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 + 2273856 * q^15 + 27753348 * q^16 - 26666124 * q^18 + 32167884 * q^21 - 48860944 * q^22 + 314067988 * q^25 - 239159788 * q^28 + 577648716 * q^30 - 771897168 * q^36 - 1165582728 * q^37 - 587874480 * q^39 + 271272540 * q^42 + 480150048 * q^43 - 3950813080 * q^46 + 4247375356 * q^49 - 3493256544 * q^51 + 6646339080 * q^57 - 5835426520 * q^58 + 21590756316 * q^60 - 21520349592 * q^63 + 17688545532 * q^64 - 17580653248 * q^67 + 22853514264 * q^70 + 136690087668 * q^72 - 168779871420 * q^78 - 183361409296 * q^79 - 32414205924 * q^81 - 77596962156 * q^84 + 150403428288 * q^85 - 5243958752 * q^88 + 173606229552 * q^91 + 400470999816 * q^93 - 342176667360 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
21.12.c.a	$21$	$12$	21.c	21.c	$2$	$28$	$28$	$16.135$		None		✓	✓	✓	21.12.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(29736\)		$\mathrm{SU}(2)[C_{2}]$