Space of modular forms of level 9216, weight 2, and trivial character

• Label: 9216.2.a
• Level: $9216$
• Weight: $2$
• Character orbit: 9216.a
• Rep. character: $\chi_{9216}(1,\cdot)$
• Character field: $\Q$
• Dimension: $156$
• Newform subspaces: $46$
• Sturm bound: $3072$
• Trace bound: $67$

Defining parameters

Level:	\( N \)	\(=\)	\( 9216 = 2^{10} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9216.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 46 \)
Sturm bound:			\(3072\)
Trace bound:			\(67\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(13\), \(17\), \(19\), \(67\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9216))\).

	Total	New	Old
Modular forms	1632	164	1468
Cusp forms	1441	156	1285
Eisenstein series	191	8	183

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	Dim
\(+\)	\(+\)	\(+\)	\(28\)
\(+\)	\(-\)	\(-\)	\(48\)
\(-\)	\(+\)	\(-\)	\(36\)
\(-\)	\(-\)	\(+\)	\(44\)
Plus space		\(+\)	\(72\)
Minus space		\(-\)	\(84\)

Trace form

\( 156 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9216))\) 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
9216.2.a.a	$9216$	$2$	9216.a	1.a	$1$	$2$	$2$	$73.590$	\(\Q(\sqrt{2}) \)	None	✓				4608.2.k.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-4q^{7}-4\beta q^{11}+3\beta q^{13}+\cdots\)
9216.2.a.b	$9216$	$2$	9216.a	1.a	$1$	$2$	$2$	$73.590$	\(\Q(\sqrt{2}) \)	None	✓				512.2.e.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-8\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-4q^{7}+2\beta q^{11}-3\beta q^{13}+\cdots\)
9216.2.a.c	$9216$	$2$	9216.a	1.a	$1$	$2$	$2$	$73.590$	\(\Q(\sqrt{2}) \)	None	✓				4608.2.k.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-4q^{7}-4\beta q^{11}-3\beta q^{13}+\cdots\)
9216.2.a.d	$9216$	$2$	9216.a	1.a	$1$	$2$	$2$	$73.590$	\(\Q(\sqrt{2}) \)	None	✓				16.2.e.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-2q^{7}+\beta q^{11}-\beta q^{13}-2q^{17}+\cdots\)
9216.2.a.e	$9216$	$2$	9216.a	1.a	$1$	$2$	$2$	$73.590$	\(\Q(\sqrt{2}) \)	None	✓				768.2.j.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2\beta q^{5}+3\beta q^{7}-4q^{11}-3\beta q^{13}+\cdots\)
9216.2.a.f	$9216$	$2$	9216.a	1.a	$1$	$2$	$2$	$73.590$	\(\Q(\sqrt{2}) \)	None	✓				1536.2.j.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-4q^{11}+\beta q^{13}+4q^{19}+4\beta q^{23}+\cdots\)
9216.2.a.g	$9216$	$2$	9216.a	1.a	$1$	$2$	$2$	$73.590$	\(\Q(\sqrt{2}) \)	\(\Q(\sqrt{-1}) \)	✓				512.2.e.c	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	\(q+3\beta q^{5}-\beta q^{13}-8q^{17}+13q^{25}+\cdots\)
9216.2.a.h	$9216$	$2$	9216.a	1.a	$1$	$2$	$2$	$73.590$	\(\Q(\sqrt{2}) \)	None	✓				1536.2.j.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-2\beta q^{7}+3\beta q^{13}-4q^{17}+\cdots\)
9216.2.a.i	$9216$	$2$	9216.a	1.a	$1$	$2$	$2$	$73.590$	\(\Q(\sqrt{2}) \)	None	✓				1536.2.j.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+2\beta q^{7}+3\beta q^{13}-4q^{17}+\cdots\)
9216.2.a.j	$9216$	$2$	9216.a	1.a	$1$	$2$	$2$	$73.590$	\(\Q(\sqrt{2}) \)	\(\Q(\sqrt{-1}) \)	✓				4608.2.k.h	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q+\beta q^{5}+\beta q^{13}-2q^{17}-3q^{25}-3\beta q^{29}+\cdots\)
9216.2.a.k	$9216$	$2$	9216.a	1.a	$1$	$2$	$2$	$73.590$	\(\Q(\sqrt{2}) \)	\(\Q(\sqrt{-1}) \)	✓				4608.2.k.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+3\beta q^{5}-5\beta q^{13}-2q^{17}+13q^{25}+\cdots\)
9216.2.a.l	$9216$	$2$	9216.a	1.a	$1$	$2$	$2$	$73.590$	\(\Q(\sqrt{2}) \)	\(\Q(\sqrt{-1}) \)	✓				4608.2.k.h	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q+\beta q^{5}-\beta q^{13}+2q^{17}-3q^{25}-3\beta q^{29}+\cdots\)
9216.2.a.m	$9216$	$2$	9216.a	1.a	$1$	$2$	$2$	$73.590$	\(\Q(\sqrt{2}) \)	\(\Q(\sqrt{-1}) \)	✓				4608.2.k.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+3\beta q^{5}+5\beta q^{13}+2q^{17}+13q^{25}+\cdots\)
9216.2.a.n	$9216$	$2$	9216.a	1.a	$1$	$2$	$2$	$73.590$	\(\Q(\sqrt{2}) \)	None	✓				768.2.j.b	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{7}-\beta q^{13}+6q^{17}-6q^{19}+6\beta q^{23}+\cdots\)
9216.2.a.o	$9216$	$2$	9216.a	1.a	$1$	$2$	$2$	$73.590$	\(\Q(\sqrt{2}) \)	None	✓				768.2.j.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{7}+\beta q^{13}+6q^{17}+6q^{19}+6\beta q^{23}+\cdots\)
9216.2.a.p	$9216$	$2$	9216.a	1.a	$1$	$2$	$2$	$73.590$	\(\Q(\sqrt{2}) \)	\(\Q(\sqrt{-1}) \)	✓				512.2.e.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+\beta q^{5}+5\beta q^{13}+8q^{17}-3q^{25}+\cdots\)
9216.2.a.q	$9216$	$2$	9216.a	1.a	$1$	$2$	$2$	$73.590$	\(\Q(\sqrt{2}) \)	None	✓				768.2.j.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2\beta q^{5}-3\beta q^{7}+4q^{11}-3\beta q^{13}+\cdots\)
9216.2.a.r	$9216$	$2$	9216.a	1.a	$1$	$2$	$2$	$73.590$	\(\Q(\sqrt{2}) \)	None	✓				1536.2.j.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+4q^{11}+\beta q^{13}-4q^{19}-4\beta q^{23}+\cdots\)
9216.2.a.s	$9216$	$2$	9216.a	1.a	$1$	$2$	$2$	$73.590$	\(\Q(\sqrt{2}) \)	None	✓				16.2.e.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+2q^{7}-\beta q^{11}-\beta q^{13}-2q^{17}+\cdots\)
9216.2.a.t	$9216$	$2$	9216.a	1.a	$1$	$2$	$2$	$73.590$	\(\Q(\sqrt{2}) \)	None	✓				4608.2.k.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+4q^{7}+4\beta q^{11}+3\beta q^{13}+\cdots\)
9216.2.a.u	$9216$	$2$	9216.a	1.a	$1$	$2$	$2$	$73.590$	\(\Q(\sqrt{2}) \)	None	✓				512.2.e.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(8\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+4q^{7}-2\beta q^{11}-3\beta q^{13}+\cdots\)
9216.2.a.v	$9216$	$2$	9216.a	1.a	$1$	$2$	$2$	$73.590$	\(\Q(\sqrt{2}) \)	None	✓				4608.2.k.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+4q^{7}+4\beta q^{11}-3\beta q^{13}+\cdots\)
9216.2.a.w	$9216$	$2$	9216.a	1.a	$1$	$4$	$4$	$73.590$	\(\Q(\zeta_{16})^+\)	None	✓				512.2.e.i	$2$	$1$	\(0\)	\(0\)	\(-8\)	\(0\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-2-\beta _{2})q^{5}+(-\beta _{1}+\beta _{3})q^{7}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
9216.2.a.x	$9216$	$2$	9216.a	1.a	$1$	$4$	$4$	$73.590$	4.4.4352.1	None	✓				48.2.j.a	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(-4\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{3})q^{5}+(-1-\beta _{2})q^{7}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
9216.2.a.y	$9216$	$2$	9216.a	1.a	$1$	$4$	$4$	$73.590$	4.4.4352.1	None	✓				48.2.j.a	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(4\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{3})q^{5}+(1+\beta _{2})q^{7}+(\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)
9216.2.a.z	$9216$	$2$	9216.a	1.a	$1$	$4$	$4$	$73.590$	\(\Q(\zeta_{16})^+\)	None	✓				1536.2.j.e	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-8\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(\beta _{2}-\beta _{3})q^{5}+(-2-\beta _{3})q^{7}+(\beta _{1}+\cdots)q^{11}+\cdots\)
9216.2.a.ba	$9216$	$2$	9216.a	1.a	$1$	$4$	$4$	$73.590$	\(\Q(\zeta_{16})^+\)	None	✓				1536.2.j.e	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-\beta _{2}-\beta _{3})q^{5}+(-2+\beta _{3})q^{7}+(\beta _{1}+\cdots)q^{11}+\cdots\)
9216.2.a.bb	$9216$	$2$	9216.a	1.a	$1$	$4$	$4$	$73.590$	\(\Q(\zeta_{24})^+\)	None	✓				256.2.e.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{5}+(-\beta _{2}-\beta _{3})q^{7}+(-3-\beta _{1}+\cdots)q^{11}+\cdots\)
9216.2.a.bc	$9216$	$2$	9216.a	1.a	$1$	$4$	$4$	$73.590$	\(\Q(\zeta_{24})^+\)	None	✓				768.2.j.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{2})q^{5}+\beta _{2}q^{7}+(-2+\beta _{3})q^{11}+\cdots\)
9216.2.a.bd	$9216$	$2$	9216.a	1.a	$1$	$4$	$4$	$73.590$	\(\Q(\sqrt{2}, \sqrt{5})\)	None	✓				1536.2.j.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+(-2+\beta _{3})q^{11}+\cdots\)
9216.2.a.be	$9216$	$2$	9216.a	1.a	$1$	$4$	$4$	$73.590$	\(\Q(\zeta_{24})^+\)	None	✓				2304.2.k.h	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{5}-\beta _{1}q^{7}+\beta _{3}q^{11}-\beta _{1}q^{13}+\cdots\)
9216.2.a.bf	$9216$	$2$	9216.a	1.a	$1$	$4$	$4$	$73.590$	\(\Q(\zeta_{24})^+\)	\(\Q(\sqrt{-3}) \)	✓				2304.2.k.g	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$2^{2}$	$N(\mathrm{U}(1))$	\(q+(-2\beta _{1}-\beta _{2})q^{7}+(\beta _{1}+2\beta _{2})q^{13}+\cdots\)
9216.2.a.bg	$9216$	$2$	9216.a	1.a	$1$	$4$	$4$	$73.590$	\(\Q(\zeta_{24})^+\)	\(\Q(\sqrt{-3}) \)	✓				2304.2.k.g	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{2}$	$N(\mathrm{U}(1))$	\(q+(2\beta _{1}+\beta _{2})q^{7}+(\beta _{1}+2\beta _{2})q^{13}+\beta _{3}q^{19}+\cdots\)
9216.2.a.bh	$9216$	$2$	9216.a	1.a	$1$	$4$	$4$	$73.590$	\(\Q(\zeta_{24})^+\)	None	✓				2304.2.k.h	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{5}-\beta _{1}q^{7}+\beta _{3}q^{11}+\beta _{1}q^{13}+\cdots\)
9216.2.a.bi	$9216$	$2$	9216.a	1.a	$1$	$4$	$4$	$73.590$	\(\Q(\zeta_{24})^+\)	None	✓				768.2.j.e	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{2})q^{5}-\beta _{2}q^{7}+(2-\beta _{3})q^{11}+\cdots\)
9216.2.a.bj	$9216$	$2$	9216.a	1.a	$1$	$4$	$4$	$73.590$	\(\Q(\sqrt{2}, \sqrt{5})\)	None	✓				1536.2.j.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+(2+\beta _{3})q^{11}+\cdots\)
9216.2.a.bk	$9216$	$2$	9216.a	1.a	$1$	$4$	$4$	$73.590$	\(\Q(\zeta_{24})^+\)	None	✓				256.2.e.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{5}+(\beta _{2}+\beta _{3})q^{7}+(3+\beta _{1})q^{11}+\cdots\)
9216.2.a.bl	$9216$	$2$	9216.a	1.a	$1$	$4$	$4$	$73.590$	\(\Q(\zeta_{16})^+\)	None	✓				1536.2.j.e	$1$	$1$	\(0\)	\(0\)	\(0\)	\(8\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(\beta _{2}-\beta _{3})q^{5}+(2+\beta _{3})q^{7}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
9216.2.a.bm	$9216$	$2$	9216.a	1.a	$1$	$4$	$4$	$73.590$	\(\Q(\zeta_{16})^+\)	None	✓				1536.2.j.e	$1$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-\beta _{2}-\beta _{3})q^{5}+(2-\beta _{3})q^{7}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
9216.2.a.bn	$9216$	$2$	9216.a	1.a	$1$	$4$	$4$	$73.590$	4.4.4352.1	None	✓				48.2.j.a	$1$	$1$	\(0\)	\(0\)	\(4\)	\(-4\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{3})q^{5}+(-1-\beta _{2})q^{7}+(\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)
9216.2.a.bo	$9216$	$2$	9216.a	1.a	$1$	$4$	$4$	$73.590$	4.4.4352.1	None	✓				48.2.j.a	$1$	$0$	\(0\)	\(0\)	\(4\)	\(4\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{3})q^{5}+(1+\beta _{2})q^{7}+(-\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
9216.2.a.bp	$9216$	$2$	9216.a	1.a	$1$	$4$	$4$	$73.590$	\(\Q(\zeta_{16})^+\)	None	✓				512.2.e.i	$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(2-\beta _{2})q^{5}+(\beta _{1}+\beta _{3})q^{7}+(2\beta _{1}-\beta _{3})q^{11}+\cdots\)
9216.2.a.bq	$9216$	$2$	9216.a	1.a	$1$	$8$	$8$	$73.590$	8.8.\(\cdots\).1	None	✓				144.2.k.c	$4$	$1$	\(0\)	\(0\)	\(0\)	\(-8\)		$+$	$+$	$+$	$2^{6}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{5}+(-1-\beta _{5})q^{7}+(-\beta _{2}+\beta _{7})q^{11}+\cdots\)
9216.2.a.br	$9216$	$2$	9216.a	1.a	$1$	$8$	$8$	$73.590$	8.8.3288334336.1	None	✓				4608.2.k.bk	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$2^{6}$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{5}-\beta _{7}q^{7}+\beta _{2}q^{11}+(-2+\beta _{5}+\cdots)q^{13}+\cdots\)
9216.2.a.bs	$9216$	$2$	9216.a	1.a	$1$	$8$	$8$	$73.590$	8.8.3288334336.1	None	✓				4608.2.k.bk	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{6}$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{5}+\beta _{7}q^{7}-\beta _{2}q^{11}+(2-\beta _{5}+\cdots)q^{13}+\cdots\)
9216.2.a.bt	$9216$	$2$	9216.a	1.a	$1$	$8$	$8$	$73.590$	8.8.\(\cdots\).1	None	✓				144.2.k.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$-$	$+$	$-$	$2^{6}$	$\mathrm{SU}(2)$	\(q-\beta _{5}q^{5}+(1-\beta _{6})q^{7}+(-\beta _{2}-\beta _{5}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9216))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9216)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(256))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(384))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(512))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(576))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(768))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1024))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1152))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1536))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2304))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3072))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4608))\)\(^{\oplus 2}\)