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

• Label: 735.2.g
• Level: $735$
• Weight: $2$
• Character orbit: 735.g
• Rep. character: $\chi_{735}(734,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $3$
• Sturm bound: $224$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(224\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	128	88	40
Cusp forms	96	72	24
Eisenstein series	32	16	16

Trace form

\( 72 q + 72 q^{4} + 4 q^{9} + O(q^{10}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
735.2.g.a	$735$	$2$	735.g	105.g	$2$	$16$	$16$	$5.869$	16.0.\(\cdots\).5	\(\Q(\sqrt{-15}) \)		✓			735.2.g.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 7^{6}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{3}q^{2}+\beta _{5}q^{3}+(2-\beta _{8})q^{4}+\beta _{11}q^{5}+\cdots\)
735.2.g.b	$735$	$2$	735.g	105.g	$2$	$24$	$24$	$5.869$		None					105.2.p.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
735.2.g.c	$735$	$2$	735.g	105.g	$2$	$32$	$32$	$5.869$		None		✓	✓		735.2.g.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

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