Properties

Label 504.4.i
Level $504$
Weight $4$
Character orbit 504.i
Rep. character $\chi_{504}(125,\cdot)$
Character field $\Q$
Dimension $96$
Newform subspaces $2$
Sturm bound $384$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 504.i (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 168 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(384\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(504, [\chi])\).

Total New Old
Modular forms 296 96 200
Cusp forms 280 96 184
Eisenstein series 16 0 16

Trace form

\( 96 q + O(q^{10}) \) \( 96 q + 60 q^{16} - 492 q^{22} - 2400 q^{25} - 396 q^{28} + 540 q^{46} + 720 q^{49} - 2940 q^{58} - 1440 q^{64} - 2856 q^{70} + 240 q^{79} + 1428 q^{88} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(504, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
504.4.i.a 504.i 168.i $8$ $29.737$ 8.0.157351936.1 \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{5}q^{2}+(\beta _{1}+2\beta _{3})q^{4}-7\beta _{3}q^{7}+\cdots\)
504.4.i.b 504.i 168.i $88$ $29.737$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(504, [\chi])\) into lower level spaces

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