Space of modular forms of level 7872, weight 2, and trivial character

• Label: 7872.2.a
• Level: $7872$
• Weight: $2$
• Character orbit: 7872.a
• Rep. character: $\chi_{7872}(1,\cdot)$
• Character field: $\Q$
• Dimension: $160$
• Newform subspaces: $70$
• Sturm bound: $2688$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 7872 = 2^{6} \cdot 3 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7872.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 70 \)
Sturm bound:			\(2688\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7872))\).

	Total	New	Old
Modular forms	1368	160	1208
Cusp forms	1321	160	1161
Eisenstein series	47	0	47

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

\(2\)	\(3\)	\(41\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(160\)	\(19\)	\(141\)		\(155\)	\(19\)	\(136\)		\(5\)	\(0\)	\(5\)
\(+\)	\(+\)	\(-\)	\(-\)		\(182\)	\(22\)	\(160\)		\(176\)	\(22\)	\(154\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)		\(166\)	\(21\)	\(145\)		\(160\)	\(21\)	\(139\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)		\(176\)	\(18\)	\(158\)		\(170\)	\(18\)	\(152\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)		\(182\)	\(21\)	\(161\)		\(176\)	\(21\)	\(155\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)		\(160\)	\(18\)	\(142\)		\(154\)	\(18\)	\(136\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)		\(176\)	\(19\)	\(157\)		\(170\)	\(19\)	\(151\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)		\(166\)	\(22\)	\(144\)		\(160\)	\(22\)	\(138\)		\(6\)	\(0\)	\(6\)
Plus space			\(+\)		\(672\)	\(74\)	\(598\)		\(649\)	\(74\)	\(575\)		\(23\)	\(0\)	\(23\)
Minus space			\(-\)		\(696\)	\(86\)	\(610\)		\(672\)	\(86\)	\(586\)		\(24\)	\(0\)	\(24\)

Trace form

\( 160 q + 160 q^{9} - 16 q^{13} - 16 q^{21} + 160 q^{25} + 32 q^{29} + 16 q^{37} + 160 q^{49} + 32 q^{53} + 16 q^{61} + 32 q^{69} - 64 q^{77} + 160 q^{81} - 64 q^{85} - 16 q^{93} + 32 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7872))\) 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	41
7872.2.a.a	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				246.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+2q^{7}+q^{9}+2q^{11}+\cdots\)
7872.2.a.b	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				246.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+2q^{7}+q^{9}+6q^{11}+\cdots\)
7872.2.a.c	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				984.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}-4q^{7}+q^{9}+5q^{11}+\cdots\)
7872.2.a.d	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				3936.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+2q^{7}+q^{9}-4q^{11}+\cdots\)
7872.2.a.e	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				246.2.a.g	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{7}+q^{9}-2q^{11}+q^{13}+\cdots\)
7872.2.a.f	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				246.2.a.e	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{7}+q^{9}+2q^{11}+7q^{13}+\cdots\)
7872.2.a.g	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				3936.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+2q^{7}+q^{9}+2q^{11}+5q^{13}+\cdots\)
7872.2.a.h	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				984.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{7}+q^{9}+3q^{11}+6q^{13}+\cdots\)
7872.2.a.i	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				492.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
7872.2.a.j	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				984.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+2q^{7}+q^{9}+2q^{11}+3q^{13}+\cdots\)
7872.2.a.k	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				3936.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
7872.2.a.l	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				492.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-4q^{7}+q^{9}+5q^{11}+\cdots\)
7872.2.a.m	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				246.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots\)
7872.2.a.n	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				984.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{9}+q^{11}-4q^{13}+\cdots\)
7872.2.a.o	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				246.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+2q^{7}+q^{9}-4q^{11}+\cdots\)
7872.2.a.p	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				246.2.a.f	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots\)
7872.2.a.q	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				123.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+4q^{7}+q^{9}+5q^{11}+\cdots\)
7872.2.a.r	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				123.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}-2q^{7}+q^{9}+3q^{11}+\cdots\)
7872.2.a.s	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				246.2.a.d	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}-2q^{7}+q^{9}-6q^{11}+\cdots\)
7872.2.a.t	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				246.2.a.b	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}-2q^{7}+q^{9}-2q^{11}+\cdots\)
7872.2.a.u	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				3936.2.a.c	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-2q^{7}+q^{9}+4q^{11}+\cdots\)
7872.2.a.v	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				984.2.a.c	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+4q^{7}+q^{9}-5q^{11}+\cdots\)
7872.2.a.w	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				3936.2.a.b	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{7}+q^{9}-2q^{11}+5q^{13}+\cdots\)
7872.2.a.x	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				246.2.a.e	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+2q^{7}+q^{9}-2q^{11}+7q^{13}+\cdots\)
7872.2.a.y	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				246.2.a.g	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+2q^{7}+q^{9}+2q^{11}+q^{13}+\cdots\)
7872.2.a.z	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				492.2.a.a	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
7872.2.a.ba	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				984.2.a.d	$1$	$1$	\(0\)	\(1\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{7}+q^{9}-3q^{11}+6q^{13}+\cdots\)
7872.2.a.bb	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				984.2.a.b	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{7}+q^{9}-2q^{11}+3q^{13}+\cdots\)
7872.2.a.bc	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				123.2.a.b	$1$	$0$	\(0\)	\(1\)	\(2\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-4q^{7}+q^{9}-5q^{11}+\cdots\)
7872.2.a.bd	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				246.2.a.f	$1$	$0$	\(0\)	\(1\)	\(2\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
7872.2.a.be	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				246.2.a.c	$1$	$1$	\(0\)	\(1\)	\(2\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-2q^{7}+q^{9}+4q^{11}+\cdots\)
7872.2.a.bf	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				984.2.a.a	$1$	$1$	\(0\)	\(1\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}-q^{11}-4q^{13}+\cdots\)
7872.2.a.bg	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				246.2.a.a	$1$	$0$	\(0\)	\(1\)	\(2\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots\)
7872.2.a.bh	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				492.2.a.b	$1$	$1$	\(0\)	\(1\)	\(2\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+4q^{7}+q^{9}-5q^{11}+\cdots\)
7872.2.a.bi	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				3936.2.a.a	$1$	$0$	\(0\)	\(1\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots\)
7872.2.a.bj	$7872$	$2$	7872.a	1.a	$1$	$1$	$1$	$62.858$	\(\Q\)	None	✓				123.2.a.a	$1$	$0$	\(0\)	\(1\)	\(4\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{5}+2q^{7}+q^{9}-3q^{11}+\cdots\)
7872.2.a.bk	$7872$	$2$	7872.a	1.a	$1$	$2$	$2$	$62.858$	\(\Q(\sqrt{2}) \)	None	✓				123.2.a.c	$1$	$1$	\(0\)	\(-2\)	\(-4\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-2+\beta )q^{5}+(-2+\beta )q^{7}+\cdots\)
7872.2.a.bl	$7872$	$2$	7872.a	1.a	$1$	$2$	$2$	$62.858$	\(\Q(\sqrt{3}) \)	None	✓				492.2.a.d	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta )q^{5}+(1-\beta )q^{7}+q^{9}+\cdots\)
7872.2.a.bm	$7872$	$2$	7872.a	1.a	$1$	$2$	$2$	$62.858$	\(\Q(\sqrt{6}) \)	None	✓				492.2.a.c	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(2+\beta )q^{5}+(-2+\beta )q^{7}+q^{9}+\cdots\)
7872.2.a.bn	$7872$	$2$	7872.a	1.a	$1$	$2$	$2$	$62.858$	\(\Q(\sqrt{2}) \)	None	✓				984.2.a.e	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(2+\beta )q^{5}+(-2+\beta )q^{7}+q^{9}+\cdots\)
7872.2.a.bo	$7872$	$2$	7872.a	1.a	$1$	$2$	$2$	$62.858$	\(\Q(\sqrt{2}) \)	None	✓				123.2.a.c	$1$	$1$	\(0\)	\(2\)	\(-4\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-2+\beta )q^{5}+(2-\beta )q^{7}+q^{9}+\cdots\)
7872.2.a.bp	$7872$	$2$	7872.a	1.a	$1$	$2$	$2$	$62.858$	\(\Q(\sqrt{3}) \)	None	✓				492.2.a.d	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
7872.2.a.bq	$7872$	$2$	7872.a	1.a	$1$	$2$	$2$	$62.858$	\(\Q(\sqrt{6}) \)	None	✓				492.2.a.c	$1$	$0$	\(0\)	\(2\)	\(4\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(2+\beta )q^{5}+(2-\beta )q^{7}+q^{9}+\cdots\)
7872.2.a.br	$7872$	$2$	7872.a	1.a	$1$	$2$	$2$	$62.858$	\(\Q(\sqrt{2}) \)	None	✓				984.2.a.e	$1$	$0$	\(0\)	\(2\)	\(4\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(2+\beta )q^{5}+(2-\beta )q^{7}+q^{9}+\cdots\)
7872.2.a.bs	$7872$	$2$	7872.a	1.a	$1$	$3$	$3$	$62.858$	3.3.316.1	None	✓				123.2.a.d	$1$	$1$	\(0\)	\(-3\)	\(-4\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta _{1}+\beta _{2})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
7872.2.a.bt	$7872$	$2$	7872.a	1.a	$1$	$3$	$3$	$62.858$	3.3.1436.1	None	✓				984.2.a.g	$1$	$0$	\(0\)	\(-3\)	\(-3\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta _{1})q^{5}+(1+\beta _{1}+\beta _{2})q^{7}+\cdots\)
7872.2.a.bu	$7872$	$2$	7872.a	1.a	$1$	$3$	$3$	$62.858$	3.3.961.1	None	✓				984.2.a.h	$1$	$1$	\(0\)	\(-3\)	\(-1\)	\(6\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{1}q^{5}+2q^{7}+q^{9}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
7872.2.a.bv	$7872$	$2$	7872.a	1.a	$1$	$3$	$3$	$62.858$	3.3.892.1	None	✓				984.2.a.f	$1$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{2}q^{5}-\beta _{2}q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
7872.2.a.bw	$7872$	$2$	7872.a	1.a	$1$	$3$	$3$	$62.858$	3.3.148.1	None	✓				3936.2.a.g	$1$	$0$	\(0\)	\(-3\)	\(2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{1})q^{5}-\beta _{2}q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
7872.2.a.bx	$7872$	$2$	7872.a	1.a	$1$	$3$	$3$	$62.858$	3.3.316.1	None	✓				123.2.a.d	$1$	$1$	\(0\)	\(3\)	\(-4\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta _{1}+\beta _{2})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
7872.2.a.by	$7872$	$2$	7872.a	1.a	$1$	$3$	$3$	$62.858$	3.3.1436.1	None	✓				984.2.a.g	$1$	$0$	\(0\)	\(3\)	\(-3\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta _{1})q^{5}+(-1-\beta _{1}-\beta _{2})q^{7}+\cdots\)
7872.2.a.bz	$7872$	$2$	7872.a	1.a	$1$	$3$	$3$	$62.858$	3.3.961.1	None	✓				984.2.a.h	$1$	$1$	\(0\)	\(3\)	\(-1\)	\(-6\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{1}q^{5}-2q^{7}+q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
7872.2.a.ca	$7872$	$2$	7872.a	1.a	$1$	$3$	$3$	$62.858$	3.3.892.1	None	✓				984.2.a.f	$1$	$0$	\(0\)	\(3\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{2}q^{5}+\beta _{2}q^{7}+q^{9}+(3-\beta _{1}+\cdots)q^{11}+\cdots\)
7872.2.a.cb	$7872$	$2$	7872.a	1.a	$1$	$3$	$3$	$62.858$	3.3.148.1	None	✓				3936.2.a.g	$1$	$1$	\(0\)	\(3\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-\beta _{1})q^{5}+\beta _{2}q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
7872.2.a.cc	$7872$	$2$	7872.a	1.a	$1$	$4$	$4$	$62.858$	4.4.8468.1	None	✓				3936.2.a.l	$1$	$0$	\(0\)	\(-4\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{3}q^{5}+(-\beta _{2}+\beta _{3})q^{7}+q^{9}+\cdots\)
7872.2.a.cd	$7872$	$2$	7872.a	1.a	$1$	$4$	$4$	$62.858$	4.4.17428.1	None	✓				3936.2.a.k	$1$	$1$	\(0\)	\(-4\)	\(1\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{1}q^{5}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots\)
7872.2.a.ce	$7872$	$2$	7872.a	1.a	$1$	$4$	$4$	$62.858$	4.4.202932.1	None	✓				3936.2.a.j	$1$	$1$	\(0\)	\(-4\)	\(2\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta _{2})q^{5}+(1-\beta _{1})q^{7}+q^{9}+\cdots\)
7872.2.a.cf	$7872$	$2$	7872.a	1.a	$1$	$4$	$4$	$62.858$	4.4.15188.1	None	✓				3936.2.a.i	$1$	$1$	\(0\)	\(-4\)	\(4\)	\(-6\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta _{3})q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
7872.2.a.cg	$7872$	$2$	7872.a	1.a	$1$	$4$	$4$	$62.858$	4.4.8468.1	None	✓				3936.2.a.l	$1$	$1$	\(0\)	\(4\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{3}q^{5}+(\beta _{2}-\beta _{3})q^{7}+q^{9}+\cdots\)
7872.2.a.ch	$7872$	$2$	7872.a	1.a	$1$	$4$	$4$	$62.858$	4.4.17428.1	None	✓				3936.2.a.k	$1$	$0$	\(0\)	\(4\)	\(1\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+q^{9}+\cdots\)
7872.2.a.ci	$7872$	$2$	7872.a	1.a	$1$	$4$	$4$	$62.858$	4.4.202932.1	None	✓				3936.2.a.j	$1$	$0$	\(0\)	\(4\)	\(2\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta _{2})q^{5}+(-1+\beta _{1})q^{7}+\cdots\)
7872.2.a.cj	$7872$	$2$	7872.a	1.a	$1$	$4$	$4$	$62.858$	4.4.15188.1	None	✓				3936.2.a.i	$1$	$0$	\(0\)	\(4\)	\(4\)	\(6\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta _{3})q^{5}+(1-\beta _{2})q^{7}+q^{9}+\cdots\)
7872.2.a.ck	$7872$	$2$	7872.a	1.a	$1$	$5$	$5$	$62.858$	5.5.3858104.1	None	✓				984.2.a.i	$1$	$0$	\(0\)	\(-5\)	\(-1\)	\(2\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{4}q^{5}+\beta _{3}q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
7872.2.a.cl	$7872$	$2$	7872.a	1.a	$1$	$5$	$5$	$62.858$	5.5.6852676.1	None	✓		✓		3936.2.a.q	$1$	$1$	\(0\)	\(-5\)	\(2\)	\(0\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{1}q^{5}-\beta _{4}q^{7}+q^{9}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
7872.2.a.cm	$7872$	$2$	7872.a	1.a	$1$	$5$	$5$	$62.858$	5.5.3858104.1	None	✓		✓		984.2.a.i	$1$	$0$	\(0\)	\(5\)	\(-1\)	\(-2\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{4}q^{5}-\beta _{3}q^{7}+q^{9}+(2+\beta _{2}+\cdots)q^{11}+\cdots\)
7872.2.a.cn	$7872$	$2$	7872.a	1.a	$1$	$5$	$5$	$62.858$	5.5.6852676.1	None	✓		✓		3936.2.a.q	$1$	$0$	\(0\)	\(5\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{5}+\beta _{4}q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
7872.2.a.co	$7872$	$2$	7872.a	1.a	$1$	$6$	$6$	$62.858$	6.6.121506628.1	None	✓		✓		3936.2.a.s	$1$	$0$	\(0\)	\(-6\)	\(-3\)	\(8\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{4}q^{5}+(1-\beta _{3})q^{7}+q^{9}+(\beta _{2}+\cdots)q^{11}+\cdots\)
7872.2.a.cp	$7872$	$2$	7872.a	1.a	$1$	$6$	$6$	$62.858$	6.6.121506628.1	None	✓		✓		3936.2.a.s	$1$	$1$	\(0\)	\(6\)	\(-3\)	\(-8\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{4}q^{5}+(-1+\beta _{3})q^{7}+q^{9}+\cdots\)
7872.2.a.cq	$7872$	$2$	7872.a	1.a	$1$	$7$	$7$	$62.858$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓		✓		3936.2.a.u	$1$	$0$	\(0\)	\(-7\)	\(-6\)	\(8\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta _{1})q^{5}+(1+\beta _{2})q^{7}+\cdots\)
7872.2.a.cr	$7872$	$2$	7872.a	1.a	$1$	$7$	$7$	$62.858$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓		✓		3936.2.a.u	$1$	$1$	\(0\)	\(7\)	\(-6\)	\(-8\)		$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta _{1})q^{5}+(-1-\beta _{2})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7872))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7872)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(82))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(123))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(164))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(246))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(328))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(492))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(656))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(984))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1312))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1968))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2624))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3936))\)\(^{\oplus 2}\)