Space of modular forms of level 96, weight 3, and Character 96.h

• Label: 96.3.h
• Level: $96$
• Weight: $3$
• Character orbit: 96.h
• Rep. character: $\chi_{96}(17,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $3$
• Sturm bound: $48$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	96.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(48\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(96, [\chi])\).

	Total	New	Old
Modular forms	40	10	30
Cusp forms	24	6	18
Eisenstein series	16	4	12

Trace form

\( 6 q + 4 q^{7} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(96, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
96.3.h.a	$96$	$3$	96.h	24.h	$2$	$1$	$1$	$2.616$	\(\Q\)	\(\Q(\sqrt{-6}) \)	✓	$2$	$0$	\(0\)	\(-3\)	\(2\)	\(10\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3q^{3}+2q^{5}+10q^{7}+9q^{9}+10q^{11}+\cdots\)
96.3.h.b	$96$	$3$	96.h	24.h	$2$	$1$	$1$	$2.616$	\(\Q\)	\(\Q(\sqrt{-6}) \)	✓	$2$	$0$	\(0\)	\(3\)	\(-2\)	\(10\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3q^{3}-2q^{5}+10q^{7}+9q^{9}-10q^{11}+\cdots\)
96.3.h.c	$96$	$3$	96.h	24.h	$2$	$4$	$4$	$2.616$	\(\Q(\sqrt{2}, \sqrt{-7})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-\beta _{2})q^{3}-2\beta _{1}q^{5}-4q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(96, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(96, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)