Space of modular forms of level 21, weight 3, and Character 21.d

• Label: 21.3.d
• Level: $21$
• Weight: $3$
• Character orbit: 21.d
• Rep. character: $\chi_{21}(13,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $8$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	21.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(8\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(21, [\chi])\).

	Total	New	Old
Modular forms	8	2	6
Cusp forms	4	2	2
Eisenstein series	4	0	4

Trace form

\( 2 q + 2 q^{2} - 6 q^{4} + 2 q^{7} - 14 q^{8} - 6 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(21, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
21.3.d.a	$21$	$3$	21.d	7.b	$2$	$2$	$2$	$0.572$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(2\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+\zeta_{6}q^{3}-3q^{4}-4\zeta_{6}q^{5}+\zeta_{6}q^{6}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(21, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(21, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)