Space of modular forms of level 21, weight 18, and Character 21.g

• Label: 21.18.g
• Level: $21$
• Weight: $18$
• Character orbit: 21.g
• Rep. character: $\chi_{21}(5,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $86$
• Newform subspaces: $2$
• Sturm bound: $48$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	21.g (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(48\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(21, [\chi])\).

	Total	New	Old
Modular forms	94	94	0
Cusp forms	86	86	0
Eisenstein series	8	8	0

Trace form

\( 86 q - 3 q^{3} + 2621438 q^{4} - 7098699 q^{7} + 30469167 q^{9} + O(q^{10}) \)

Decomposition of \(S_{18}^{\mathrm{new}}(21, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
21.18.g.a	$21$	$18$	21.g	21.g	$6$	$2$	$1$	$38.477$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		✓			21.18.g.a	$4$	$0$	\(0\)	\(19683\)	\(0\)	\(-2758181\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(3^{8}+3^{8}\zeta_{6})q^{3}+(-2^{17}+2^{17}\zeta_{6})q^{4}+\cdots\)
21.18.g.b	$21$	$18$	21.g	21.g	$6$	$84$	$42$	$38.477$		None		✓	✓		21.18.g.b	$4$	$0$	\(0\)	\(-19686\)	\(0\)	\(-4340518\)		$\mathrm{SU}(2)[C_{6}]$