Space of modular forms of level 96, weight 2, and Character 96.n

• Label: 96.2.n
• Level: $96$
• Weight: $2$
• Character orbit: 96.n
• Rep. character: $\chi_{96}(13,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $32$
• Newform subspaces: $1$
• Sturm bound: $32$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	96.n (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 32 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(32\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(96, [\chi])\).

	Total	New	Old
Modular forms	72	32	40
Cusp forms	56	32	24
Eisenstein series	16	0	16

Trace form

32 * q - 8 * q^10 - 16 * q^12 - 32 * q^14 - 8 * q^16 - 8 * q^18 - 32 * q^20 - 8 * q^22 - 16 * q^23 - 8 * q^24 + 40 * q^26 + 40 * q^28 - 48 * q^31 + 40 * q^32 + 40 * q^34 - 48 * q^35 + 40 * q^38 + 8 * q^40 - 16 * q^43 + 8 * q^44 - 32 * q^46 + 24 * q^50 + 16 * q^51 - 8 * q^52 - 32 * q^53 + 8 * q^54 + 32 * q^55 + 56 * q^56 - 32 * q^58 + 64 * q^59 + 48 * q^60 - 32 * q^61 + 48 * q^62 + 16 * q^63 + 24 * q^64 + 48 * q^66 + 16 * q^67 - 8 * q^68 - 32 * q^69 - 24 * q^70 + 64 * q^71 - 32 * q^74 + 32 * q^75 - 56 * q^76 - 32 * q^77 + 24 * q^78 - 56 * q^80 - 40 * q^82 - 64 * q^86 - 48 * q^88 - 48 * q^91 - 80 * q^92 - 32 * q^94 - 40 * q^96 - 80 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(96, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
96.2.n.a	$96$	$2$	96.n	32.g	$8$	$32$	$8$	$0.767$		None		✓	✓	✓	96.2.n.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{2}^{\mathrm{old}}(96, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(96, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)