Space of modular forms of level 27, weight 3, and Character 27.d

• Label: 27.3.d
• Level: $27$
• Weight: $3$
• Character orbit: 27.d
• Rep. character: $\chi_{27}(8,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $9$
• Trace bound: $0$

Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(27, [\chi])\).

	Total	New	Old
Modular forms	18	6	12
Cusp forms	6	2	4
Eisenstein series	12	4	8

Trace form

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

Decomposition of \(S_{3}^{\mathrm{new}}(27, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
27.3.d.a	$27$	$3$	27.d	9.d	$6$	$2$	$1$	$0.736$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(3\)	\(0\)	\(-6\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-4+2\zeta_{6})q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(27, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(27, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)