Space of modular forms of level 504, weight 4, and Character 504.be

• Label: 504.4.be
• Level: $504$
• Weight: $4$
• Character orbit: 504.be
• Rep. character: $\chi_{504}(139,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $568$
• Sturm bound: $384$

Defining parameters

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	504.be (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 504 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(384\)

Dimensions

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

	Total	New	Old
Modular forms	584	584	0
Cusp forms	568	568	0
Eisenstein series	16	16	0

Trace form

\( 568 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 8 q^{9} + O(q^{10}) \)

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

The newforms in this space have not yet been added to the LMFDB.