Space of modular forms of level 27, weight 8, and Character 27.e

• Label: 27.8.e
• Level: $27$
• Weight: $8$
• Character orbit: 27.e
• Rep. character: $\chi_{27}(4,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $120$
• Newform subspaces: $1$
• Sturm bound: $24$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	27.e (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 27 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(24\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(27, [\chi])\).

	Total	New	Old
Modular forms	132	132	0
Cusp forms	120	120	0
Eisenstein series	12	12	0

Trace form

\( 120 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 219 q^{5} + 1386 q^{6} - 6 q^{7} - 4611 q^{8} - 1728 q^{9} + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(27, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
27.8.e.a	$27$	$8$	27.e	27.e	$9$	$120$	$20$	$8.434$		None		$2$	$0$	\(-6\)	\(-6\)	\(-219\)	\(-6\)		$\mathrm{SU}(2)[C_{9}]$