Space of modular forms of level 81, weight 2, and Character 81.e

• Label: 81.2.e
• Level: $81$
• Weight: $2$
• Character orbit: 81.e
• Rep. character: $\chi_{81}(10,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $18$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	81.e (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 27 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(18\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(81, [\chi])\).

	Total	New	Old
Modular forms	72	24	48
Cusp forms	36	12	24
Eisenstein series	36	12	24

Trace form

\( 12 q + 6 q^{2} - 6 q^{4} + 3 q^{5} - 6 q^{7} - 6 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(81, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
81.2.e.a	$81$	$2$	81.e	27.e	$9$	$12$	$2$	$0.647$	12.0.\(\cdots\).1	None		$2$	$0$	\(6\)	\(0\)	\(3\)	\(-6\)	$3$	$\mathrm{SU}(2)[C_{9}]$	\(q+(1+\beta _{3}-\beta _{8})q^{2}+(1+\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(81, [\chi])\) into lower level spaces

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