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

• Label: 108.6.i
• Level: $108$
• Weight: $6$
• Character orbit: 108.i
• Rep. character: $\chi_{108}(13,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $90$
• 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.i (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 27 \)
Character field:			\(\Q(\zeta_{9})\)
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	558	90	468
Cusp forms	522	90	432
Eisenstein series	36	0	36

Trace form

\( 90 q - 87 q^{5} + 330 q^{9} + O(q^{10}) \)

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.i.a	$108$	$6$	108.i	27.e	$9$	$90$	$15$	$17.321$		None		$2$	$0$	\(0\)	\(0\)	\(-87\)	\(0\)		$\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{6}^{\mathrm{old}}(108, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(108, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)