Space of modular forms of level 96, weight 9, and Character 96.e

• Label: 96.9.e
• Level: $96$
• Weight: $9$
• Character orbit: 96.e
• Rep. character: $\chi_{96}(65,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $2$
• Sturm bound: $144$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 9 \)
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:			\(144\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(96, [\chi])\).

	Total	New	Old
Modular forms	136	32	104
Cusp forms	120	32	88
Eisenstein series	16	0	16

Trace form

32 * q - 3808 * q^9 - 51392 * q^13 - 341696 * q^21 - 1862624 * q^25 + 3868928 * q^33 + 9131840 * q^37 + 16972288 * q^45 + 19518560 * q^49 - 8093888 * q^57 + 8197952 * q^61 - 2496000 * q^69 + 79043136 * q^73 + 66121760 * q^81 + 149838848 * q^85 - 78466240 * q^93 + 63367744 * q^97

Decomposition of \(S_{9}^{\mathrm{new}}(96, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
96.9.e.a	$96$	$9$	96.e	3.b	$2$	$16$	$16$	$39.108$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			96.9.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{110}\cdot 3^{30}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+\beta _{3}q^{5}+(\beta _{1}-3\beta _{2})q^{7}+(-435+\cdots)q^{9}+\cdots\)
96.9.e.b	$96$	$9$	96.e	3.b	$2$	$16$	$16$	$39.108$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			96.9.e.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{110}\cdot 3^{24}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}-\beta _{3}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(96, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(96, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)