Space of modular forms of level 108, weight 6, and Character 108.l

• Label: 108.6.l
• Level: $108$
• Weight: $6$
• Character orbit: 108.l
• Rep. character: $\chi_{108}(11,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $528$
• Newform subspaces: $1$
• Sturm bound: $108$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	108.l (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 108 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(108\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(108, [\chi])\).

	Total	New	Old
Modular forms	552	552	0
Cusp forms	528	528	0
Eisenstein series	24	24	0

Trace form

\( 528 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(108, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
108.6.l.a	$108$	$6$	108.l	108.l	$18$	$528$	$88$	$17.321$		None		$4$	$0$	\(-6\)	\(0\)	\(-12\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$