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

• Label: 1008.4.ds
• Level: $1008$
• Weight: $4$
• Character orbit: 1008.ds
• Rep. character: $\chi_{1008}(269,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $768$
• Sturm bound: $768$

Defining parameters

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1008.ds (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 336 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(768\)

Dimensions

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

	Total	New	Old
Modular forms	2336	768	1568
Cusp forms	2272	768	1504
Eisenstein series	64	0	64

Trace form

\( 768 q + O(q^{10}) \)

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

\( S_{4}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)