Space of modular forms of level 189, weight 2, and Character 189.w

• Label: 189.2.w
• Level: $189$
• Weight: $2$
• Character orbit: 189.w
• Rep. character: $\chi_{189}(25,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $132$
• Newform subspaces: $1$
• Sturm bound: $48$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.w (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 189 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(48\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(189, [\chi])\).

	Total	New	Old
Modular forms	156	156	0
Cusp forms	132	132	0
Eisenstein series	24	24	0

Trace form

\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(189, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
189.2.w.a	$189$	$2$	189.w	189.w	$9$	$132$	$22$	$1.509$		None		$2$	$0$	\(-3\)	\(-3\)	\(-3\)	\(-6\)		$\mathrm{SU}(2)[C_{9}]$