Space of modular forms of level 735, weight 2, and Character 735.bu

• Label: 735.2.bu
• Level: $735$
• Weight: $2$
• Character orbit: 735.bu
• Rep. character: $\chi_{735}(52,\cdot)$
• Character field: $\Q(\zeta_{84})$
• Dimension: $1344$
• Newform subspaces: $1$
• Sturm bound: $224$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.bu (of order \(84\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 245 \)
Character field:			\(\Q(\zeta_{84})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(224\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(735, [\chi])\).

	Total	New	Old
Modular forms	2784	1344	1440
Cusp forms	2592	1344	1248
Eisenstein series	192	0	192

Trace form

\( 1344 q + 12 q^{5} - 8 q^{7} + 24 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(735, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
735.2.bu.a	$735$	$2$	735.bu	245.x	$84$	$1344$	$56$	$5.869$		None		$4$	$0$	\(0\)	\(0\)	\(12\)	\(-8\)		$\mathrm{SU}(2)[C_{84}]$

Decomposition of \(S_{2}^{\mathrm{old}}(735, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(735, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 2}\)