Space of modular forms of level 4560, weight 2, and trivial character

• Label: 4560.2.a
• Level: $4560$
• Weight: $2$
• Character orbit: 4560.a
• Rep. character: $\chi_{4560}(1,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $48$
• Sturm bound: $1920$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4560.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 48 \)
Sturm bound:			\(1920\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4560))\).

	Total	New	Old
Modular forms	984	72	912
Cusp forms	937	72	865
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.

\(2\)	\(3\)	\(5\)	\(19\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	$+$	\(4\)
\(+\)	\(+\)	\(+\)	\(-\)	$-$	\(5\)
\(+\)	\(+\)	\(-\)	\(+\)	$-$	\(6\)
\(+\)	\(+\)	\(-\)	\(-\)	$+$	\(3\)
\(+\)	\(-\)	\(+\)	\(+\)	$-$	\(5\)
\(+\)	\(-\)	\(+\)	\(-\)	$+$	\(4\)
\(+\)	\(-\)	\(-\)	\(+\)	$+$	\(3\)
\(+\)	\(-\)	\(-\)	\(-\)	$-$	\(6\)
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(5\)
\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(4\)
\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(4\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(5\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(3\)
Plus space				\(+\)	\(28\)
Minus space				\(-\)	\(44\)

Trace form

\( 72 q - 8 q^{7} + 72 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4560))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	19
4560.2.a.a	$4560$	$2$	4560.a	1.a	$1$	$1$	$1$	$36.412$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-4\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-4q^{7}+q^{9}+2q^{13}+q^{15}+\cdots\)
4560.2.a.b	$4560$	$2$	4560.a	1.a	$1$	$1$	$1$	$36.412$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{7}+q^{9}-6q^{11}-4q^{13}+\cdots\)
4560.2.a.c	$4560$	$2$	4560.a	1.a	$1$	$1$	$1$	$36.412$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{7}+q^{9}-4q^{13}+q^{15}+\cdots\)
4560.2.a.d	$4560$	$2$	4560.a	1.a	$1$	$1$	$1$	$36.412$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
4560.2.a.e	$4560$	$2$	4560.a	1.a	$1$	$1$	$1$	$36.412$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
4560.2.a.f	$4560$	$2$	4560.a	1.a	$1$	$1$	$1$	$36.412$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+2q^{7}+q^{9}-4q^{13}+q^{15}+\cdots\)
4560.2.a.g	$4560$	$2$	4560.a	1.a	$1$	$1$	$1$	$36.412$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(2\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+2q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
4560.2.a.h	$4560$	$2$	4560.a	1.a	$1$	$1$	$1$	$36.412$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+2q^{7}+q^{9}+6q^{11}+q^{15}+\cdots\)
4560.2.a.i	$4560$	$2$	4560.a	1.a	$1$	$1$	$1$	$36.412$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(4\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+4q^{7}+q^{9}-2q^{11}+6q^{13}+\cdots\)
4560.2.a.j	$4560$	$2$	4560.a	1.a	$1$	$1$	$1$	$36.412$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-4\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-4q^{7}+q^{9}+2q^{13}-q^{15}+\cdots\)
4560.2.a.k	$4560$	$2$	4560.a	1.a	$1$	$1$	$1$	$36.412$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(-4\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-4q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
4560.2.a.l	$4560$	$2$	4560.a	1.a	$1$	$1$	$1$	$36.412$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(-4\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-4q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
4560.2.a.m	$4560$	$2$	4560.a	1.a	$1$	$1$	$1$	$36.412$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{7}+q^{9}+2q^{13}-q^{15}+\cdots\)
4560.2.a.n	$4560$	$2$	4560.a	1.a	$1$	$1$	$1$	$36.412$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
4560.2.a.o	$4560$	$2$	4560.a	1.a	$1$	$1$	$1$	$36.412$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+2q^{7}+q^{9}-2q^{11}+4q^{13}+\cdots\)
4560.2.a.p	$4560$	$2$	4560.a	1.a	$1$	$1$	$1$	$36.412$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(2\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+2q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots\)
4560.2.a.q	$4560$	$2$	4560.a	1.a	$1$	$1$	$1$	$36.412$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(4\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+4q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
4560.2.a.r	$4560$	$2$	4560.a	1.a	$1$	$1$	$1$	$36.412$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{7}+q^{9}+6q^{11}-q^{15}+\cdots\)
4560.2.a.s	$4560$	$2$	4560.a	1.a	$1$	$1$	$1$	$36.412$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
4560.2.a.t	$4560$	$2$	4560.a	1.a	$1$	$1$	$1$	$36.412$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+2q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
4560.2.a.u	$4560$	$2$	4560.a	1.a	$1$	$1$	$1$	$36.412$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+2q^{7}+q^{9}-4q^{11}-q^{15}+\cdots\)
4560.2.a.v	$4560$	$2$	4560.a	1.a	$1$	$1$	$1$	$36.412$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+2q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots\)
4560.2.a.w	$4560$	$2$	4560.a	1.a	$1$	$1$	$1$	$36.412$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-4\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-4q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
4560.2.a.x	$4560$	$2$	4560.a	1.a	$1$	$1$	$1$	$36.412$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(-4\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-4q^{7}+q^{9}-6q^{13}+q^{15}+\cdots\)
4560.2.a.y	$4560$	$2$	4560.a	1.a	$1$	$1$	$1$	$36.412$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{7}+q^{9}-6q^{11}+4q^{13}+\cdots\)
4560.2.a.z	$4560$	$2$	4560.a	1.a	$1$	$1$	$1$	$36.412$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{7}+q^{9}-2q^{13}+q^{15}+\cdots\)
4560.2.a.ba	$4560$	$2$	4560.a	1.a	$1$	$1$	$1$	$36.412$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
4560.2.a.bb	$4560$	$2$	4560.a	1.a	$1$	$1$	$1$	$36.412$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}-2q^{13}+q^{15}-6q^{17}+\cdots\)
4560.2.a.bc	$4560$	$2$	4560.a	1.a	$1$	$1$	$1$	$36.412$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+2q^{7}+q^{9}+6q^{13}+q^{15}+\cdots\)
4560.2.a.bd	$4560$	$2$	4560.a	1.a	$1$	$1$	$1$	$36.412$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+2q^{7}+q^{9}+2q^{11}+q^{15}+\cdots\)
4560.2.a.be	$4560$	$2$	4560.a	1.a	$1$	$2$	$2$	$36.412$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-6\)		$+$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+(-3-\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
4560.2.a.bf	$4560$	$2$	4560.a	1.a	$1$	$2$	$2$	$36.412$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+\beta q^{7}+q^{9}+(-2+3\beta )q^{11}+\cdots\)
4560.2.a.bg	$4560$	$2$	4560.a	1.a	$1$	$2$	$2$	$36.412$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(4\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+(2+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
4560.2.a.bh	$4560$	$2$	4560.a	1.a	$1$	$2$	$2$	$36.412$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(1+\beta )q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
4560.2.a.bi	$4560$	$2$	4560.a	1.a	$1$	$2$	$2$	$36.412$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(6\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(3+\beta )q^{7}+q^{9}+(1-3\beta )q^{11}+\cdots\)
4560.2.a.bj	$4560$	$2$	4560.a	1.a	$1$	$2$	$2$	$36.412$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+(-2+\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
4560.2.a.bk	$4560$	$2$	4560.a	1.a	$1$	$2$	$2$	$36.412$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(-2\)		$+$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+(-1-\beta )q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
4560.2.a.bl	$4560$	$2$	4560.a	1.a	$1$	$2$	$2$	$36.412$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+(-1-\beta )q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
4560.2.a.bm	$4560$	$2$	4560.a	1.a	$1$	$2$	$2$	$36.412$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+\beta q^{7}+q^{9}-\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
4560.2.a.bn	$4560$	$2$	4560.a	1.a	$1$	$2$	$2$	$36.412$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+\beta q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
4560.2.a.bo	$4560$	$2$	4560.a	1.a	$1$	$2$	$2$	$36.412$	\(\Q(\sqrt{7}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+(1+\beta )q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
4560.2.a.bp	$4560$	$2$	4560.a	1.a	$1$	$2$	$2$	$36.412$	\(\Q(\sqrt{7}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(2\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+(1+\beta )q^{7}+q^{9}+(3+\beta )q^{11}+\cdots\)
4560.2.a.bq	$4560$	$2$	4560.a	1.a	$1$	$3$	$3$	$36.412$	3.3.1016.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(-3\)	\(0\)		$+$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-\beta _{2}q^{7}+q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
4560.2.a.br	$4560$	$2$	4560.a	1.a	$1$	$3$	$3$	$36.412$	3.3.564.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(3\)	\(-4\)		$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(-1+\beta _{2})q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
4560.2.a.bs	$4560$	$2$	4560.a	1.a	$1$	$3$	$3$	$36.412$	3.3.1772.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(3\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-\beta _{2}q^{7}+q^{9}+(-2-\beta _{2})q^{11}+\cdots\)
4560.2.a.bt	$4560$	$2$	4560.a	1.a	$1$	$3$	$3$	$36.412$	3.3.568.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(-3\)	\(2\)		$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+(1+\beta _{2})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
4560.2.a.bu	$4560$	$2$	4560.a	1.a	$1$	$3$	$3$	$36.412$	3.3.1524.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(3\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+\beta _{1}q^{7}+q^{9}+(1+\beta _{2})q^{11}+\cdots\)
4560.2.a.bv	$4560$	$2$	4560.a	1.a	$1$	$3$	$3$	$36.412$	3.3.316.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(3\)	\(2\)		$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+(1-\beta _{1})q^{7}+q^{9}+(1+\beta _{2})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4560))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4560)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(60))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(190))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(228))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(285))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(380))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(456))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(570))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(760))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(912))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1140))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1520))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2280))\)\(^{\oplus 2}\)