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

• Label: 21.7.d
• Level: $21$
• Weight: $7$
• Character orbit: 21.d
• Rep. character: $\chi_{21}(13,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $18$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	21.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
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	8	10
Cusp forms	14	8	6
Eisenstein series	4	0	4

Trace form

\( 8 q + 10 q^{2} + 346 q^{4} + 28 q^{7} - 1462 q^{8} - 1944 q^{9} + O(q^{10}) \)

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.d.a	$21$	$7$	21.d	7.b	$2$	$8$	$8$	$4.831$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(10\)	\(0\)	\(0\)	\(28\)	$2^{5}\cdot 3^{7}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{1})q^{2}-\beta _{4}q^{3}+(44+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)

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

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