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

• Label: 84.12.b
• Level: $84$
• Weight: $12$
• Character orbit: 84.b
• Rep. character: $\chi_{84}(55,\cdot)$
• Character field: $\Q$
• Dimension: $88$
• Newform subspaces: $2$
• Sturm bound: $192$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	84.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(192\)
Trace bound:			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	180	88	92
Cusp forms	172	88	84
Eisenstein series	8	0	8

Trace form

\( 88 q - 46 q^{2} + 3082 q^{4} - 37390 q^{8} + 5196312 q^{9} + O(q^{10}) \)

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.b.a	$84$	$12$	84.b	28.d	$2$	$44$	$44$	$64.541$		None		$2$	$0$	\(-23\)	\(-10692\)	\(0\)	\(-134\)		$\mathrm{SU}(2)[C_{2}]$
84.12.b.b	$84$	$12$	84.b	28.d	$2$	$44$	$44$	$64.541$		None		$2$	$0$	\(-23\)	\(10692\)	\(0\)	\(134\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{12}^{\mathrm{old}}(84, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(84, [\chi]) \cong \)