Space of modular forms of level 84, weight 4, and Character 84.o

• Label: 84.4.o
• Level: $84$
• Weight: $4$
• Character orbit: 84.o
• Rep. character: $\chi_{84}(19,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $48$
• Newform subspaces: $2$
• Sturm bound: $64$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	84.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(64\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(84, [\chi])\).

	Total	New	Old
Modular forms	104	48	56
Cusp forms	88	48	40
Eisenstein series	16	0	16

Trace form

\( 48 q - 2 q^{2} - 10 q^{4} - 152 q^{8} - 216 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(84, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
84.4.o.a	$84$	$4$	84.o	28.f	$6$	$24$	$12$	$4.956$		None		$2$	$0$	\(-1\)	\(-36\)	\(0\)	\(10\)		$\mathrm{SU}(2)[C_{6}]$
84.4.o.b	$84$	$4$	84.o	28.f	$6$	$24$	$12$	$4.956$		None		$2$	$0$	\(-1\)	\(36\)	\(0\)	\(-10\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(84, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(84, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)