Space of modular forms of level 21, weight 2, and Character 21.g

• Label: 21.2.g
• Level: $21$
• Weight: $2$
• Character orbit: 21.g
• Rep. character: $\chi_{21}(5,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $5$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	21.g (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(5\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(21, [\chi])\).

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

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(21, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
21.2.g.a	$21$	$2$	21.g	21.g	$6$	$2$	$1$	$0.168$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(-3\)	\(0\)	\(1\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(2+\cdots)q^{7}+\cdots\)