Space of modular forms of level 3648, weight 2, and trivial character

• Label: 3648.2.a
• Level: $3648$
• Weight: $2$
• Character orbit: 3648.a
• Rep. character: $\chi_{3648}(1,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $52$
• Sturm bound: $1280$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 3648 = 2^{6} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3648.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 52 \)
Sturm bound:			\(1280\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(23\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3648))\).

	Total	New	Old
Modular forms	664	72	592
Cusp forms	617	72	545
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.

\(2\)	\(3\)	\(19\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(9\)
\(+\)	\(+\)	\(-\)	\(-\)	\(8\)
\(+\)	\(-\)	\(+\)	\(-\)	\(11\)
\(+\)	\(-\)	\(-\)	\(+\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)	\(9\)
\(-\)	\(+\)	\(-\)	\(+\)	\(10\)
\(-\)	\(-\)	\(+\)	\(+\)	\(7\)
\(-\)	\(-\)	\(-\)	\(-\)	\(12\)
Plus space			\(+\)	\(32\)
Minus space			\(-\)	\(40\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3648))\) 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	19
3648.2.a.a	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-4\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
3648.2.a.b	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+3q^{7}+q^{9}-3q^{11}+\cdots\)
3648.2.a.c	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
3648.2.a.d	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}-2q^{13}+2q^{15}+\cdots\)
3648.2.a.e	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}+2q^{11}-2q^{13}+\cdots\)
3648.2.a.f	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+4q^{7}+q^{9}+6q^{11}+\cdots\)
3648.2.a.g	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+3q^{7}+q^{9}-5q^{11}+2q^{13}+\cdots\)
3648.2.a.h	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+3q^{7}+q^{9}+3q^{11}+6q^{13}+\cdots\)
3648.2.a.i	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{7}+q^{9}+4q^{13}+6q^{17}+\cdots\)
3648.2.a.j	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{7}+q^{9}+4q^{11}-2q^{17}+\cdots\)
3648.2.a.k	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}-2q^{17}-q^{19}+6q^{23}+\cdots\)
3648.2.a.l	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}+5q^{11}-4q^{13}+\cdots\)
3648.2.a.m	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}+3q^{11}-q^{15}+\cdots\)
3648.2.a.n	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
3648.2.a.o	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{9}-6q^{13}-2q^{15}+\cdots\)
3648.2.a.p	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}-3q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
3648.2.a.q	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}-q^{7}+q^{9}-5q^{11}+6q^{13}+\cdots\)
3648.2.a.r	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}+5q^{7}+q^{9}+q^{11}-2q^{13}+\cdots\)
3648.2.a.s	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-4\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots\)
3648.2.a.t	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}-3q^{7}+q^{9}+3q^{11}+\cdots\)
3648.2.a.u	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-4q^{7}+q^{9}-6q^{11}+\cdots\)
3648.2.a.v	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}-2q^{11}-2q^{13}+\cdots\)
3648.2.a.w	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}-2q^{13}-2q^{15}+\cdots\)
3648.2.a.x	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
3648.2.a.y	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-3q^{7}+q^{9}-3q^{11}+6q^{13}+\cdots\)
3648.2.a.z	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(-3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-3q^{7}+q^{9}+5q^{11}+2q^{13}+\cdots\)
3648.2.a.ba	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}-2q^{17}+q^{19}-6q^{23}+\cdots\)
3648.2.a.bb	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{7}+q^{9}-4q^{11}-2q^{17}+\cdots\)
3648.2.a.bc	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{7}+q^{9}+4q^{13}+6q^{17}+\cdots\)
3648.2.a.bd	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}-3q^{11}+q^{15}+\cdots\)
3648.2.a.be	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}-5q^{11}-4q^{13}+\cdots\)
3648.2.a.bf	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}-6q^{13}+2q^{15}+\cdots\)
3648.2.a.bg	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots\)
3648.2.a.bh	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(3\)	\(-5\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}-5q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
3648.2.a.bi	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(3\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}+q^{7}+q^{9}+5q^{11}+6q^{13}+\cdots\)
3648.2.a.bj	$3648$	$2$	3648.a	1.a	$1$	$1$	$1$	$29.129$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(3\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}+3q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
3648.2.a.bk	$3648$	$2$	3648.a	1.a	$1$	$2$	$2$	$29.129$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-3\)	\(1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta )q^{5}+(1-\beta )q^{7}+q^{9}+\cdots\)
3648.2.a.bl	$3648$	$2$	3648.a	1.a	$1$	$2$	$2$	$29.129$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta q^{5}+\beta q^{7}+q^{9}+(-4+\beta )q^{11}+\cdots\)
3648.2.a.bm	$3648$	$2$	3648.a	1.a	$1$	$2$	$2$	$29.129$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(1\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+\beta q^{7}+q^{9}+(4-\beta )q^{11}+\cdots\)
3648.2.a.bn	$3648$	$2$	3648.a	1.a	$1$	$2$	$2$	$29.129$	\(\Q(\sqrt{41}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+(2-\beta )q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
3648.2.a.bo	$3648$	$2$	3648.a	1.a	$1$	$2$	$2$	$29.129$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(3\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}+(-1+\beta )q^{7}+q^{9}+\cdots\)
3648.2.a.bp	$3648$	$2$	3648.a	1.a	$1$	$2$	$2$	$29.129$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(3\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}+(1-\beta )q^{7}+q^{9}+\cdots\)
3648.2.a.bq	$3648$	$2$	3648.a	1.a	$1$	$2$	$2$	$29.129$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-3\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
3648.2.a.br	$3648$	$2$	3648.a	1.a	$1$	$2$	$2$	$29.129$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta q^{5}-\beta q^{7}+q^{9}+(4-\beta )q^{11}+\cdots\)
3648.2.a.bs	$3648$	$2$	3648.a	1.a	$1$	$2$	$2$	$29.129$	\(\Q(\sqrt{41}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(1\)	\(-3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+(-2+\beta )q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
3648.2.a.bt	$3648$	$2$	3648.a	1.a	$1$	$2$	$2$	$29.129$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(1\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}-\beta q^{7}+q^{9}+(-4+\beta )q^{11}+\cdots\)
3648.2.a.bu	$3648$	$2$	3648.a	1.a	$1$	$2$	$2$	$29.129$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(3\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{5}+(-1+\beta )q^{7}+q^{9}+\cdots\)
3648.2.a.bv	$3648$	$2$	3648.a	1.a	$1$	$2$	$2$	$29.129$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(3\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{5}+(1-\beta )q^{7}+q^{9}+\cdots\)
3648.2.a.bw	$3648$	$2$	3648.a	1.a	$1$	$3$	$3$	$29.129$	3.3.229.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-5\)	\(1\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(-2-\beta _{2})q^{5}-\beta _{1}q^{7}+q^{9}+\cdots\)
3648.2.a.bx	$3648$	$2$	3648.a	1.a	$1$	$3$	$3$	$29.129$	3.3.469.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(3\)	\(-5\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{1})q^{5}+(-2+\beta _{2})q^{7}+\cdots\)
3648.2.a.by	$3648$	$2$	3648.a	1.a	$1$	$3$	$3$	$29.129$	3.3.229.1	None	✓	$1$	$1$	\(0\)	\(3\)	\(-5\)	\(-1\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(-2-\beta _{2})q^{5}+\beta _{1}q^{7}+q^{9}+\cdots\)
3648.2.a.bz	$3648$	$2$	3648.a	1.a	$1$	$3$	$3$	$29.129$	3.3.469.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(3\)	\(5\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-\beta _{1})q^{5}+(2-\beta _{2})q^{7}+q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3648))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3648)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(228))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(456))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(608))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(912))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1216))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1824))\)\(^{\oplus 2}\)