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

• Label: 21.8.c
• Level: $21$
• Weight: $8$
• Character orbit: 21.c
• Rep. character: $\chi_{21}(20,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $21$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
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:			\(21\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	20	20	0
Cusp forms	16	16	0
Eisenstein series	4	4	0

Trace form

16 * q - 772 * q^4 - 1288 * q^7 - 936 * q^9 - 11664 * q^15 - 4220 * q^16 - 8172 * q^18 - 56952 * q^21 + 115440 * q^22 + 97648 * q^25 + 192724 * q^28 + 180396 * q^30 - 1179792 * q^36 - 916016 * q^37 + 149760 * q^39 - 1237572 * q^42 + 2166448 * q^43 - 1071384 * q^46 + 2157568 * q^49 + 5051376 * q^51 - 4847256 * q^57 - 6730584 * q^58 + 4488156 * q^60 - 1872360 * q^63 + 8448764 * q^64 - 8510416 * q^67 - 117096 * q^70 + 8622900 * q^72 - 18151452 * q^78 - 9746320 * q^79 + 14598144 * q^81 + 9550548 * q^84 + 13490928 * q^85 - 10653600 * q^88 - 18219936 * q^91 - 17884080 * q^93 - 21577824 * q^99

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	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
21.8.c.a	$21$	$8$	21.c	21.c	$2$	$16$	$16$	$6.560$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓	✓	✓	21.8.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-1288\)	$2^{13}\cdot 3^{19}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(-48+\beta _{3})q^{4}+\cdots\)