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

• Label: 81.2.c
• Level: $81$
• Weight: $2$
• Character orbit: 81.c
• Rep. character: $\chi_{81}(28,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $18$
• Trace bound: $1$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	30	10	20
Cusp forms	6	6	0
Eisenstein series	24	4	20

Trace form

\( 6 q - 3 q^{7} + O(q^{10}) \)

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.c.a	$81$	$2$	81.c	9.c	$3$	$2$	$1$	$0.647$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$	$\mathrm{U}(1)[D_{3}]$	\(q+2\zeta_{6}q^{4}+(1-\zeta_{6})q^{7}-5\zeta_{6}q^{13}+\cdots\)
81.2.c.b	$81$	$2$	81.c	9.c	$3$	$4$	$2$	$0.647$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{12}^{2}q^{2}+(-1+\zeta_{12})q^{4}+(-\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)