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

• Label: 735.4.ba
• Level: $735$
• Weight: $4$
• Character orbit: 735.ba
• Rep. character: $\chi_{735}(104,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $1992$
• Sturm bound: $448$

Defining parameters

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	735.ba (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 735 \)
Character field:			\(\Q(\zeta_{14})\)
Sturm bound:			\(448\)

Dimensions

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

	Total	New	Old
Modular forms	2040	2040	0
Cusp forms	1992	1992	0
Eisenstein series	48	48	0

Trace form

\( 1992 q - 1332 q^{4} - 42 q^{6} - 80 q^{9} + O(q^{10}) \)

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

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