be
Rep. character \(\chi_{504}(139,\cdot)\)
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.be (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

\( 184q - 2q^{2} - 2q^{4} - 8q^{8} - 8q^{9} + O(q^{10}) \) \( 184q - 2q^{2} - 2q^{4} - 8q^{8} - 8q^{9} - 4q^{11} - 10q^{14} - 2q^{16} - 10q^{18} + 6q^{22} - 80q^{25} - 12q^{28} + 4q^{30} - 12q^{32} + 12q^{35} - 46q^{36} + 10q^{42} - 4q^{43} - 36q^{44} - 16q^{46} - 2q^{49} + 16q^{50} - 24q^{51} + 40q^{56} + 16q^{57} - 10q^{58} + 40q^{60} - 8q^{64} + 36q^{65} - 4q^{67} - 76q^{72} - 40q^{74} + 60q^{78} + 8q^{81} + 40q^{84} + 32q^{86} - 18q^{88} + 20q^{91} - 26q^{92} - 132q^{98} + 28q^{99} + O(q^{100}) \)

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database