Space of modular forms of level 96, weight 3, and Character 96.g

• Label: 96.3.g
• Level: $96$
• Weight: $3$
• Character orbit: 96.g
• Rep. character: $\chi_{96}(31,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $48$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	96.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(48\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(96, [\chi])\).

	Total	New	Old
Modular forms	40	4	36
Cusp forms	24	4	20
Eisenstein series	16	0	16

Trace form

\( 4 q - 8 q^{5} - 12 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(96, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
96.3.g.a	$96$	$3$	96.g	4.b	$2$	$4$	$4$	$2.616$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}^{2}q^{3}+(-2-\zeta_{12}^{3})q^{5}+(\zeta_{12}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(96, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(96, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)