Space of modular forms of level 171, weight 3, and Character 171.bf

• Label: 171.3.bf
• Level: $171$
• Weight: $3$
• Character orbit: 171.bf
• Rep. character: $\chi_{171}(23,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $228$
• Newform subspaces: $1$
• Sturm bound: $60$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	171.bf (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 171 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(60\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(171, [\chi])\).

	Total	New	Old
Modular forms	252	252	0
Cusp forms	228	228	0
Eisenstein series	24	24	0

Trace form

\( 228 q - 9 q^{2} - 12 q^{3} - 3 q^{4} - 9 q^{5} + 6 q^{6} - 6 q^{7} - 24 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(171, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
171.3.bf.a	$171$	$3$	171.bf	171.af	$18$	$228$	$38$	$4.659$		None		$2$	$0$	\(-9\)	\(-12\)	\(-9\)	\(-6\)		$\mathrm{SU}(2)[C_{18}]$