Space of modular forms of level 81, weight 3, and Character 81.f

• Label: 81.3.f
• Level: $81$
• Weight: $3$
• Character orbit: 81.f
• Rep. character: $\chi_{81}(8,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $30$
• Newform subspaces: $1$
• Sturm bound: $27$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	81.f (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 27 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(27\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(81, [\chi])\).

	Total	New	Old
Modular forms	126	42	84
Cusp forms	90	30	60
Eisenstein series	36	12	24

Trace form

\( 30 q + 6 q^{2} - 6 q^{4} + 15 q^{5} - 6 q^{7} + 9 q^{8} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(81, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
81.3.f.a	$81$	$3$	81.f	27.f	$18$	$30$	$5$	$2.207$		None		$2$	$0$	\(6\)	\(0\)	\(15\)	\(-6\)		$\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{3}^{\mathrm{old}}(81, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(81, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)