Space of modular forms of level 9600, weight 2, and trivial character

• Label: 9600.2.a
• Level: $9600$
• Weight: $2$
• Character orbit: 9600.a
• Rep. character: $\chi_{9600}(1,\cdot)$
• Character field: $\Q$
• Dimension: $152$
• Newform subspaces: $100$
• Sturm bound: $3840$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 9600 = 2^{7} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9600.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 100 \)
Sturm bound:			\(3840\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(17\), \(29\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9600))\).

	Total	New	Old
Modular forms	2016	152	1864
Cusp forms	1825	152	1673
Eisenstein series	191	0	191

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

\(2\)	\(3\)	\(5\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(240\)	\(17\)	\(223\)		\(217\)	\(17\)	\(200\)		\(23\)	\(0\)	\(23\)
\(+\)	\(+\)	\(-\)	\(-\)		\(260\)	\(22\)	\(238\)		\(236\)	\(22\)	\(214\)		\(24\)	\(0\)	\(24\)
\(+\)	\(-\)	\(+\)	\(-\)		\(252\)	\(19\)	\(233\)		\(228\)	\(19\)	\(209\)		\(24\)	\(0\)	\(24\)
\(+\)	\(-\)	\(-\)	\(+\)		\(256\)	\(18\)	\(238\)		\(232\)	\(18\)	\(214\)		\(24\)	\(0\)	\(24\)
\(-\)	\(+\)	\(+\)	\(-\)		\(264\)	\(19\)	\(245\)		\(240\)	\(19\)	\(221\)		\(24\)	\(0\)	\(24\)
\(-\)	\(+\)	\(-\)	\(+\)		\(244\)	\(18\)	\(226\)		\(220\)	\(18\)	\(202\)		\(24\)	\(0\)	\(24\)
\(-\)	\(-\)	\(+\)	\(+\)		\(252\)	\(17\)	\(235\)		\(228\)	\(17\)	\(211\)		\(24\)	\(0\)	\(24\)
\(-\)	\(-\)	\(-\)	\(-\)		\(248\)	\(22\)	\(226\)		\(224\)	\(22\)	\(202\)		\(24\)	\(0\)	\(24\)
Plus space			\(+\)		\(992\)	\(70\)	\(922\)		\(897\)	\(70\)	\(827\)		\(95\)	\(0\)	\(95\)
Minus space			\(-\)		\(1024\)	\(82\)	\(942\)		\(928\)	\(82\)	\(846\)		\(96\)	\(0\)	\(96\)

Trace form

\( 152 q + 152 q^{9} - 16 q^{17} - 16 q^{41} + 120 q^{49} - 32 q^{57} + 16 q^{73} + 152 q^{81} + 48 q^{89} - 80 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9600))\) 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	5
9600.2.a.a	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.a.f	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{7}+q^{9}-6q^{11}+4q^{13}+\cdots\)
9600.2.a.b	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{7}+q^{9}-2q^{11}+4q^{21}+\cdots\)
9600.2.a.c	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.f.b	$1$	$2$	\(0\)	\(-1\)	\(0\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{7}+q^{9}-6q^{13}-2q^{17}+\cdots\)
9600.2.a.d	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.f.b	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{7}+q^{9}+6q^{13}+2q^{17}+\cdots\)
9600.2.a.e	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				384.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
9600.2.a.f	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.a.c	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots\)
9600.2.a.g	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
9600.2.a.h	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				384.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
9600.2.a.i	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{7}+q^{9}+6q^{11}+2q^{13}+\cdots\)
9600.2.a.j	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.f.a	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}-4q^{11}-2q^{13}+2q^{17}+\cdots\)
9600.2.a.k	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.f.a	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}-4q^{11}+2q^{13}+2q^{17}+\cdots\)
9600.2.a.l	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}-2q^{11}-4q^{13}-q^{27}+\cdots\)
9600.2.a.m	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.f.e	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}-2q^{11}-2q^{13}-2q^{17}+\cdots\)
9600.2.a.n	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.f.e	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}-2q^{11}+2q^{13}-2q^{17}+\cdots\)
9600.2.a.o	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}-2q^{11}+4q^{13}-q^{27}+\cdots\)
9600.2.a.p	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.f.e	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}+2q^{11}-2q^{13}+2q^{17}+\cdots\)
9600.2.a.q	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.f.e	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}+2q^{11}+2q^{13}+2q^{17}+\cdots\)
9600.2.a.r	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.f.a	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}+4q^{11}-2q^{13}-2q^{17}+\cdots\)
9600.2.a.s	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.f.a	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}+4q^{11}+2q^{13}-2q^{17}+\cdots\)
9600.2.a.t	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				384.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
9600.2.a.u	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.a.c	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{7}+q^{9}-2q^{11}+6q^{13}+\cdots\)
9600.2.a.v	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
9600.2.a.w	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				384.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
9600.2.a.x	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots\)
9600.2.a.y	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.a.f	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{7}+q^{9}-6q^{11}-4q^{13}+\cdots\)
9600.2.a.z	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{7}+q^{9}-2q^{11}-4q^{21}+\cdots\)
9600.2.a.ba	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.f.b	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{7}+q^{9}-6q^{13}+2q^{17}+\cdots\)
9600.2.a.bb	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.f.b	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{7}+q^{9}+6q^{13}-2q^{17}+\cdots\)
9600.2.a.bc	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.f.b	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{7}+q^{9}-6q^{13}+2q^{17}+\cdots\)
9600.2.a.bd	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.f.b	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{7}+q^{9}+6q^{13}-2q^{17}+\cdots\)
9600.2.a.be	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.a.a	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{7}+q^{9}+2q^{11}-4q^{21}+\cdots\)
9600.2.a.bf	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.a.f	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{7}+q^{9}+6q^{11}-4q^{13}+\cdots\)
9600.2.a.bg	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.a.b	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots\)
9600.2.a.bh	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				384.2.a.b	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
9600.2.a.bi	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.a.e	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
9600.2.a.bj	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.a.c	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots\)
9600.2.a.bk	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				384.2.a.a	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
9600.2.a.bl	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.f.a	$1$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}-4q^{11}-2q^{13}-2q^{17}+\cdots\)
9600.2.a.bm	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.f.a	$1$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}-4q^{11}+2q^{13}-2q^{17}+\cdots\)
9600.2.a.bn	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.f.e	$1$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}-2q^{11}-2q^{13}+2q^{17}+\cdots\)
9600.2.a.bo	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.f.e	$1$	$0$	\(0\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}-2q^{11}+2q^{13}+2q^{17}+\cdots\)
9600.2.a.bp	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.a.d	$1$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}+2q^{11}-4q^{13}+q^{27}+\cdots\)
9600.2.a.bq	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.f.e	$1$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}+2q^{11}-2q^{13}-2q^{17}+\cdots\)
9600.2.a.br	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.f.e	$1$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}+2q^{11}+2q^{13}-2q^{17}+\cdots\)
9600.2.a.bs	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.a.d	$1$	$0$	\(0\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}+2q^{11}+4q^{13}+q^{27}+\cdots\)
9600.2.a.bt	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.f.a	$1$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}+4q^{11}-2q^{13}+2q^{17}+\cdots\)
9600.2.a.bu	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.f.a	$1$	$0$	\(0\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}+4q^{11}+2q^{13}+2q^{17}+\cdots\)
9600.2.a.bv	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.a.b	$1$	$0$	\(0\)	\(1\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{7}+q^{9}-6q^{11}+2q^{13}+\cdots\)
9600.2.a.bw	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				384.2.a.b	$1$	$1$	\(0\)	\(1\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
9600.2.a.bx	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.a.e	$1$	$0$	\(0\)	\(1\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
9600.2.a.by	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.a.c	$1$	$1$	\(0\)	\(1\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{7}+q^{9}+2q^{11}-6q^{13}+\cdots\)
9600.2.a.bz	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				384.2.a.a	$1$	$0$	\(0\)	\(1\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
9600.2.a.ca	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.f.b	$1$	$0$	\(0\)	\(1\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{7}+q^{9}-6q^{13}-2q^{17}+\cdots\)
9600.2.a.cb	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.f.b	$1$	$0$	\(0\)	\(1\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{7}+q^{9}+6q^{13}+2q^{17}+\cdots\)
9600.2.a.cc	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.a.a	$1$	$0$	\(0\)	\(1\)	\(0\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{7}+q^{9}+2q^{11}+4q^{21}+\cdots\)
9600.2.a.cd	$9600$	$2$	9600.a	1.a	$1$	$1$	$1$	$76.656$	\(\Q\)	None	✓				1920.2.a.f	$1$	$0$	\(0\)	\(1\)	\(0\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{7}+q^{9}+6q^{11}+4q^{13}+\cdots\)
9600.2.a.ce	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{2}) \)	None	✓	✓			9600.2.a.ce	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta )q^{7}+q^{9}+(-2+3\beta )q^{11}+\cdots\)
9600.2.a.cf	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{6}) \)	None	✓	✓			9600.2.a.cf	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta )q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
9600.2.a.cg	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{6}) \)	None	✓	✓			9600.2.a.cg	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
9600.2.a.ch	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{10}) \)	None	✓	✓			9600.2.a.ch	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
9600.2.a.ci	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{10}) \)	None	✓	✓			9600.2.a.ch	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
9600.2.a.cj	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{6}) \)	None	✓	✓			9600.2.a.cg	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
9600.2.a.ck	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{6}) \)	None	✓	✓			9600.2.a.cf	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta )q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
9600.2.a.cl	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{17}) \)	None	✓				1920.2.a.y	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta )q^{7}+q^{9}+2q^{11}+\cdots\)
9600.2.a.cm	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{2}) \)	None	✓	✓			9600.2.a.ce	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta )q^{7}+q^{9}+(2-3\beta )q^{11}+\cdots\)
9600.2.a.cn	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{6}) \)	None	✓	✓			9600.2.a.cf	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
9600.2.a.co	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{2}) \)	None	✓	✓			9600.2.a.ce	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{7}+q^{9}+(-2-3\beta )q^{11}+\cdots\)
9600.2.a.cp	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{10}) \)	None	✓	✓			9600.2.a.ch	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{7}+q^{9}-\beta q^{11}-q^{13}+\cdots\)
9600.2.a.cq	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{6}) \)	None	✓	✓			9600.2.a.cg	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{7}+q^{9}+\beta q^{11}+(-1+\cdots)q^{13}+\cdots\)
9600.2.a.cr	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{6}) \)	None	✓	✓			9600.2.a.cg	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{7}+q^{9}-\beta q^{11}+(1+\cdots)q^{13}+\cdots\)
9600.2.a.cs	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{10}) \)	None	✓	✓			9600.2.a.ch	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{7}+q^{9}+\beta q^{11}+q^{13}+\cdots\)
9600.2.a.ct	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{17}) \)	None	✓				1920.2.a.y	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{7}+q^{9}+2q^{11}+(1+\cdots)q^{13}+\cdots\)
9600.2.a.cu	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{2}) \)	None	✓	✓			9600.2.a.ce	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{7}+q^{9}+(2+3\beta )q^{11}+\cdots\)
9600.2.a.cv	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{6}) \)	None	✓	✓			9600.2.a.cf	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
9600.2.a.cw	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{17}) \)	None	✓				1920.2.a.y	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta )q^{7}+q^{9}-2q^{11}+\cdots\)
9600.2.a.cx	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{2}) \)	None	✓	✓			9600.2.a.ce	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta )q^{7}+q^{9}+(-2+3\beta )q^{11}+\cdots\)
9600.2.a.cy	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{6}) \)	None	✓	✓			9600.2.a.cf	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta )q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
9600.2.a.cz	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{10}) \)	None	✓	✓			9600.2.a.ch	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
9600.2.a.da	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{6}) \)	None	✓	✓			9600.2.a.cg	$1$	$0$	\(0\)	\(2\)	\(0\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
9600.2.a.db	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{6}) \)	None	✓	✓			9600.2.a.cg	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
9600.2.a.dc	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{10}) \)	None	✓	✓			9600.2.a.ch	$1$	$0$	\(0\)	\(2\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
9600.2.a.dd	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{6}) \)	None	✓	✓			9600.2.a.cf	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta )q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
9600.2.a.de	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{2}) \)	None	✓	✓			9600.2.a.ce	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta )q^{7}+q^{9}+(2-3\beta )q^{11}+\cdots\)
9600.2.a.df	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{6}) \)	None	✓	✓			9600.2.a.cf	$1$	$1$	\(0\)	\(2\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
9600.2.a.dg	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{17}) \)	None	✓				1920.2.a.y	$1$	$1$	\(0\)	\(2\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{7}+q^{9}-2q^{11}+(-1+\cdots)q^{13}+\cdots\)
9600.2.a.dh	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{2}) \)	None	✓	✓			9600.2.a.ce	$1$	$1$	\(0\)	\(2\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{7}+q^{9}+(-2-3\beta )q^{11}+\cdots\)
9600.2.a.di	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{6}) \)	None	✓	✓			9600.2.a.cg	$1$	$0$	\(0\)	\(2\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{7}+q^{9}+\beta q^{11}+(-1+\cdots)q^{13}+\cdots\)
9600.2.a.dj	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{10}) \)	None	✓	✓			9600.2.a.ch	$1$	$0$	\(0\)	\(2\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{7}+q^{9}-\beta q^{11}-q^{13}+\cdots\)
9600.2.a.dk	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{10}) \)	None	✓	✓			9600.2.a.ch	$1$	$0$	\(0\)	\(2\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{7}+q^{9}+\beta q^{11}+q^{13}+\cdots\)
9600.2.a.dl	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{6}) \)	None	✓	✓			9600.2.a.cg	$1$	$0$	\(0\)	\(2\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{7}+q^{9}-\beta q^{11}+(1+\cdots)q^{13}+\cdots\)
9600.2.a.dm	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{2}) \)	None	✓	✓			9600.2.a.ce	$1$	$0$	\(0\)	\(2\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{7}+q^{9}+(2+3\beta )q^{11}+\cdots\)
9600.2.a.dn	$9600$	$2$	9600.a	1.a	$1$	$2$	$2$	$76.656$	\(\Q(\sqrt{6}) \)	None	✓	✓			9600.2.a.cf	$1$	$0$	\(0\)	\(2\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
9600.2.a.do	$9600$	$2$	9600.a	1.a	$1$	$3$	$3$	$76.656$	3.3.148.1	None	✓		✓		1920.2.f.m	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta _{1})q^{7}+q^{9}+(-2-\beta _{2})q^{11}+\cdots\)
9600.2.a.dp	$9600$	$2$	9600.a	1.a	$1$	$3$	$3$	$76.656$	3.3.148.1	None	✓				1920.2.f.m	$1$	$0$	\(0\)	\(-3\)	\(0\)	\(-4\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta _{1})q^{7}+q^{9}+(2+\beta _{2})q^{11}+\cdots\)
9600.2.a.dq	$9600$	$2$	9600.a	1.a	$1$	$3$	$3$	$76.656$	3.3.148.1	None	✓				1920.2.f.m	$1$	$0$	\(0\)	\(-3\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{1})q^{7}+q^{9}+(-2-\beta _{2})q^{11}+\cdots\)
9600.2.a.dr	$9600$	$2$	9600.a	1.a	$1$	$3$	$3$	$76.656$	3.3.148.1	None	✓				1920.2.f.m	$1$	$0$	\(0\)	\(-3\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{1})q^{7}+q^{9}+(2+\beta _{2})q^{11}+\cdots\)
9600.2.a.ds	$9600$	$2$	9600.a	1.a	$1$	$3$	$3$	$76.656$	3.3.148.1	None	✓				1920.2.f.m	$1$	$0$	\(0\)	\(3\)	\(0\)	\(-4\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta _{1})q^{7}+q^{9}+(-2-\beta _{2})q^{11}+\cdots\)
9600.2.a.dt	$9600$	$2$	9600.a	1.a	$1$	$3$	$3$	$76.656$	3.3.148.1	None	✓				1920.2.f.m	$1$	$0$	\(0\)	\(3\)	\(0\)	\(-4\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta _{1})q^{7}+q^{9}+(2+\beta _{2})q^{11}+\cdots\)
9600.2.a.du	$9600$	$2$	9600.a	1.a	$1$	$3$	$3$	$76.656$	3.3.148.1	None	✓		✓		1920.2.f.m	$1$	$1$	\(0\)	\(3\)	\(0\)	\(4\)		$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-\beta _{1})q^{7}+q^{9}+(-2-\beta _{2})q^{11}+\cdots\)
9600.2.a.dv	$9600$	$2$	9600.a	1.a	$1$	$3$	$3$	$76.656$	3.3.148.1	None	✓				1920.2.f.m	$1$	$0$	\(0\)	\(3\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-\beta _{1})q^{7}+q^{9}+(2+\beta _{2})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9600))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9600)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(300))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(384))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(400))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(480))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(600))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(640))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(800))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(960))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1600))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1920))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2400))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4800))\)\(^{\oplus 2}\)