Space of modular forms of level 81, weight 8, and Character 81.g

• Label: 81.8.g
• Level: $81$
• Weight: $8$
• Character orbit: 81.g
• Rep. character: $\chi_{81}(4,\cdot)$
• Character field: $\Q(\zeta_{27})$
• Dimension: $1116$
• Newform subspaces: $1$
• Sturm bound: $72$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	81.g (of order \(27\) and degree \(18\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 81 \)
Character field:			\(\Q(\zeta_{27})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(72\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(81, [\chi])\).

	Total	New	Old
Modular forms	1152	1152	0
Cusp forms	1116	1116	0
Eisenstein series	36	36	0

Trace form

\( 1116 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(81, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
81.8.g.a	$81$	$8$	81.g	81.g	$27$	$1116$	$62$	$25.303$		None		✓	✓	✓	81.8.g.a	$2$	$0$	\(-18\)	\(-18\)	\(-18\)	\(-18\)		$\mathrm{SU}(2)[C_{27}]$