Space of modular forms of level 96, weight 4, and Character 96.f

• Label: 96.4.f
• Level: $96$
• Weight: $4$
• Character orbit: 96.f
• Rep. character: $\chi_{96}(47,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $2$
• Sturm bound: $64$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	96.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(64\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(96, [\chi])\).

	Total	New	Old
Modular forms	56	14	42
Cusp forms	40	10	30
Eisenstein series	16	4	12

Trace form

\( 10 q + 2 q^{3} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(96, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
96.4.f.a	$96$	$4$	96.f	24.f	$2$	$2$	$2$	$5.664$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(-10\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(-5+\beta )q^{3}+(23-10\beta )q^{9}-50\beta q^{11}+\cdots\)
96.4.f.b	$96$	$4$	96.f	24.f	$2$	$8$	$8$	$5.664$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$4$	$0$	\(0\)	\(12\)	\(0\)	\(0\)	$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{2})q^{3}+\beta _{4}q^{5}-\beta _{6}q^{7}+(-9+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(96, [\chi])\) into lower level spaces

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