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

• Label: 84.12.k
• Level: $84$
• Weight: $12$
• Character orbit: 84.k
• Rep. character: $\chi_{84}(5,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $58$
• Newform subspaces: $2$
• Sturm bound: $192$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	84.k (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(192\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	364	58	306
Cusp forms	340	58	282
Eisenstein series	24	0	24

Trace form

\( 58 q + 49691 q^{7} + 4800 q^{9} + O(q^{10}) \)

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.k.a	$84$	$12$	84.k	21.g	$6$	$2$	$1$	$64.541$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(729\)	\(0\)	\(76885\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(3^{5}+3^{5}\zeta_{6})q^{3}+(51346-25807\zeta_{6})q^{7}+\cdots\)
84.12.k.b	$84$	$12$	84.k	21.g	$6$	$56$	$28$	$64.541$		None		$4$	$0$	\(0\)	\(-729\)	\(0\)	\(-27194\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{12}^{\mathrm{old}}(84, [\chi]) \cong \) \(S_{12}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)