Space of modular forms of level 21, weight 7, and Character 21.b

• Label: 21.7.b
• Level: $21$
• Weight: $7$
• Character orbit: 21.b
• Rep. character: $\chi_{21}(8,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $18$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
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:			\(18\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(21, [\chi])\).

	Total	New	Old
Modular forms	18	12	6
Cusp forms	14	12	2
Eisenstein series	4	0	4

Trace form

\( 12 q + 52 q^{3} - 516 q^{4} + 350 q^{6} - 644 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(21, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
21.7.b.a	$21$	$7$	21.b	3.b	$2$	$12$	$12$	$4.831$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(52\)	\(0\)	\(0\)	$2^{2}\cdot 3^{8}\cdot 7^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(4-\beta _{3})q^{3}+(-43+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(21, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(21, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 2}\)