Properties

Label 504.2.i
Level 504
Weight 2
Character orbit i
Rep. character \(\chi_{504}(125,\cdot)\)
Character field \(\Q\)
Dimension 32
Newforms 2
Sturm bound 192
Trace bound 1

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Defining parameters

Level: \( N \) = \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 504.i (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 168 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(192\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(504, [\chi])\).

Total New Old
Modular forms 104 32 72
Cusp forms 88 32 56
Eisenstein series 16 0 16

Trace form

\(32q \) \(\mathstrut +\mathstrut O(q^{10}) \) \(32q \) \(\mathstrut -\mathstrut 4q^{16} \) \(\mathstrut +\mathstrut 28q^{22} \) \(\mathstrut -\mathstrut 32q^{25} \) \(\mathstrut +\mathstrut 4q^{28} \) \(\mathstrut -\mathstrut 44q^{46} \) \(\mathstrut -\mathstrut 16q^{49} \) \(\mathstrut -\mathstrut 4q^{58} \) \(\mathstrut +\mathstrut 96q^{64} \) \(\mathstrut -\mathstrut 24q^{70} \) \(\mathstrut -\mathstrut 16q^{79} \) \(\mathstrut -\mathstrut 76q^{88} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.i.a \(8\) \(4.024\) 8.0.157351936.1 \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{2}-\beta _{5})q^{7}+\beta _{3}q^{8}+\cdots\)
504.2.i.b \(24\) \(4.024\) None \(0\) \(0\) \(0\) \(0\)

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

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