Space of modular forms of level 96, weight 6, and Character 96.c

• Label: 96.6.c
• Level: $96$
• Weight: $6$
• Character orbit: 96.c
• Rep. character: $\chi_{96}(95,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $96$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	96.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(96\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(96, [\chi])\).

	Total	New	Old
Modular forms	88	20	68
Cusp forms	72	20	52
Eisenstein series	16	0	16

Trace form

\( 20 q - 44 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(96, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
96.6.c.a	$96$	$6$	96.c	12.b	$2$	$20$	$20$	$15.397$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓	✓	✓	96.6.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{134}\cdot 3^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}+\beta _{6}q^{5}+\beta _{2}q^{7}+(-2-\beta _{7}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(96, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(96, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)