Space of modular forms of level 117, weight 4, and Character 117.r

• Label: 117.4.r
• Level: $117$
• Weight: $4$
• Character orbit: 117.r
• Rep. character: $\chi_{117}(43,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $80$
• Newform subspaces: $1$
• Sturm bound: $56$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	117.r (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 117 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(56\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(117, [\chi])\).

	Total	New	Old
Modular forms	88	88	0
Cusp forms	80	80	0
Eisenstein series	8	8	0

Trace form

\( 80 q - 3 q^{2} - q^{3} + 153 q^{4} - 3 q^{6} - 17 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(117, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
117.4.r.a	$117$	$4$	117.r	117.r	$6$	$80$	$40$	$6.903$		None		$2$	$0$	\(-3\)	\(-1\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$