Properties

Label 504.2.j
Level 504
Weight 2
Character orbit j
Rep. character \(\chi_{504}(323,\cdot)\)
Character field \(\Q\)
Dimension 24
Newforms 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.j (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 24 \)
Character field: \(\Q\)
Newforms: \( 1 \)
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 104 24 80
Cusp forms 88 24 64
Eisenstein series 16 0 16

Trace form

\( 24q - 8q^{4} + O(q^{10}) \) \( 24q - 8q^{4} + 24q^{10} + 12q^{16} + 32q^{19} + 12q^{22} + 24q^{25} + 4q^{28} - 8q^{40} - 64q^{43} - 12q^{46} - 24q^{49} - 16q^{52} - 12q^{58} + 16q^{64} + 16q^{67} + 24q^{70} + 8q^{76} + 24q^{82} - 84q^{88} - 72q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(504, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
504.2.j.a \(24\) \(4.024\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(504, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)