Space of modular forms of level 84, weight 9, and Character 84.d

• Label: 84.9.d
• Level: $84$
• Weight: $9$
• Character orbit: 84.d
• Rep. character: $\chi_{84}(13,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $1$
• Sturm bound: $144$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	84.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(144\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(84, [\chi])\).

	Total	New	Old
Modular forms	134	10	124
Cusp forms	122	10	112
Eisenstein series	12	0	12

Trace form

\( 10 q - 2338 q^{7} - 21870 q^{9} + O(q^{10}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(84, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
84.9.d.a	$84$	$9$	84.d	7.b	$2$	$10$	$10$	$34.220$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2338\)	$2^{15}\cdot 3^{15}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(3\beta _{1}+\beta _{5})q^{5}+(-234+7\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(84, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(84, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)