Space of modular forms of level 27, weight 7, and Character 27.f

• Label: 27.7.f
• Level: $27$
• Weight: $7$
• Character orbit: 27.f
• Rep. character: $\chi_{27}(2,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $102$
• Newform subspaces: $1$
• Sturm bound: $21$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 27 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(21\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(27, [\chi])\).

	Total	New	Old
Modular forms	114	114	0
Cusp forms	102	102	0
Eisenstein series	12	12	0

Trace form

\( 102 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 210 q^{5} - 342 q^{6} - 6 q^{7} - 9 q^{8} + 1242 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(27, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
27.7.f.a	$27$	$7$	27.f	27.f	$18$	$102$	$17$	$6.211$		None		$2$	$0$	\(-6\)	\(-6\)	\(210\)	\(-6\)		$\mathrm{SU}(2)[C_{18}]$