Space of modular forms of level 21, weight 4, and Character 21.c

• Label: 21.4.c
• Level: $21$
• Weight: $4$
• Character orbit: 21.c
• Rep. character: $\chi_{21}(20,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $10$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	21.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(10\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(21, [\chi])\).

	Total	New	Old
Modular forms	10	10	0
Cusp forms	6	6	0
Eisenstein series	4	4	0

Trace form

6 * q - 20 * q^4 + 8 * q^7 + 42 * q^9 - 204 * q^15 - 92 * q^16 + 204 * q^18 + 78 * q^21 + 544 * q^22 - 342 * q^25 - 412 * q^28 - 204 * q^30 - 1296 * q^36 + 700 * q^37 + 924 * q^39 + 1428 * q^42 + 1216 * q^43 - 1496 * q^46 - 1266 * q^49 - 1224 * q^51 - 1800 * q^57 + 952 * q^58 + 1836 * q^60 + 1212 * q^63 + 3548 * q^64 - 2016 * q^67 - 2856 * q^70 - 204 * q^72 - 4692 * q^78 + 3150 * q^81 + 2052 * q^84 + 2448 * q^85 - 544 * q^88 + 1920 * q^91 - 372 * q^93 - 1632 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(21, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
21.4.c.a	$21$	$4$	21.c	21.c	$2$	$2$	$2$	$1.239$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		✓			21.4.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-20\)	$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{3}+8 q^{4}+(3\beta-10)q^{7}-27 q^{9}+\cdots\)
21.4.c.b	$21$	$4$	21.c	21.c	$2$	$4$	$4$	$1.239$	\(\Q(\sqrt{-6}, \sqrt{-17})\)	None		✓	✓		21.4.c.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(28\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+\beta _{3}q^{3}-9q^{4}+(-\beta _{1}-2\beta _{3})q^{5}+\cdots\)