Space of modular forms of level 117, weight 2, and Character 117.r

• Label: 117.2.r
• Level: $117$
• Weight: $2$
• Character orbit: 117.r
• Rep. character: $\chi_{117}(43,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $28$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.r (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 117 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(28\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(117, [\chi])\).

	Total	New	Old
Modular forms	32	32	0
Cusp forms	24	24	0
Eisenstein series	8	8	0

Trace form

\( 24 q - 3 q^{2} - q^{3} + 11 q^{4} - 3 q^{6} + q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(117, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
117.2.r.a	$117$	$2$	117.r	117.r	$6$	$2$	$1$	$0.934$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-3\)	\(-3\)	\(-3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+(1+\cdots)q^{4}+\cdots\)
117.2.r.b	$117$	$2$	117.r	117.r	$6$	$22$	$11$	$0.934$		None		$2$	$0$	\(0\)	\(2\)	\(3\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$