Space of modular forms of level 10368, weight 2, and trivial character

• Label: 10368.2.a
• Level: $10368$
• Weight: $2$
• Character orbit: 10368.a
• Rep. character: $\chi_{10368}(1,\cdot)$
• Character field: $\Q$
• Dimension: $192$
• Newform subspaces: $64$
• Sturm bound: $3456$

Defining parameters

Level:	\( N \)	\(=\)	\( 10368 = 2^{7} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	10368.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 64 \)
Sturm bound:			\(3456\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(10368))\).

	Total	New	Old
Modular forms	1824	192	1632
Cusp forms	1633	192	1441
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.

\(2\)	\(3\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(448\)	\(46\)	\(402\)		\(401\)	\(46\)	\(355\)		\(47\)	\(0\)	\(47\)
\(+\)	\(-\)	\(-\)		\(460\)	\(50\)	\(410\)		\(412\)	\(50\)	\(362\)		\(48\)	\(0\)	\(48\)
\(-\)	\(+\)	\(-\)		\(464\)	\(50\)	\(414\)		\(416\)	\(50\)	\(366\)		\(48\)	\(0\)	\(48\)
\(-\)	\(-\)	\(+\)		\(452\)	\(46\)	\(406\)		\(404\)	\(46\)	\(358\)		\(48\)	\(0\)	\(48\)
Plus space		\(+\)		\(900\)	\(92\)	\(808\)		\(805\)	\(92\)	\(713\)		\(95\)	\(0\)	\(95\)
Minus space		\(-\)		\(924\)	\(100\)	\(824\)		\(828\)	\(100\)	\(728\)		\(96\)	\(0\)	\(96\)

Trace form

\( 192 q + 192 q^{25} + 192 q^{49}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(10368))\) 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
10368.2.a.a	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-3\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-2q^{7}-4q^{11}-3q^{13}+3q^{17}+\cdots\)
10368.2.a.b	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-3\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-2q^{7}-4q^{11}+3q^{13}-3q^{17}+\cdots\)
10368.2.a.c	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-3\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+2q^{7}+4q^{11}-3q^{13}+3q^{17}+\cdots\)
10368.2.a.d	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-3\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+2q^{7}+4q^{11}+3q^{13}-3q^{17}+\cdots\)
10368.2.a.e	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-2q^{7}-5q^{11}-4q^{13}-q^{17}+\cdots\)
10368.2.a.f	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-2q^{7}-5q^{11}+4q^{13}+q^{17}+\cdots\)
10368.2.a.g	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+2q^{7}+5q^{11}-4q^{13}-q^{17}+\cdots\)
10368.2.a.h	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+2q^{7}+5q^{11}+4q^{13}+q^{17}+\cdots\)
10368.2.a.i	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-4q^{7}-2q^{11}-q^{13}+7q^{17}+\cdots\)
10368.2.a.j	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-4q^{7}-2q^{11}+q^{13}-7q^{17}+\cdots\)
10368.2.a.k	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}-4q^{11}-q^{13}-5q^{17}+\cdots\)
10368.2.a.l	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}-4q^{11}+q^{13}+5q^{17}+\cdots\)
10368.2.a.m	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}+4q^{11}-q^{13}-5q^{17}+\cdots\)
10368.2.a.n	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}+4q^{11}+q^{13}+5q^{17}+\cdots\)
10368.2.a.o	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{7}+2q^{11}-q^{13}+7q^{17}+\cdots\)
10368.2.a.p	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-1\)	\(4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{7}+2q^{11}+q^{13}-7q^{17}+\cdots\)
10368.2.a.q	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{7}+2q^{11}-q^{13}-7q^{17}+\cdots\)
10368.2.a.r	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{7}+2q^{11}+q^{13}+7q^{17}+\cdots\)
10368.2.a.s	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}+4q^{11}-q^{13}+5q^{17}+\cdots\)
10368.2.a.t	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}+4q^{11}+q^{13}-5q^{17}+\cdots\)
10368.2.a.u	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-4q^{11}-q^{13}+5q^{17}+\cdots\)
10368.2.a.v	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-4q^{11}+q^{13}-5q^{17}+\cdots\)
10368.2.a.w	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{7}-2q^{11}-q^{13}-7q^{17}+\cdots\)
10368.2.a.x	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(1\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{7}-2q^{11}+q^{13}+7q^{17}+\cdots\)
10368.2.a.y	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-2q^{7}+5q^{11}-4q^{13}+q^{17}+\cdots\)
10368.2.a.z	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-2q^{7}+5q^{11}+4q^{13}-q^{17}+\cdots\)
10368.2.a.ba	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+2q^{7}-5q^{11}-4q^{13}+q^{17}+\cdots\)
10368.2.a.bb	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+2q^{7}-5q^{11}+4q^{13}-q^{17}+\cdots\)
10368.2.a.bc	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(3\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-2q^{7}+4q^{11}-3q^{13}-3q^{17}+\cdots\)
10368.2.a.bd	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(3\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-2q^{7}+4q^{11}+3q^{13}+3q^{17}+\cdots\)
10368.2.a.be	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(3\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+2q^{7}-4q^{11}-3q^{13}-3q^{17}+\cdots\)
10368.2.a.bf	$10368$	$2$	10368.a	1.a	$1$	$1$	$1$	$82.789$	\(\Q\)	None	✓	?				$-1$		\(0\)	\(0\)	\(3\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+2q^{7}-4q^{11}+3q^{13}+3q^{17}+\cdots\)
10368.2.a.bg	$10368$	$2$	10368.a	1.a	$1$	$3$	$3$	$82.789$	\(\Q(\zeta_{18})^+\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-3\)	\(0\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
10368.2.a.bh	$10368$	$2$	10368.a	1.a	$1$	$3$	$3$	$82.789$	\(\Q(\zeta_{18})^+\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-3\)	\(0\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
10368.2.a.bi	$10368$	$2$	10368.a	1.a	$1$	$3$	$3$	$82.789$	\(\Q(\zeta_{18})^+\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-3\)	\(0\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
10368.2.a.bj	$10368$	$2$	10368.a	1.a	$1$	$3$	$3$	$82.789$	\(\Q(\zeta_{18})^+\)	None	✓	?				$-1$		\(0\)	\(0\)	\(-3\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
10368.2.a.bk	$10368$	$2$	10368.a	1.a	$1$	$3$	$3$	$82.789$	\(\Q(\zeta_{18})^+\)	None	✓	?				$-1$		\(0\)	\(0\)	\(3\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
10368.2.a.bl	$10368$	$2$	10368.a	1.a	$1$	$3$	$3$	$82.789$	\(\Q(\zeta_{18})^+\)	None	✓	?				$-1$		\(0\)	\(0\)	\(3\)	\(0\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
10368.2.a.bm	$10368$	$2$	10368.a	1.a	$1$	$3$	$3$	$82.789$	\(\Q(\zeta_{18})^+\)	None	✓	?				$-1$		\(0\)	\(0\)	\(3\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
10368.2.a.bn	$10368$	$2$	10368.a	1.a	$1$	$3$	$3$	$82.789$	\(\Q(\zeta_{18})^+\)	None	✓	?				$-1$		\(0\)	\(0\)	\(3\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
10368.2.a.bo	$10368$	$2$	10368.a	1.a	$1$	$5$	$5$	$82.789$	5.5.1686096.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
10368.2.a.bp	$10368$	$2$	10368.a	1.a	$1$	$5$	$5$	$82.789$	5.5.1686096.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
10368.2.a.bq	$10368$	$2$	10368.a	1.a	$1$	$5$	$5$	$82.789$	5.5.1686096.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
10368.2.a.br	$10368$	$2$	10368.a	1.a	$1$	$5$	$5$	$82.789$	5.5.1686096.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
10368.2.a.bs	$10368$	$2$	10368.a	1.a	$1$	$5$	$5$	$82.789$	5.5.1686096.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
10368.2.a.bt	$10368$	$2$	10368.a	1.a	$1$	$5$	$5$	$82.789$	5.5.1686096.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
10368.2.a.bu	$10368$	$2$	10368.a	1.a	$1$	$5$	$5$	$82.789$	5.5.1686096.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
10368.2.a.bv	$10368$	$2$	10368.a	1.a	$1$	$5$	$5$	$82.789$	5.5.1686096.1	None	✓	?				$-1$		\(0\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
10368.2.a.bw	$10368$	$2$	10368.a	1.a	$1$	$6$	$6$	$82.789$	6.6.31083264.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
10368.2.a.bx	$10368$	$2$	10368.a	1.a	$1$	$6$	$6$	$82.789$	6.6.31083264.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
10368.2.a.by	$10368$	$2$	10368.a	1.a	$1$	$6$	$6$	$82.789$	6.6.31083264.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-4\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
10368.2.a.bz	$10368$	$2$	10368.a	1.a	$1$	$6$	$6$	$82.789$	6.6.31083264.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
10368.2.a.ca	$10368$	$2$	10368.a	1.a	$1$	$6$	$6$	$82.789$	6.6.592838784.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(-6\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
10368.2.a.cb	$10368$	$2$	10368.a	1.a	$1$	$6$	$6$	$82.789$	6.6.592838784.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(-6\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
10368.2.a.cc	$10368$	$2$	10368.a	1.a	$1$	$6$	$6$	$82.789$	6.6.592838784.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(6\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
10368.2.a.cd	$10368$	$2$	10368.a	1.a	$1$	$6$	$6$	$82.789$	6.6.592838784.1	None	✓	?				$-1$		\(0\)	\(0\)	\(-2\)	\(6\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
10368.2.a.ce	$10368$	$2$	10368.a	1.a	$1$	$6$	$6$	$82.789$	6.6.592838784.1	None	✓	?	✓			$-1$		\(0\)	\(0\)	\(2\)	\(-6\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
10368.2.a.cf	$10368$	$2$	10368.a	1.a	$1$	$6$	$6$	$82.789$	6.6.592838784.1	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(-6\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
10368.2.a.cg	$10368$	$2$	10368.a	1.a	$1$	$6$	$6$	$82.789$	6.6.592838784.1	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(6\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
10368.2.a.ch	$10368$	$2$	10368.a	1.a	$1$	$6$	$6$	$82.789$	6.6.592838784.1	None	✓	?				$-1$		\(0\)	\(0\)	\(2\)	\(6\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
10368.2.a.ci	$10368$	$2$	10368.a	1.a	$1$	$6$	$6$	$82.789$	6.6.31083264.1	None	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
10368.2.a.cj	$10368$	$2$	10368.a	1.a	$1$	$6$	$6$	$82.789$	6.6.31083264.1	None	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
10368.2.a.ck	$10368$	$2$	10368.a	1.a	$1$	$6$	$6$	$82.789$	6.6.31083264.1	None	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
10368.2.a.cl	$10368$	$2$	10368.a	1.a	$1$	$6$	$6$	$82.789$	6.6.31083264.1	None	✓	?				$-1$		\(0\)	\(0\)	\(4\)	\(0\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(10368))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(10368)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(162))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(216))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(324))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(384))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(432))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(576))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(648))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(864))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1152))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1296))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1728))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2592))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3456))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(5184))\)\(^{\oplus 2}\)