Space of modular forms of level 189, weight 6, and Character 189.s

• Label: 189.6.s
• Level: $189$
• Weight: $6$
• Character orbit: 189.s
• Rep. character: $\chi_{189}(17,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $76$
• Newform subspaces: $1$
• Sturm bound: $144$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	189.s (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(144\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(189, [\chi])\).

	Total	New	Old
Modular forms	252	84	168
Cusp forms	228	76	152
Eisenstein series	24	8	16

Trace form

\( 76 q + 3 q^{2} + 577 q^{4} + 6 q^{5} - 30 q^{7} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(189, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
189.6.s.a	$189$	$6$	189.s	63.s	$6$	$76$	$38$	$30.313$		None			63.6.i.a	$2$	$0$	\(3\)	\(0\)	\(6\)	\(-30\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{6}^{\mathrm{old}}(189, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(189, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)