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

• Label: 96.2.d
• Level: $96$
• Weight: $2$
• Character orbit: 96.d
• Rep. character: $\chi_{96}(49,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• 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.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
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	24	2	22
Cusp forms	8	2	6
Eisenstein series	16	0	16

Trace form

2 * q + 4 * q^7 - 2 * q^9 - 4 * q^15 - 4 * q^17 - 8 * q^23 + 2 * q^25 - 4 * q^31 + 8 * q^39 + 4 * q^41 + 24 * q^47 - 6 * q^49 + 8 * q^57 - 4 * q^63 + 16 * q^65 - 24 * q^71 - 12 * q^73 - 20 * q^79 + 2 * q^81 + 12 * q^87 - 20 * q^89 + 16 * q^95 - 4 * q^97

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.d.a	$96$	$2$	96.d	8.b	$2$	$2$	$2$	$0.767$	\(\Q(\sqrt{-1}) \)	None			✓	✓	24.2.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+2 i q^{5}+2 q^{7}-q^{9}-4 i q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(96, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 3}\)