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 + 3 * q^11 - 2 * q^13 - 2 * q^14 - q^16 - 6 * q^17 - 6 * q^18 - 2 * q^19 + 6 * q^21 + 3 * q^22 + 6 * q^23 - 3 * q^24 + 5 * q^25 + 4 * q^26 + 4 * q^28 - 6 * q^29 + 4 * q^31 - q^32 - 9 * q^33 + 3 * q^34 + 3 * q^36 - 8 * q^37 + q^38 - 9 * q^41 + q^43 - 6 * q^44 - 12 * q^46 + 6 * q^47 + 3 * q^48 + 3 * q^49 + 5 * q^50 + 9 * q^51 - 2 * q^52 + 24 * q^53 + 9 * q^54 - 2 * q^56 + 3 * q^57 - 6 * q^58 - 3 * q^59 - 8 * q^61 - 8 * q^62 - 12 * q^63 + 2 * q^64 - 5 * q^67 + 3 * q^68 - 24 * q^71 + 3 * q^72 + 22 * q^73 + 4 * q^74 - 15 * q^75 + q^76 + 6 * q^77 - 6 * q^78 + 4 * q^79 - 9 * q^81 + 18 * q^82 - 12 * q^83 - 6 * q^84 + q^86 + 18 * q^87 + 3 * q^88 + 12 * q^89 + 8 * q^91 + 6 * q^92 + 6 * q^94 - 5 * q^97 - 6 * q^98 + 18 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	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		✓	✓	✓	18.2.c.a	$2$	$0$	\(-1\)	\(-3\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)