Properties

Label 504.2.cs
Level 504
Weight 2
Character orbit cs
Rep. character \(\chi_{504}(85,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 144
Newform subspaces 2
Sturm bound 192
Trace bound 6

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Defining parameters

Level: \( N \) = \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 504.cs (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(192\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(5\)

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

\( 144q - 6q^{6} + 12q^{8} + O(q^{10}) \) \( 144q - 6q^{6} + 12q^{8} + 12q^{12} - 22q^{18} + 14q^{20} + 24q^{23} - 2q^{24} + 72q^{25} - 56q^{26} - 56q^{30} - 10q^{32} + 16q^{33} + 12q^{34} - 28q^{38} - 24q^{39} + 12q^{40} - 8q^{41} - 20q^{42} - 64q^{44} + 24q^{46} - 24q^{48} - 72q^{49} + 46q^{50} - 18q^{52} + 42q^{54} + 8q^{57} + 18q^{58} - 16q^{60} + 48q^{62} - 60q^{64} + 118q^{66} + 78q^{68} - 112q^{71} + 34q^{72} - 12q^{76} + 8q^{78} + 88q^{80} - 8q^{81} - 36q^{82} + 14q^{84} - 42q^{86} - 104q^{87} - 24q^{88} - 160q^{90} + 66q^{92} + 6q^{94} - 64q^{95} - 24q^{96} + O(q^{100}) \)

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.cs.a \(72\) \(4.024\) None \(0\) \(0\) \(0\) \(36\)
504.2.cs.b \(72\) \(4.024\) None \(0\) \(0\) \(0\) \(-36\)

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