Space of modular forms of level 84, weight 12, and Character 84.n

• Label: 84.12.n
• Level: $84$
• Weight: $12$
• Character orbit: 84.n
• Rep. character: $\chi_{84}(11,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $344$
• Newform subspaces: $1$
• Sturm bound: $192$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	84.n (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 84 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(192\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(84, [\chi])\).

	Total	New	Old
Modular forms	360	360	0
Cusp forms	344	344	0
Eisenstein series	16	16	0

Trace form

\( 344 q - 2 q^{4} + 4092 q^{6} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(84, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
84.12.n.a	$84$	$12$	84.n	84.n	$6$	$344$	$172$	$64.541$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$