Space of modular forms of level 171, weight 2, and Character 171.f

• Label: 171.2.f
• Level: $171$
• Weight: $2$
• Character orbit: 171.f
• Rep. character: $\chi_{171}(64,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $16$
• Newform subspaces: $3$
• Sturm bound: $40$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.f (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(40\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(171, [\chi])\).

	Total	New	Old
Modular forms	48	20	28
Cusp forms	32	16	16
Eisenstein series	16	4	12

Trace form

\( 16 q - 8 q^{4} + 2 q^{5} - 8 q^{7} + 12 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(171, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
171.2.f.a	$171$	$2$	171.f	19.c	$3$	$2$	$1$	$1.365$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+q^{7}+3q^{8}+\cdots\)
171.2.f.b	$171$	$2$	171.f	19.c	$3$	$6$	$3$	$1.365$	6.0.954288.1	None		$2$	$0$	\(-1\)	\(0\)	\(2\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{4}-\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+2\beta _{3}+\cdots)q^{4}+\cdots\)
171.2.f.c	$171$	$2$	171.f	19.c	$3$	$8$	$4$	$1.365$	8.0.764411904.5	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{5}q^{2}+(-1-\beta _{3}+\beta _{4}-\beta _{6})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(171, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(171, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 2}\)