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

• Label: 735.2.bm
• Level: $735$
• Weight: $2$
• Character orbit: 735.bm
• Rep. character: $\chi_{735}(26,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $888$
• Newform subspaces: $2$
• Sturm bound: $224$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.bm (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 147 \)
Character field:			\(\Q(\zeta_{42})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(224\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	1392	888	504
Cusp forms	1296	888	408
Eisenstein series	96	0	96

Trace form

\( 888 q - 72 q^{4} + 14 q^{6} + 6 q^{7} + 16 q^{9} + O(q^{10}) \)

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.bm.a	$735$	$2$	735.bm	147.o	$42$	$444$	$37$	$5.869$		None		$2$	$0$	\(0\)	\(0\)	\(-37\)	\(3\)		$\mathrm{SU}(2)[C_{42}]$
735.2.bm.b	$735$	$2$	735.bm	147.o	$42$	$444$	$37$	$5.869$		None		$2$	$0$	\(0\)	\(0\)	\(37\)	\(3\)		$\mathrm{SU}(2)[C_{42}]$

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

\( S_{2}^{\mathrm{old}}(735, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)