Space of modular forms of level 96, weight 2, and trivial character

• Label: 96.2.a
• Level: $96$
• Weight: $2$
• Character orbit: 96.a
• Rep. character: $\chi_{96}(1,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $2$
• Sturm bound: $32$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	96.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(32\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(96))\).

	Total	New	Old
Modular forms	24	2	22
Cusp forms	9	2	7
Eisenstein series	15	0	15

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
\(+\)	\(+\)	\(+\)		\(4\)	\(0\)	\(4\)		\(1\)	\(0\)	\(1\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)		\(6\)	\(1\)	\(5\)		\(2\)	\(1\)	\(1\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(-\)		\(8\)	\(1\)	\(7\)		\(4\)	\(1\)	\(3\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(+\)		\(6\)	\(0\)	\(6\)		\(2\)	\(0\)	\(2\)		\(4\)	\(0\)	\(4\)
Plus space		\(+\)		\(10\)	\(0\)	\(10\)		\(3\)	\(0\)	\(3\)		\(7\)	\(0\)	\(7\)
Minus space		\(-\)		\(14\)	\(2\)	\(12\)		\(6\)	\(2\)	\(4\)		\(8\)	\(0\)	\(8\)

Trace form

2 * q + 4 * q^5 + 2 * q^9 - 4 * q^13 - 12 * q^17 - 8 * q^21 - 2 * q^25 + 4 * q^29 + 8 * q^33 - 4 * q^37 + 4 * q^41 + 4 * q^45 + 18 * q^49 + 20 * q^53 - 8 * q^57 + 12 * q^61 - 8 * q^65 - 12 * q^73 - 32 * q^77 + 2 * q^81 - 24 * q^85 + 20 * q^89 + 8 * q^93 - 28 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(96))\) 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
96.2.a.a	$96$	$2$	96.a	1.a	$1$	$1$	$1$	$0.767$	\(\Q\)	None	✓	✓	✓	✓	96.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots\)
96.2.a.b	$96$	$2$	96.a	1.a	$1$	$1$	$1$	$0.767$	\(\Q\)	None	✓	✓	✓	✓	96.2.a.a	$1$	$0$	\(0\)	\(1\)	\(2\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(96))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(96)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 2}\)