Space of modular forms of level 21, weight 6, and Character 21.c

• Label: 21.6.c
• Level: $21$
• Weight: $6$
• Character orbit: 21.c
• Rep. character: $\chi_{21}(20,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $16$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
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:			\(16\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(21, [\chi])\).

	Total	New	Old
Modular forms	16	16	0
Cusp forms	12	12	0
Eisenstein series	4	4	0

Trace form

12 * q - 196 * q^4 + 112 * q^7 - 492 * q^9 + 1392 * q^15 + 4868 * q^16 - 3804 * q^18 + 4116 * q^21 - 8752 * q^22 + 7812 * q^25 - 8204 * q^28 - 27876 * q^30 + 54864 * q^36 + 27464 * q^37 - 16080 * q^39 - 3444 * q^42 - 73840 * q^43 + 59144 * q^46 + 6972 * q^49 + 23760 * q^51 + 103968 * q^57 - 71512 * q^58 - 152676 * q^60 - 120624 * q^63 - 198788 * q^64 + 79344 * q^67 + 368760 * q^70 + 226644 * q^72 + 394644 * q^78 - 247104 * q^79 - 248868 * q^81 - 608076 * q^84 - 320112 * q^85 + 595456 * q^88 + 310128 * q^91 + 397272 * q^93 + 696576 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(21, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
21.6.c.a	$21$	$6$	21.c	21.c	$2$	$12$	$12$	$3.368$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓	✓	21.6.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(112\)	$2^{7}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}-\beta _{4}q^{3}+(-2^{4}-\beta _{1})q^{4}+\cdots\)