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

• Label: 96.2.o
• Level: $96$
• Weight: $2$
• Character orbit: 96.o
• Rep. character: $\chi_{96}(11,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $56$
• 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.o (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 96 \)
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	72	0
Cusp forms	56	56	0
Eisenstein series	16	16	0

Trace form

56 * q - 4 * q^3 - 8 * q^4 - 4 * q^6 - 8 * q^7 - 4 * q^9 - 16 * q^10 - 4 * q^12 - 8 * q^13 - 8 * q^15 - 40 * q^16 - 4 * q^18 - 8 * q^19 - 4 * q^21 - 24 * q^22 + 16 * q^24 - 8 * q^25 - 28 * q^27 - 8 * q^28 + 44 * q^30 - 8 * q^33 - 24 * q^34 + 48 * q^36 - 8 * q^37 - 28 * q^39 + 24 * q^40 + 56 * q^42 - 8 * q^43 - 4 * q^45 + 24 * q^46 + 48 * q^48 - 16 * q^51 + 48 * q^52 + 40 * q^54 + 24 * q^55 - 4 * q^57 + 96 * q^58 + 8 * q^60 - 40 * q^61 + 40 * q^64 - 28 * q^66 + 56 * q^67 - 4 * q^69 + 40 * q^70 - 64 * q^72 - 8 * q^73 + 16 * q^75 + 48 * q^76 - 92 * q^78 + 16 * q^79 - 48 * q^82 - 136 * q^84 - 48 * q^85 + 52 * q^87 - 48 * q^88 - 136 * q^90 + 40 * q^91 + 8 * q^93 - 64 * q^94 - 104 * q^96 - 16 * q^97 + 60 * q^99

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.o.a	$96$	$2$	96.o	96.o	$8$	$56$	$14$	$0.767$		None		✓	✓	✓	96.2.o.a	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{8}]$