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

• Label: 96.3.e
• Level: $96$
• Weight: $3$
• Character orbit: 96.e
• Rep. character: $\chi_{96}(65,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $48$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	96.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(48\)
Trace bound:			\(9\)
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	8	32
Cusp forms	24	8	16
Eisenstein series	16	0	16

Trace form

\( 8 q + 8 q^{9} + 16 q^{13} + 16 q^{21} - 56 q^{25} - 64 q^{33} - 112 q^{37} - 128 q^{45} + 152 q^{49} + 208 q^{57} + 272 q^{61} + 384 q^{69} - 240 q^{73} - 376 q^{81} - 256 q^{85} - 496 q^{93} + 400 q^{97}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
96.3.e.a	$96$	$3$	96.e	3.b	$2$	$4$	$4$	$2.616$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		✓			96.3.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(2\beta _{1}-\beta _{3})q^{7}+(-3+\cdots)q^{9}+\cdots\)
96.3.e.b	$96$	$3$	96.e	3.b	$2$	$4$	$4$	$2.616$	\(\Q(\sqrt{-2}, \sqrt{7})\)	None		✓			96.3.e.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{3})q^{3}-\beta _{2}q^{5}+(-\beta _{1}-2\beta _{3})q^{7}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(96, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)