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

• Label: 117.4.x
• Level: $117$
• Weight: $4$
• Character orbit: 117.x
• Rep. character: $\chi_{117}(2,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $160$
• 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.x (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 117 \)
Character field:			\(\Q(\zeta_{12})\)
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	176	176	0
Cusp forms	160	160	0
Eisenstein series	16	16	0

Trace form

\( 160 q - 6 q^{2} - 2 q^{3} - 6 q^{5} + 88 q^{6} + 10 q^{7} + 66 q^{8} - 2 q^{9} + O(q^{10}) \)

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.x.a	$117$	$4$	117.x	117.x	$12$	$160$	$40$	$6.903$		None		$2$	$0$	\(-6\)	\(-2\)	\(-6\)	\(10\)		$\mathrm{SU}(2)[C_{12}]$