Space of modular forms of level 108, weight 5, and Character 108.g

• Label: 108.5.g
• Level: $108$
• Weight: $5$
• Character orbit: 108.g
• Rep. character: $\chi_{108}(17,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $90$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	108.g (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(90\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(108, [\chi])\).

	Total	New	Old
Modular forms	162	8	154
Cusp forms	126	8	118
Eisenstein series	36	0	36

Trace form

\( 8 q + 9 q^{5} + 13 q^{7} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(108, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
108.5.g.a	$108$	$5$	108.g	9.d	$6$	$8$	$4$	$11.164$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(9\)	\(13\)	$2^{2}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2+\beta _{2}+\beta _{4}+\beta _{7})q^{5}+(3-\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(108, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(108, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)