Space of modular forms of level 21, weight 3, and Character 21.b

• Label: 21.3.b
• Level: $21$
• Weight: $3$
• Character orbit: 21.b
• Rep. character: $\chi_{21}(8,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $8$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	21.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(8\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(21, [\chi])\).

	Total	New	Old
Modular forms	8	4	4
Cusp forms	4	4	0
Eisenstein series	4	0	4

Trace form

4 * q - 2 * q^3 - 12 * q^4 + 14 * q^6 - 20 * q^9 + 28 * q^10 - 22 * q^12 - 36 * q^13 + 28 * q^15 + 36 * q^16 + 56 * q^18 + 12 * q^19 + 14 * q^21 - 56 * q^22 - 126 * q^24 - 12 * q^25 + 10 * q^27 - 56 * q^28 - 28 * q^30 + 136 * q^31 + 28 * q^33 + 116 * q^36 + 16 * q^37 + 4 * q^39 + 84 * q^40 + 70 * q^42 - 160 * q^43 - 140 * q^45 - 168 * q^46 + 38 * q^48 + 28 * q^49 - 84 * q^51 + 164 * q^52 - 154 * q^54 + 56 * q^55 + 64 * q^57 + 112 * q^58 + 140 * q^60 - 156 * q^61 - 28 * q^63 + 4 * q^64 - 28 * q^66 - 24 * q^67 + 168 * q^69 - 28 * q^70 - 32 * q^73 + 146 * q^75 - 316 * q^76 - 196 * q^78 + 128 * q^79 - 68 * q^81 + 392 * q^82 - 14 * q^84 + 168 * q^85 + 28 * q^87 + 168 * q^88 - 112 * q^90 - 28 * q^91 - 96 * q^93 - 336 * q^94 - 98 * q^96 - 8 * q^97 + 112 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(21, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
21.3.b.a	$21$	$3$	21.b	3.b	$2$	$4$	$4$	$0.572$	4.0.65856.1	None		✓	✓	✓	21.3.b.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(-3+\cdots)q^{4}+\cdots\)