Space of modular forms of level 21, weight 12, and Character 21.c

• Label: 21.12.c
• Level: $21$
• Weight: $12$
• Character orbit: 21.c
• Rep. character: $\chi_{21}(20,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $1$
• Sturm bound: $32$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	21.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(32\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(21, [\chi])\).

	Total	New	Old
Modular forms	32	32	0
Cusp forms	28	28	0
Eisenstein series	4	4	0

Trace form

\( 28 q - 28676 q^{4} + 29736 q^{7} + 22476 q^{9} + O(q^{10}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(21, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
21.12.c.a	$21$	$12$	21.c	21.c	$2$	$28$	$28$	$16.135$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(29736\)		$\mathrm{SU}(2)[C_{2}]$