Space of modular forms of level 189, weight 4, and Character 189.s

• Label: 189.4.s
• Level: $189$
• Weight: $4$
• Character orbit: 189.s
• Rep. character: $\chi_{189}(17,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $44$
• Newform subspaces: $1$
• Sturm bound: $96$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(96\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(189, [\chi])\).

	Total	New	Old
Modular forms	156	52	104
Cusp forms	132	44	88
Eisenstein series	24	8	16

Trace form

\( 44 q + 3 q^{2} + 81 q^{4} + 6 q^{5} + 5 q^{7} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(189, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
189.4.s.a	$189$	$4$	189.s	63.s	$6$	$44$	$22$	$11.151$		None		$2$	$0$	\(3\)	\(0\)	\(6\)	\(5\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(189, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(189, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)