Space of modular forms of level 21, weight 8, and Character 21.g

• Label: 21.8.g
• Level: $21$
• Weight: $8$
• Character orbit: 21.g
• Rep. character: $\chi_{21}(5,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $34$
• Newform subspaces: $2$
• Sturm bound: $21$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
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:			\(21\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(21, [\chi])\).

	Total	New	Old
Modular forms	42	42	0
Cusp forms	34	34	0
Eisenstein series	8	8	0

Trace form

\( 34 q - 3 q^{3} + 1022 q^{4} + 701 q^{7} - 1329 q^{9} + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(21, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
21.8.g.a	$21$	$8$	21.g	21.g	$6$	$2$	$1$	$6.560$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		✓	21.8.g.a	$4$	$0$	\(0\)	\(81\)	\(0\)	\(-1763\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(3^{3}+3^{3}\zeta_{6})q^{3}+(-2^{7}+2^{7}\zeta_{6})q^{4}+\cdots\)
21.8.g.b	$21$	$8$	21.g	21.g	$6$	$32$	$16$	$6.560$		None		✓	21.8.g.b	$4$	$0$	\(0\)	\(-84\)	\(0\)	\(2464\)		$\mathrm{SU}(2)[C_{6}]$