Space of modular forms of level 96, weight 12, and trivial character

• Label: 96.12.a
• Level: $96$
• Weight: $12$
• Character orbit: 96.a
• Rep. character: $\chi_{96}(1,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $10$
• Sturm bound: $192$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	96.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(192\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(96))\).

	Total	New	Old
Modular forms	184	22	162
Cusp forms	168	22	146
Eisenstein series	16	0	16

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(3\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(6\)
\(+\)	\(-\)	$-$	\(5\)
\(-\)	\(+\)	$-$	\(5\)
\(-\)	\(-\)	$+$	\(6\)
Plus space		\(+\)	\(12\)
Minus space		\(-\)	\(10\)

Trace form

\( 22 q - 5284 q^{5} + 1299078 q^{9} + O(q^{10}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(96))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3
96.12.a.a	$96$	$12$	96.a	1.a	$1$	$1$	$1$	$73.761$	\(\Q\)	None	✓	✓	96.12.a.a	$1$	$0$	\(0\)	\(-243\)	\(-6070\)	\(-16100\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3^{5}q^{3}-6070q^{5}-16100q^{7}+3^{10}q^{9}+\cdots\)
96.12.a.b	$96$	$12$	96.a	1.a	$1$	$1$	$1$	$73.761$	\(\Q\)	None	✓	✓	96.12.a.a	$1$	$0$	\(0\)	\(243\)	\(-6070\)	\(16100\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3^{5}q^{3}-6070q^{5}+16100q^{7}+3^{10}q^{9}+\cdots\)
96.12.a.c	$96$	$12$	96.a	1.a	$1$	$2$	$2$	$73.761$	\(\Q(\sqrt{12391}) \)	None	✓	✓	96.12.a.c	$1$	$1$	\(0\)	\(-486\)	\(-7020\)	\(-56520\)		$-$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q-3^{5}q^{3}+(-3510+5\beta )q^{5}+(-28260+\cdots)q^{7}+\cdots\)
96.12.a.d	$96$	$12$	96.a	1.a	$1$	$2$	$2$	$73.761$	\(\Q(\sqrt{1945}) \)	None	✓	✓	96.12.a.d	$1$	$0$	\(0\)	\(-486\)	\(5300\)	\(38872\)		$+$	$+$	$+$	$2^{5}\cdot 3$	$\mathrm{SU}(2)$	\(q-3^{5}q^{3}+(2650-3\beta )q^{5}+(19436+\cdots)q^{7}+\cdots\)
96.12.a.e	$96$	$12$	96.a	1.a	$1$	$2$	$2$	$73.761$	\(\Q(\sqrt{12391}) \)	None	✓	✓	96.12.a.c	$1$	$1$	\(0\)	\(486\)	\(-7020\)	\(56520\)		$+$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+3^{5}q^{3}+(-3510+5\beta )q^{5}+(28260+\cdots)q^{7}+\cdots\)
96.12.a.f	$96$	$12$	96.a	1.a	$1$	$2$	$2$	$73.761$	\(\Q(\sqrt{1945}) \)	None	✓	✓	96.12.a.d	$1$	$0$	\(0\)	\(486\)	\(5300\)	\(-38872\)		$-$	$-$	$+$	$2^{5}\cdot 3$	$\mathrm{SU}(2)$	\(q+3^{5}q^{3}+(2650-3\beta )q^{5}+(-19436+\cdots)q^{7}+\cdots\)
96.12.a.g	$96$	$12$	96.a	1.a	$1$	$3$	$3$	$73.761$	3.3.2158836.1	None	✓	✓	96.12.a.g	$1$	$0$	\(0\)	\(-729\)	\(726\)	\(-6516\)		$+$	$+$	$+$	$2^{14}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q-3^{5}q^{3}+(242+\beta _{1})q^{5}+(-2172+\cdots)q^{7}+\cdots\)
96.12.a.h	$96$	$12$	96.a	1.a	$1$	$3$	$3$	$73.761$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓	96.12.a.h	$1$	$1$	\(0\)	\(-729\)	\(4422\)	\(39996\)		$-$	$+$	$-$	$2^{14}\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q-3^{5}q^{3}+(1474+\beta _{1})q^{5}+(13332+\cdots)q^{7}+\cdots\)
96.12.a.i	$96$	$12$	96.a	1.a	$1$	$3$	$3$	$73.761$	3.3.2158836.1	None	✓	✓	96.12.a.g	$1$	$1$	\(0\)	\(729\)	\(726\)	\(6516\)		$+$	$-$	$-$	$2^{14}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+3^{5}q^{3}+(242+\beta _{1})q^{5}+(2172-3\beta _{1}+\cdots)q^{7}+\cdots\)
96.12.a.j	$96$	$12$	96.a	1.a	$1$	$3$	$3$	$73.761$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓	96.12.a.h	$1$	$0$	\(0\)	\(729\)	\(4422\)	\(-39996\)		$-$	$-$	$+$	$2^{14}\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q+3^{5}q^{3}+(1474+\beta _{1})q^{5}+(-13332+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(96))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(96)) \simeq \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 10}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 5}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 2}\)