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

• Label: 171.2.m
• Level: $171$
• Weight: $2$
• Character orbit: 171.m
• Rep. character: $\chi_{171}(8,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $40$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.m (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(40\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	48	16	32
Cusp forms	32	16	16
Eisenstein series	16	0	16

Trace form

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

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.m.a	$171$	$2$	171.m	57.f	$6$	$16$	$8$	$1.365$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{1}q^{2}+(-\beta _{3}+2\beta _{4}+\beta _{10})q^{4}+\cdots\)

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

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