Space of modular forms of level 735, weight 4, and Character 735.g

• Label: 735.4.g
• Level: $735$
• Weight: $4$
• Character orbit: 735.g
• Rep. character: $\chi_{735}(734,\cdot)$
• Character field: $\Q$
• Dimension: $232$
• Sturm bound: $448$

Defining parameters

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	735.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q\)
Sturm bound:			\(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(735, [\chi])\).

	Total	New	Old
Modular forms	352	248	104
Cusp forms	320	232	88
Eisenstein series	32	16	16

Trace form

\( 232 q + 904 q^{4} + 64 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(735, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(735, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(735, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)