Space of modular forms of level 9792, weight 2, and trivial character

• Label: 9792.2.a
• Level: $9792$
• Weight: $2$
• Character orbit: 9792.a
• Rep. character: $\chi_{9792}(1,\cdot)$
• Character field: $\Q$
• Dimension: $160$
• Newform subspaces: $96$
• Sturm bound: $3456$
• Trace bound: $29$

Defining parameters

Level:	\( N \)	\(=\)	\( 9792 = 2^{6} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9792.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 96 \)
Sturm bound:			\(3456\)
Trace bound:			\(29\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(13\), \(19\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9792))\).

	Total	New	Old
Modular forms	1776	160	1616
Cusp forms	1681	160	1521
Eisenstein series	95	0	95

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

\(2\)	\(3\)	\(17\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(212\)	\(16\)	\(196\)		\(201\)	\(16\)	\(185\)		\(11\)	\(0\)	\(11\)
\(+\)	\(+\)	\(-\)	\(-\)		\(228\)	\(16\)	\(212\)		\(216\)	\(16\)	\(200\)		\(12\)	\(0\)	\(12\)
\(+\)	\(-\)	\(+\)	\(-\)		\(224\)	\(26\)	\(198\)		\(212\)	\(26\)	\(186\)		\(12\)	\(0\)	\(12\)
\(+\)	\(-\)	\(-\)	\(+\)		\(224\)	\(22\)	\(202\)		\(212\)	\(22\)	\(190\)		\(12\)	\(0\)	\(12\)
\(-\)	\(+\)	\(+\)	\(-\)		\(232\)	\(16\)	\(216\)		\(220\)	\(16\)	\(204\)		\(12\)	\(0\)	\(12\)
\(-\)	\(+\)	\(-\)	\(+\)		\(216\)	\(16\)	\(200\)		\(204\)	\(16\)	\(188\)		\(12\)	\(0\)	\(12\)
\(-\)	\(-\)	\(+\)	\(+\)		\(220\)	\(22\)	\(198\)		\(208\)	\(22\)	\(186\)		\(12\)	\(0\)	\(12\)
\(-\)	\(-\)	\(-\)	\(-\)		\(220\)	\(26\)	\(194\)		\(208\)	\(26\)	\(182\)		\(12\)	\(0\)	\(12\)
Plus space			\(+\)		\(872\)	\(76\)	\(796\)		\(825\)	\(76\)	\(749\)		\(47\)	\(0\)	\(47\)
Minus space			\(-\)		\(904\)	\(84\)	\(820\)		\(856\)	\(84\)	\(772\)		\(48\)	\(0\)	\(48\)

Trace form

\( 160 q - 16 q^{13} + 160 q^{25} - 16 q^{29} - 32 q^{37} + 160 q^{49} - 64 q^{53} - 16 q^{61} - 16 q^{77} + 32 q^{89} + 32 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9792))\) 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	17
9792.2.a.a	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				102.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}-2q^{7}+6q^{13}+q^{17}-4q^{19}+\cdots\)
9792.2.a.b	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				102.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}+2q^{7}+6q^{13}+q^{17}+4q^{19}+\cdots\)
9792.2.a.c	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				408.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-4q^{7}+q^{11}+5q^{13}-q^{17}+\cdots\)
9792.2.a.d	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				1632.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-2q^{7}+3q^{11}-3q^{13}+q^{17}+\cdots\)
9792.2.a.e	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				612.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-2q^{7}+3q^{11}+q^{13}-q^{17}+\cdots\)
9792.2.a.f	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				1632.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+2q^{7}-3q^{11}-3q^{13}+q^{17}+\cdots\)
9792.2.a.g	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				612.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+2q^{7}-3q^{11}+q^{13}-q^{17}+\cdots\)
9792.2.a.h	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				408.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+4q^{7}-q^{11}+5q^{13}-q^{17}+\cdots\)
9792.2.a.i	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				17.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-4q^{7}+2q^{13}-q^{17}-4q^{19}+\cdots\)
9792.2.a.j	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				136.2.a.a	$1$	$2$	\(0\)	\(0\)	\(-2\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-2q^{7}-6q^{11}-2q^{13}-q^{17}+\cdots\)
9792.2.a.k	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				102.2.a.c	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-4q^{11}+2q^{13}-q^{17}-4q^{19}+\cdots\)
9792.2.a.l	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				102.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+4q^{11}+2q^{13}-q^{17}+4q^{19}+\cdots\)
9792.2.a.m	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				136.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+2q^{7}+6q^{11}-2q^{13}-q^{17}+\cdots\)
9792.2.a.n	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				17.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+4q^{7}+2q^{13}-q^{17}+4q^{19}+\cdots\)
9792.2.a.o	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				204.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-4q^{7}-3q^{11}-3q^{13}+q^{17}+\cdots\)
9792.2.a.p	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				153.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}-3q^{11}+5q^{13}+q^{17}+\cdots\)
9792.2.a.q	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				1632.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}-q^{11}+q^{13}-q^{17}+\cdots\)
9792.2.a.r	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				1224.2.a.c	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}+3q^{11}+q^{13}+q^{17}+\cdots\)
9792.2.a.s	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				1632.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}+5q^{11}+5q^{13}-q^{17}+\cdots\)
9792.2.a.t	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				1632.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-5q^{11}+5q^{13}-q^{17}+\cdots\)
9792.2.a.u	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				1224.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-3q^{11}+q^{13}+q^{17}+\cdots\)
9792.2.a.v	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				1632.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}+q^{11}+q^{13}-q^{17}+\cdots\)
9792.2.a.w	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				153.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}+3q^{11}+5q^{13}+q^{17}+\cdots\)
9792.2.a.x	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				204.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{7}+3q^{11}-3q^{13}+q^{17}+\cdots\)
9792.2.a.y	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				34.2.a.a	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}+6q^{11}-2q^{13}+q^{17}+4q^{19}+\cdots\)
9792.2.a.z	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				544.2.a.c	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-4q^{11}-2q^{13}+q^{17}+4q^{19}+\cdots\)
9792.2.a.ba	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				102.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-2q^{13}+q^{17}-4q^{19}-6q^{23}+\cdots\)
9792.2.a.bb	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				408.2.a.c	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-2q^{13}+q^{17}+4q^{19}+2q^{23}+\cdots\)
9792.2.a.bc	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				1632.2.a.d	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+6q^{13}+q^{17}-4q^{19}+6q^{23}+\cdots\)
9792.2.a.bd	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				136.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{11}+6q^{13}+q^{17}+4q^{19}+4q^{23}+\cdots\)
9792.2.a.be	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				136.2.a.b	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{11}+6q^{13}+q^{17}-4q^{19}-4q^{23}+\cdots\)
9792.2.a.bf	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				408.2.a.c	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-2q^{13}+q^{17}-4q^{19}-2q^{23}+\cdots\)
9792.2.a.bg	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				102.2.a.b	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-2q^{13}+q^{17}+4q^{19}+6q^{23}+\cdots\)
9792.2.a.bh	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				1632.2.a.d	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}+6q^{13}+q^{17}+4q^{19}-6q^{23}+\cdots\)
9792.2.a.bi	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				544.2.a.c	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}+4q^{11}-2q^{13}+q^{17}-4q^{19}+\cdots\)
9792.2.a.bj	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				34.2.a.a	$1$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}-6q^{11}-2q^{13}+q^{17}-4q^{19}+\cdots\)
9792.2.a.bk	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				1632.2.a.e	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-5q^{11}+q^{13}+q^{17}+\cdots\)
9792.2.a.bl	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				1224.2.a.c	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-3q^{11}+q^{13}-q^{17}+\cdots\)
9792.2.a.bm	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				153.2.a.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}+3q^{11}+5q^{13}-q^{17}+\cdots\)
9792.2.a.bn	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				204.2.a.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-5q^{11}+5q^{13}-q^{17}+q^{19}+\cdots\)
9792.2.a.bo	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				204.2.a.b	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+5q^{11}+5q^{13}-q^{17}-q^{19}+\cdots\)
9792.2.a.bp	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				153.2.a.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-3q^{11}+5q^{13}-q^{17}+\cdots\)
9792.2.a.bq	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				1224.2.a.c	$1$	$0$	\(0\)	\(0\)	\(1\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}+3q^{11}+q^{13}-q^{17}+\cdots\)
9792.2.a.br	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				1632.2.a.e	$1$	$0$	\(0\)	\(0\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}+5q^{11}+q^{13}+q^{17}+\cdots\)
9792.2.a.bs	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				408.2.a.d	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-4q^{7}+4q^{11}-6q^{13}-q^{17}+\cdots\)
9792.2.a.bt	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				544.2.a.a	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-2q^{7}+2q^{11}-2q^{13}-q^{17}+\cdots\)
9792.2.a.bu	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				1632.2.a.f	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-4q^{11}+2q^{13}-q^{17}+8q^{23}+\cdots\)
9792.2.a.bv	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				1632.2.a.f	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+4q^{11}+2q^{13}-q^{17}-8q^{23}+\cdots\)
9792.2.a.bw	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				544.2.a.a	$1$	$1$	\(0\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+2q^{7}-2q^{11}-2q^{13}-q^{17}+\cdots\)
9792.2.a.bx	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				408.2.a.d	$1$	$1$	\(0\)	\(0\)	\(2\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+4q^{7}-4q^{11}-6q^{13}-q^{17}+\cdots\)
9792.2.a.by	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				51.2.a.a	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-4q^{7}-3q^{11}+q^{13}+q^{17}+\cdots\)
9792.2.a.bz	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				612.2.a.a	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-2q^{7}-3q^{11}+q^{13}+q^{17}+\cdots\)
9792.2.a.ca	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				408.2.a.a	$1$	$1$	\(0\)	\(0\)	\(3\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-q^{11}-3q^{13}+q^{17}-q^{19}+\cdots\)
9792.2.a.cb	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				408.2.a.a	$1$	$0$	\(0\)	\(0\)	\(3\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+q^{11}-3q^{13}+q^{17}+q^{19}+\cdots\)
9792.2.a.cc	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				612.2.a.a	$1$	$0$	\(0\)	\(0\)	\(3\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+2q^{7}+3q^{11}+q^{13}+q^{17}+\cdots\)
9792.2.a.cd	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				51.2.a.a	$1$	$0$	\(0\)	\(0\)	\(3\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+4q^{7}+3q^{11}+q^{13}+q^{17}+\cdots\)
9792.2.a.ce	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				544.2.a.b	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}-4q^{7}+2q^{11}-2q^{13}+q^{17}+\cdots\)
9792.2.a.cf	$9792$	$2$	9792.a	1.a	$1$	$1$	$1$	$78.190$	\(\Q\)	None	✓				544.2.a.b	$1$	$0$	\(0\)	\(0\)	\(4\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}+4q^{7}-2q^{11}-2q^{13}+q^{17}+\cdots\)
9792.2.a.cg	$9792$	$2$	9792.a	1.a	$1$	$2$	$2$	$78.190$	\(\Q(\sqrt{2}) \)	None	✓				544.2.a.g	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-3\beta q^{7}+\beta q^{11}+4q^{13}+q^{17}+\cdots\)
9792.2.a.ch	$9792$	$2$	9792.a	1.a	$1$	$2$	$2$	$78.190$	\(\Q(\sqrt{10}) \)	None	✓				544.2.a.h	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-\beta q^{7}-\beta q^{11}+4q^{13}+q^{17}+\cdots\)
9792.2.a.ci	$9792$	$2$	9792.a	1.a	$1$	$2$	$2$	$78.190$	\(\Q(\sqrt{17}) \)	None	✓				1632.2.a.m	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{5}+(-2+2\beta )q^{7}+(1-\beta )q^{11}+\cdots\)
9792.2.a.cj	$9792$	$2$	9792.a	1.a	$1$	$2$	$2$	$78.190$	\(\Q(\sqrt{17}) \)	None	✓				1632.2.a.m	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{5}+(2-2\beta )q^{7}+(-1+\beta )q^{11}+\cdots\)
9792.2.a.ck	$9792$	$2$	9792.a	1.a	$1$	$2$	$2$	$78.190$	\(\Q(\sqrt{5}) \)	None	✓				4896.2.a.s	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}+\beta q^{11}+q^{13}-q^{17}+\beta q^{19}+\cdots\)
9792.2.a.cl	$9792$	$2$	9792.a	1.a	$1$	$2$	$2$	$78.190$	\(\Q(\sqrt{57}) \)	None	✓				408.2.a.f	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-8\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{5}-4q^{7}+(2-\beta )q^{11}-\beta q^{13}+\cdots\)
9792.2.a.cm	$9792$	$2$	9792.a	1.a	$1$	$2$	$2$	$78.190$	\(\Q(\sqrt{17}) \)	None	✓				408.2.a.e	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{5}+(-2+2\beta )q^{7}+(-4-\beta )q^{11}+\cdots\)
9792.2.a.cn	$9792$	$2$	9792.a	1.a	$1$	$2$	$2$	$78.190$	\(\Q(\sqrt{17}) \)	None	✓				408.2.a.e	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{5}+(2-2\beta )q^{7}+(4+\beta )q^{11}+(2+\cdots)q^{13}+\cdots\)
9792.2.a.co	$9792$	$2$	9792.a	1.a	$1$	$2$	$2$	$78.190$	\(\Q(\sqrt{57}) \)	None	✓				408.2.a.f	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(8\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{5}+4q^{7}+(-2+\beta )q^{11}-\beta q^{13}+\cdots\)
9792.2.a.cp	$9792$	$2$	9792.a	1.a	$1$	$2$	$2$	$78.190$	\(\Q(\sqrt{6}) \)	None	✓				306.2.a.e	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(-2-\beta )q^{7}+2\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
9792.2.a.cq	$9792$	$2$	9792.a	1.a	$1$	$2$	$2$	$78.190$	\(\Q(\sqrt{6}) \)	None	✓				306.2.a.e	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(-2+\beta )q^{7}+2\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
9792.2.a.cr	$9792$	$2$	9792.a	1.a	$1$	$2$	$2$	$78.190$	\(\Q(\sqrt{3}) \)	None	✓				68.2.a.a	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2\beta q^{5}+(-1+\beta )q^{7}+(-3-\beta )q^{11}+\cdots\)
9792.2.a.cs	$9792$	$2$	9792.a	1.a	$1$	$2$	$2$	$78.190$	\(\Q(\sqrt{3}) \)	None	✓				68.2.a.a	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2\beta q^{5}+(1-\beta )q^{7}+(3+\beta )q^{11}+(-2+\cdots)q^{13}+\cdots\)
9792.2.a.ct	$9792$	$2$	9792.a	1.a	$1$	$2$	$2$	$78.190$	\(\Q(\sqrt{6}) \)	None	✓				306.2.a.e	$1$	$1$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(2+\beta )q^{7}-2\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
9792.2.a.cu	$9792$	$2$	9792.a	1.a	$1$	$2$	$2$	$78.190$	\(\Q(\sqrt{6}) \)	None	✓				306.2.a.e	$1$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(2-\beta )q^{7}-2\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
9792.2.a.cv	$9792$	$2$	9792.a	1.a	$1$	$2$	$2$	$78.190$	\(\Q(\sqrt{33}) \)	None	✓				1632.2.a.n	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-2q^{7}+\beta q^{11}+(-2-\beta )q^{13}+\cdots\)
9792.2.a.cw	$9792$	$2$	9792.a	1.a	$1$	$2$	$2$	$78.190$	\(\Q(\sqrt{33}) \)	None	✓				1632.2.a.n	$1$	$1$	\(0\)	\(0\)	\(1\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+2q^{7}-\beta q^{11}+(-2-\beta )q^{13}+\cdots\)
9792.2.a.cx	$9792$	$2$	9792.a	1.a	$1$	$2$	$2$	$78.190$	\(\Q(\sqrt{5}) \)	None	✓				4896.2.a.s	$2$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{5}+\beta q^{11}+q^{13}+q^{17}-\beta q^{19}+\cdots\)
9792.2.a.cy	$9792$	$2$	9792.a	1.a	$1$	$2$	$2$	$78.190$	\(\Q(\sqrt{17}) \)	None	✓				51.2.a.b	$1$	$0$	\(0\)	\(0\)	\(3\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}+(-1+\beta )q^{11}+(-3+\beta )q^{13}+\cdots\)
9792.2.a.cz	$9792$	$2$	9792.a	1.a	$1$	$2$	$2$	$78.190$	\(\Q(\sqrt{17}) \)	None	✓				51.2.a.b	$1$	$1$	\(0\)	\(0\)	\(3\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}+(1-\beta )q^{11}+(-3+\beta )q^{13}+\cdots\)
9792.2.a.da	$9792$	$2$	9792.a	1.a	$1$	$2$	$2$	$78.190$	\(\Q(\sqrt{5}) \)	None	✓				136.2.a.c	$1$	$1$	\(0\)	\(0\)	\(4\)	\(-2\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+2q^{5}+(-1-\beta )q^{7}+(-1-\beta )q^{11}+\cdots\)
9792.2.a.db	$9792$	$2$	9792.a	1.a	$1$	$2$	$2$	$78.190$	\(\Q(\sqrt{5}) \)	None	✓				136.2.a.c	$1$	$0$	\(0\)	\(0\)	\(4\)	\(2\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+2q^{5}+(1-\beta )q^{7}+(1-\beta )q^{11}-2\beta q^{13}+\cdots\)
9792.2.a.dc	$9792$	$2$	9792.a	1.a	$1$	$3$	$3$	$78.190$	3.3.148.1	None	✓				544.2.a.i	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-2\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{2})q^{5}+(-1+\beta _{2})q^{7}+(-3+\cdots)q^{11}+\cdots\)
9792.2.a.dd	$9792$	$2$	9792.a	1.a	$1$	$3$	$3$	$78.190$	3.3.148.1	None	✓				544.2.a.i	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{2})q^{5}+(1-\beta _{2})q^{7}+(3+\beta _{1}+\cdots)q^{11}+\cdots\)
9792.2.a.de	$9792$	$2$	9792.a	1.a	$1$	$3$	$3$	$78.190$	3.3.1304.1	None	✓				1224.2.a.l	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{2})q^{5}+(-1-\beta _{2})q^{7}+(-1+\cdots)q^{11}+\cdots\)
9792.2.a.df	$9792$	$2$	9792.a	1.a	$1$	$3$	$3$	$78.190$	3.3.1304.1	None	✓				1224.2.a.l	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{2})q^{5}+(1+\beta _{2})q^{7}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
9792.2.a.dg	$9792$	$2$	9792.a	1.a	$1$	$3$	$3$	$78.190$	3.3.229.1	None	✓				1632.2.a.q	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-6\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{5}-2q^{7}+(1+\beta _{1}+\beta _{2})q^{11}+\cdots\)
9792.2.a.dh	$9792$	$2$	9792.a	1.a	$1$	$3$	$3$	$78.190$	3.3.1304.1	None	✓				1224.2.a.l	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{2})q^{5}+(-1-\beta _{2})q^{7}+(1+\cdots)q^{11}+\cdots\)
9792.2.a.di	$9792$	$2$	9792.a	1.a	$1$	$3$	$3$	$78.190$	3.3.1304.1	None	✓				1224.2.a.l	$1$	$1$	\(0\)	\(0\)	\(1\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{2})q^{5}+(1+\beta _{2})q^{7}+(-1+\cdots)q^{11}+\cdots\)
9792.2.a.dj	$9792$	$2$	9792.a	1.a	$1$	$3$	$3$	$78.190$	3.3.229.1	None	✓				1632.2.a.q	$1$	$0$	\(0\)	\(0\)	\(1\)	\(6\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{5}+2q^{7}+(-1-\beta _{1}-\beta _{2})q^{11}+\cdots\)
9792.2.a.dk	$9792$	$2$	9792.a	1.a	$1$	$3$	$3$	$78.190$	3.3.316.1	None	✓				1632.2.a.r	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-2\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{5}+(-1-\beta _{1}-\beta _{2})q^{7}+\cdots\)
9792.2.a.dl	$9792$	$2$	9792.a	1.a	$1$	$3$	$3$	$78.190$	3.3.316.1	None	✓				1632.2.a.r	$1$	$0$	\(0\)	\(0\)	\(3\)	\(2\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{5}+(1+\beta _{1}+\beta _{2})q^{7}+\beta _{2}q^{11}+\cdots\)
9792.2.a.dm	$9792$	$2$	9792.a	1.a	$1$	$4$	$4$	$78.190$	4.4.13768.1	None	✓				4896.2.a.bg	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-4\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{5}+(-1+\beta _{1})q^{7}+(1+\cdots)q^{11}+\cdots\)
9792.2.a.dn	$9792$	$2$	9792.a	1.a	$1$	$4$	$4$	$78.190$	4.4.13768.1	None	✓				4896.2.a.bg	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(4\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{5}+(1-\beta _{1})q^{7}+(-1+\cdots)q^{11}+\cdots\)
9792.2.a.do	$9792$	$2$	9792.a	1.a	$1$	$4$	$4$	$78.190$	4.4.13768.1	None	✓				4896.2.a.bg	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-4\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{5}+(-1+\beta _{1})q^{7}+(-1+\cdots)q^{11}+\cdots\)
9792.2.a.dp	$9792$	$2$	9792.a	1.a	$1$	$4$	$4$	$78.190$	4.4.13768.1	None	✓				4896.2.a.bg	$1$	$0$	\(0\)	\(0\)	\(2\)	\(4\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{5}+(1-\beta _{1})q^{7}+(1+\beta _{2}+\cdots)q^{11}+\cdots\)
9792.2.a.dq	$9792$	$2$	9792.a	1.a	$1$	$6$	$6$	$78.190$	6.6.102503232.1	None	✓		✓		4896.2.a.bk	$2$	$1$	\(0\)	\(0\)	\(-6\)	\(0\)		$-$	$+$	$-$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{3})q^{5}+\beta _{2}q^{7}+\beta _{5}q^{11}+\cdots\)
9792.2.a.dr	$9792$	$2$	9792.a	1.a	$1$	$6$	$6$	$78.190$	6.6.102503232.1	None	✓		✓		4896.2.a.bk	$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$-$	$+$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{3})q^{5}-\beta _{2}q^{7}+\beta _{5}q^{11}+(-1+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9792))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9792)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 21}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(153))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(204))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(272))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(306))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(408))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(544))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(576))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(612))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(816))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1088))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1632))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2448))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3264))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4896))\)\(^{\oplus 2}\)