Space of modular forms of level 1008, weight 4, and Character 1008.cx

• Label: 1008.4.cx
• Level: $1008$
• Weight: $4$
• Character orbit: 1008.cx
• Rep. character: $\chi_{1008}(223,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $288$
• Sturm bound: $768$

Defining parameters

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1008.cx (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 252 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1008, [\chi])\).

	Total	New	Old
Modular forms	1176	288	888
Cusp forms	1128	288	840
Eisenstein series	48	0	48

Trace form

\( 288 q + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)