Space of modular forms of level 96, weight 4, and trivial character

• Label: 96.4.a
• Level: $96$
• Weight: $4$
• Character orbit: 96.a
• Rep. character: $\chi_{96}(1,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $6$
• Sturm bound: $64$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	96.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(64\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(96))\).

	Total	New	Old
Modular forms	56	6	50
Cusp forms	40	6	34
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		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(16\)	\(2\)	\(14\)		\(12\)	\(2\)	\(10\)		\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(-\)		\(14\)	\(1\)	\(13\)		\(10\)	\(1\)	\(9\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(-\)		\(12\)	\(1\)	\(11\)		\(8\)	\(1\)	\(7\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(+\)		\(14\)	\(2\)	\(12\)		\(10\)	\(2\)	\(8\)		\(4\)	\(0\)	\(4\)
Plus space		\(+\)		\(30\)	\(4\)	\(26\)		\(22\)	\(4\)	\(18\)		\(8\)	\(0\)	\(8\)
Minus space		\(-\)		\(26\)	\(2\)	\(24\)		\(18\)	\(2\)	\(16\)		\(8\)	\(0\)	\(8\)

Trace form

6 * q - 4 * q^5 + 54 * q^9 + 164 * q^13 + 156 * q^17 - 120 * q^21 - 150 * q^25 + 284 * q^29 + 24 * q^33 - 636 * q^37 - 1300 * q^41 - 36 * q^45 + 854 * q^49 - 212 * q^53 + 168 * q^57 - 1324 * q^61 - 280 * q^65 + 1212 * q^73 + 3872 * q^77 + 486 * q^81 + 2456 * q^85 + 220 * q^89 - 2760 * q^93 - 2260 * q^97

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(96))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	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
96.4.a.a	$96$	$4$	96.a	1.a	$1$	$1$	$1$	$5.664$	\(\Q\)	None	✓	✓			96.4.a.a	$1$	$0$	\(0\)	\(-3\)	\(-14\)	\(36\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-14q^{5}+6^{2}q^{7}+9q^{9}+6^{2}q^{11}+\cdots\)
96.4.a.b	$96$	$4$	96.a	1.a	$1$	$1$	$1$	$5.664$	\(\Q\)	None	✓	✓	✓	✓	96.4.a.b	$1$	$1$	\(0\)	\(-3\)	\(2\)	\(-12\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+2q^{5}-12q^{7}+9q^{9}-60q^{11}+\cdots\)
96.4.a.c	$96$	$4$	96.a	1.a	$1$	$1$	$1$	$5.664$	\(\Q\)	None	✓	✓			96.4.a.c	$1$	$0$	\(0\)	\(-3\)	\(10\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+10q^{5}-4q^{7}+9q^{9}+20q^{11}+\cdots\)
96.4.a.d	$96$	$4$	96.a	1.a	$1$	$1$	$1$	$5.664$	\(\Q\)	None	✓	✓	✓	✓	96.4.a.a	$1$	$1$	\(0\)	\(3\)	\(-14\)	\(-36\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-14q^{5}-6^{2}q^{7}+9q^{9}-6^{2}q^{11}+\cdots\)
96.4.a.e	$96$	$4$	96.a	1.a	$1$	$1$	$1$	$5.664$	\(\Q\)	None	✓	✓			96.4.a.b	$1$	$0$	\(0\)	\(3\)	\(2\)	\(12\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+2q^{5}+12q^{7}+9q^{9}+60q^{11}+\cdots\)
96.4.a.f	$96$	$4$	96.a	1.a	$1$	$1$	$1$	$5.664$	\(\Q\)	None	✓	✓			96.4.a.c	$1$	$0$	\(0\)	\(3\)	\(10\)	\(4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+10q^{5}+4q^{7}+9q^{9}-20q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(96))\) into lower level spaces

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