Space of modular forms of level 1008, weight 3, and Character 1008.dv

• Label: 1008.3.dv
• Level: $1008$
• Weight: $3$
• Character orbit: 1008.dv
• Rep. character: $\chi_{1008}(395,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $512$
• Sturm bound: $576$

Defining parameters

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1008.dv (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 336 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1008, [\chi])\).

	Total	New	Old
Modular forms	1568	512	1056
Cusp forms	1504	512	992
Eisenstein series	64	0	64

Trace form

\( 512 q + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)