Space of modular forms of level 167, weight 2, and Character 167.c

• Label: 167.2.c
• Level: $167$
• Weight: $2$
• Character orbit: 167.c
• Rep. character: $\chi_{167}(2,\cdot)$
• Character field: $\Q(\zeta_{83})$
• Dimension: $1066$
• Newform subspaces: $1$
• Sturm bound: $28$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 167 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	167.c (of order \(83\) and degree \(82\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 167 \)
Character field:			\(\Q(\zeta_{83})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(28\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(167, [\chi])\).

	Total	New	Old
Modular forms	1230	1230	0
Cusp forms	1066	1066	0
Eisenstein series	164	164	0

Trace form

\( 1066 q - 81 q^{2} - 81 q^{3} - 89 q^{4} - 79 q^{5} - 63 q^{6} - 81 q^{7} - 71 q^{8} - 84 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(167, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
167.2.c.a	$167$	$2$	167.c	167.c	$83$	$1066$	$13$	$1.334$		None		$2$	$0$	\(-81\)	\(-81\)	\(-79\)	\(-81\)		$\mathrm{SU}(2)[C_{83}]$