Space of modular forms of level 21, weight 5, and Character 21.b

• Label: 21.5.b
• Level: $21$
• Weight: $5$
• Character orbit: 21.b
• Rep. character: $\chi_{21}(8,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $13$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
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:			\(13\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(21, [\chi])\).

	Total	New	Old
Modular forms	12	8	4
Cusp forms	8	8	0
Eisenstein series	4	0	4

Trace form

\( 8 q - 2 q^{3} - 36 q^{4} - 34 q^{6} + 64 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(21, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
21.5.b.a	$21$	$5$	21.b	3.b	$2$	$8$	$8$	$2.171$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2\cdot 3^{3}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-5+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots\)