Space of modular forms of level 18, weight 2, and Character 18.c

• Label: 18.2.c
• Level: $18$
• Weight: $2$
• Character orbit: 18.c
• Rep. character: $\chi_{18}(7,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $6$
• Trace bound: $0$

Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(18, [\chi])\).

	Total	New	Old
Modular forms	10	2	8
Cusp forms	2	2	0
Eisenstein series	8	0	8

Trace form

\( 2 q - q^{2} - 3 q^{3} - q^{4} + 3 q^{6} - 2 q^{7} + 2 q^{8} + 3 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(18, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
18.2.c.a	$18$	$2$	18.c	9.c	$3$	$2$	$1$	$0.144$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(-3\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)