Space of modular forms of level 3, weight 9, and Character 3.b

• Label: 3.9.b
• Level: $3$
• Weight: $9$
• Character orbit: 3.b
• Rep. character: $\chi_{3}(2,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $3$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(3\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(3, [\chi])\).

	Total	New	Old
Modular forms	4	4	0
Cusp forms	2	2	0
Eisenstein series	2	2	0

Trace form

\( 2 q + 90 q^{3} - 496 q^{4} + 3024 q^{6} - 3500 q^{7} - 5022 q^{9} + O(q^{10}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(3, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3.9.b.a	$3$	$9$	3.b	3.b	$2$	$2$	$2$	$1.222$	\(\Q(\sqrt{-14}) \)	None		$2$	$0$	\(0\)	\(90\)	\(0\)	\(-3500\)	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+(45-3\beta )q^{3}-248q^{4}-10\beta q^{5}+\cdots\)