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

• Label: 84.9.p
• Level: $84$
• Weight: $9$
• Character orbit: 84.p
• Rep. character: $\chi_{84}(53,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $42$
• Newform subspaces: $2$
• Sturm bound: $144$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	84.p (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(144\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	268	42	226
Cusp forms	244	42	202
Eisenstein series	24	0	24

Trace form

\( 42 q - 4307 q^{7} - 1790 q^{9} + O(q^{10}) \)

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.p.a	$84$	$9$	84.p	21.h	$6$	$2$	$1$	$34.220$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(-81\)	\(0\)	\(-4273\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q-3^{4}\zeta_{6}q^{3}+(-2769+1265\zeta_{6})q^{7}+\cdots\)
84.9.p.b	$84$	$9$	84.p	21.h	$6$	$40$	$20$	$34.220$		None		$4$	$0$	\(0\)	\(81\)	\(0\)	\(-34\)		$\mathrm{SU}(2)[C_{6}]$

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

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