Space of modular forms of level 192, weight 2, and trivial character

• Label: 192.2.a
• Level: $192$
• Weight: $2$
• Character orbit: 192.a
• Rep. character: $\chi_{192}(1,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $4$
• Sturm bound: $64$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(64\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(192))\).

	Total	New	Old
Modular forms	44	4	40
Cusp forms	21	4	17
Eisenstein series	23	0	23

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
\(+\)	\(+\)	\(+\)		\(10\)	\(1\)	\(9\)		\(5\)	\(1\)	\(4\)		\(5\)	\(0\)	\(5\)
\(+\)	\(-\)	\(-\)		\(12\)	\(2\)	\(10\)		\(6\)	\(2\)	\(4\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)		\(12\)	\(1\)	\(11\)		\(6\)	\(1\)	\(5\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)		\(10\)	\(0\)	\(10\)		\(4\)	\(0\)	\(4\)		\(6\)	\(0\)	\(6\)
Plus space		\(+\)		\(20\)	\(1\)	\(19\)		\(9\)	\(1\)	\(8\)		\(11\)	\(0\)	\(11\)
Minus space		\(-\)		\(24\)	\(3\)	\(21\)		\(12\)	\(3\)	\(9\)		\(12\)	\(0\)	\(12\)

Trace form

4 * q + 4 * q^9 + 8 * q^13 - 8 * q^17 + 8 * q^21 - 4 * q^25 - 16 * q^29 - 8 * q^37 - 8 * q^41 + 4 * q^49 - 16 * q^53 - 8 * q^61 - 16 * q^69 + 8 * q^73 + 32 * q^77 + 4 * q^81 + 32 * q^85 + 8 * q^89 + 8 * q^93 - 24 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(192))\) 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
192.2.a.a	$192$	$2$	192.a	1.a	$1$	$1$	$1$	$1.533$	\(\Q\)	None	✓		✓	✓	96.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
192.2.a.b	$192$	$2$	192.a	1.a	$1$	$1$	$1$	$1.533$	\(\Q\)	None	✓		✓	✓	24.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
192.2.a.c	$192$	$2$	192.a	1.a	$1$	$1$	$1$	$1.533$	\(\Q\)	None	✓				96.2.a.a	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots\)
192.2.a.d	$192$	$2$	192.a	1.a	$1$	$1$	$1$	$1.533$	\(\Q\)	None	✓				24.2.a.a	$1$	$0$	\(0\)	\(1\)	\(2\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(192))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(192)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 2}\)