Properties

Label 504.2.br
Level 504
Weight 2
Character orbit br
Rep. character \(\chi_{504}(155,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 144
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.br (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 72 \)
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 200 144 56
Cusp forms 184 144 40
Eisenstein series 16 0 16

Trace form

\( 144q + 6q^{6} + O(q^{10}) \) \( 144q + 6q^{6} - 12q^{12} + 34q^{18} - 42q^{20} - 30q^{24} - 72q^{25} + 24q^{27} - 36q^{30} - 30q^{32} - 16q^{33} + 12q^{34} - 12q^{36} + 12q^{40} + 24q^{41} - 20q^{42} - 24q^{46} - 24q^{48} + 72q^{49} - 78q^{50} + 18q^{52} + 10q^{54} + 8q^{57} - 18q^{58} - 72q^{59} + 88q^{60} - 12q^{64} + 2q^{66} + 78q^{68} + 42q^{72} + 84q^{74} - 112q^{75} + 12q^{76} + 112q^{78} - 8q^{81} - 36q^{82} - 14q^{84} + 30q^{86} + 24q^{88} + 104q^{90} - 114q^{92} - 42q^{94} - 80q^{96} - 64q^{99} + O(q^{100}) \)

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.br.a \(144\) \(4.024\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(504, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(504, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database