Space of modular forms of level 4752, weight 2, and trivial character

• Label: 4752.2.a
• Level: $4752$
• Weight: $2$
• Character orbit: 4752.a
• Rep. character: $\chi_{4752}(1,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $44$
• Sturm bound: $1728$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 4752 = 2^{4} \cdot 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4752.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 44 \)
Sturm bound:			\(1728\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(7\), \(13\), \(17\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4752))\).

	Total	New	Old
Modular forms	900	80	820
Cusp forms	829	80	749
Eisenstein series	71	0	71

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

\(2\)	\(3\)	\(11\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(108\)	\(10\)	\(98\)		\(100\)	\(10\)	\(90\)		\(8\)	\(0\)	\(8\)
\(+\)	\(+\)	\(-\)	\(-\)		\(117\)	\(12\)	\(105\)		\(108\)	\(12\)	\(96\)		\(9\)	\(0\)	\(9\)
\(+\)	\(-\)	\(+\)	\(-\)		\(114\)	\(10\)	\(104\)		\(105\)	\(10\)	\(95\)		\(9\)	\(0\)	\(9\)
\(+\)	\(-\)	\(-\)	\(+\)		\(111\)	\(8\)	\(103\)		\(102\)	\(8\)	\(94\)		\(9\)	\(0\)	\(9\)
\(-\)	\(+\)	\(+\)	\(-\)		\(117\)	\(11\)	\(106\)		\(108\)	\(11\)	\(97\)		\(9\)	\(0\)	\(9\)
\(-\)	\(+\)	\(-\)	\(+\)		\(108\)	\(9\)	\(99\)		\(99\)	\(9\)	\(90\)		\(9\)	\(0\)	\(9\)
\(-\)	\(-\)	\(+\)	\(+\)		\(111\)	\(9\)	\(102\)		\(102\)	\(9\)	\(93\)		\(9\)	\(0\)	\(9\)
\(-\)	\(-\)	\(-\)	\(-\)		\(114\)	\(11\)	\(103\)		\(105\)	\(11\)	\(94\)		\(9\)	\(0\)	\(9\)
Plus space			\(+\)		\(438\)	\(36\)	\(402\)		\(403\)	\(36\)	\(367\)		\(35\)	\(0\)	\(35\)
Minus space			\(-\)		\(462\)	\(44\)	\(418\)		\(426\)	\(44\)	\(382\)		\(36\)	\(0\)	\(36\)

Trace form

\( 80 q + 4 q^{7} - 4 q^{19} + 80 q^{25} - 40 q^{31} + 32 q^{37} - 32 q^{43} + 88 q^{49} + 48 q^{61} + 4 q^{67} + 8 q^{73} + 20 q^{79} + 48 q^{85} - 4 q^{91} + 8 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4752))\) 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	11
4752.2.a.a	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	\(\Q\)	None	✓				2376.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-4q^{7}-q^{11}+3q^{13}+3q^{17}+\cdots\)
4752.2.a.b	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	\(\Q\)	None	✓				594.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+4q^{7}+q^{11}+5q^{13}-3q^{17}+\cdots\)
4752.2.a.c	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	\(\Q\)	None	✓				297.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-q^{7}-q^{11}-5q^{13}-2q^{17}+\cdots\)
4752.2.a.d	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	\(\Q\)	None	✓				594.2.a.c	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-q^{7}+q^{11}-2q^{13}-q^{17}+\cdots\)
4752.2.a.e	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	\(\Q\)	None	✓				1188.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{7}-q^{11}+3q^{13}-2q^{17}+\cdots\)
4752.2.a.f	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	\(\Q\)	None	✓				594.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{7}-q^{11}+6q^{13}-5q^{17}+\cdots\)
4752.2.a.g	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	\(\Q\)	None	✓				297.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+5q^{7}-q^{11}-2q^{13}+7q^{17}+\cdots\)
4752.2.a.h	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	\(\Q\)	None	✓				594.2.a.d	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-4q^{7}-q^{11}+q^{13}-5q^{17}+\cdots\)
4752.2.a.i	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	\(\Q\)	None	✓				2376.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}-q^{11}-3q^{13}+5q^{19}+4q^{23}+\cdots\)
4752.2.a.j	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	\(\Q\)	None	✓				2376.2.a.b	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}+q^{11}-3q^{13}+5q^{19}-4q^{23}+\cdots\)
4752.2.a.k	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	\(\Q\)	None	✓				1188.2.a.b	$1$	$1$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-q^{11}-4q^{13}-3q^{17}+4q^{19}+\cdots\)
4752.2.a.l	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	\(\Q\)	None	✓				1188.2.a.b	$1$	$1$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}+q^{11}-4q^{13}+3q^{17}+4q^{19}+\cdots\)
4752.2.a.m	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	\(\Q\)	None	✓				594.2.a.d	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{7}+q^{11}+q^{13}+5q^{17}+\cdots\)
4752.2.a.n	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	\(\Q\)	None	✓				594.2.a.c	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-q^{7}-q^{11}-2q^{13}+q^{17}+\cdots\)
4752.2.a.o	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	\(\Q\)	None	✓				297.2.a.a	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-q^{7}+q^{11}-5q^{13}+2q^{17}+\cdots\)
4752.2.a.p	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	\(\Q\)	None	✓				1188.2.a.a	$1$	$0$	\(0\)	\(0\)	\(2\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+q^{7}+q^{11}+3q^{13}+2q^{17}+\cdots\)
4752.2.a.q	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	\(\Q\)	None	✓				594.2.a.b	$1$	$0$	\(0\)	\(0\)	\(2\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+q^{7}+q^{11}+6q^{13}+5q^{17}+\cdots\)
4752.2.a.r	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	\(\Q\)	None	✓				297.2.a.b	$1$	$0$	\(0\)	\(0\)	\(2\)	\(5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+5q^{7}+q^{11}-2q^{13}-7q^{17}+\cdots\)
4752.2.a.s	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	\(\Q\)	None	✓				2376.2.a.a	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-4q^{7}+q^{11}+3q^{13}-3q^{17}+\cdots\)
4752.2.a.t	$4752$	$2$	4752.a	1.a	$1$	$1$	$1$	$37.945$	\(\Q\)	None	✓				594.2.a.a	$1$	$0$	\(0\)	\(0\)	\(3\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+4q^{7}-q^{11}+5q^{13}+3q^{17}+\cdots\)
4752.2.a.u	$4752$	$2$	4752.a	1.a	$1$	$2$	$2$	$37.945$	\(\Q(\sqrt{10}) \)	None	✓				594.2.a.i	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{5}-2q^{7}-q^{11}+(1+\beta )q^{13}+\cdots\)
4752.2.a.v	$4752$	$2$	4752.a	1.a	$1$	$2$	$2$	$37.945$	\(\Q(\sqrt{7}) \)	None	✓				1188.2.a.e	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{5}+\beta q^{7}+q^{11}-\beta q^{13}+\cdots\)
4752.2.a.w	$4752$	$2$	4752.a	1.a	$1$	$2$	$2$	$37.945$	\(\Q(\sqrt{3}) \)	None	✓				297.2.a.e	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{5}+(2+\beta )q^{7}+q^{11}+(-2+\cdots)q^{13}+\cdots\)
4752.2.a.x	$4752$	$2$	4752.a	1.a	$1$	$2$	$2$	$37.945$	\(\Q(\sqrt{7}) \)	None	✓				2376.2.a.i	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{7}-q^{11}+(2-\beta )q^{17}-2\beta q^{19}+\cdots\)
4752.2.a.y	$4752$	$2$	4752.a	1.a	$1$	$2$	$2$	$37.945$	\(\Q(\sqrt{7}) \)	None	✓				2376.2.a.i	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{7}+q^{11}+(-2-\beta )q^{17}+2\beta q^{19}+\cdots\)
4752.2.a.z	$4752$	$2$	4752.a	1.a	$1$	$2$	$2$	$37.945$	\(\Q(\sqrt{2}) \)	None	✓				2376.2.a.e	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2\beta q^{5}+(1+\beta )q^{7}-q^{11}+(-4-2\beta )q^{13}+\cdots\)
4752.2.a.ba	$4752$	$2$	4752.a	1.a	$1$	$2$	$2$	$37.945$	\(\Q(\sqrt{2}) \)	None	✓				2376.2.a.f	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(1-\beta )q^{7}-q^{11}+(-1-\beta )q^{13}+\cdots\)
4752.2.a.bb	$4752$	$2$	4752.a	1.a	$1$	$2$	$2$	$37.945$	\(\Q(\sqrt{2}) \)	None	✓				2376.2.a.e	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2\beta q^{5}+(1-\beta )q^{7}+q^{11}+(-4+2\beta )q^{13}+\cdots\)
4752.2.a.bc	$4752$	$2$	4752.a	1.a	$1$	$2$	$2$	$37.945$	\(\Q(\sqrt{2}) \)	None	✓				2376.2.a.f	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(1+\beta )q^{7}+q^{11}+(-1+\beta )q^{13}+\cdots\)
4752.2.a.bd	$4752$	$2$	4752.a	1.a	$1$	$2$	$2$	$37.945$	\(\Q(\sqrt{10}) \)	None	✓				594.2.a.i	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}-2q^{7}+q^{11}+(1-\beta )q^{13}+\cdots\)
4752.2.a.be	$4752$	$2$	4752.a	1.a	$1$	$2$	$2$	$37.945$	\(\Q(\sqrt{7}) \)	None	✓				1188.2.a.e	$1$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}-\beta q^{7}-q^{11}+\beta q^{13}+\cdots\)
4752.2.a.bf	$4752$	$2$	4752.a	1.a	$1$	$2$	$2$	$37.945$	\(\Q(\sqrt{3}) \)	None	✓				297.2.a.e	$1$	$1$	\(0\)	\(0\)	\(2\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}+(2-\beta )q^{7}-q^{11}+(-2+\cdots)q^{13}+\cdots\)
4752.2.a.bg	$4752$	$2$	4752.a	1.a	$1$	$3$	$3$	$37.945$	3.3.564.1	None	✓		✓		297.2.a.g	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-7\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{5}+(-2-\beta _{1})q^{7}+q^{11}+\cdots\)
4752.2.a.bh	$4752$	$2$	4752.a	1.a	$1$	$3$	$3$	$37.945$	3.3.788.1	None	✓				2376.2.a.l	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{2})q^{5}-\beta _{1}q^{7}+q^{11}+(1+\cdots)q^{13}+\cdots\)
4752.2.a.bi	$4752$	$2$	4752.a	1.a	$1$	$3$	$3$	$37.945$	3.3.1016.1	None	✓		✓		2376.2.a.m	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{5}+(-\beta _{1}-\beta _{2})q^{7}+q^{11}+\cdots\)
4752.2.a.bj	$4752$	$2$	4752.a	1.a	$1$	$3$	$3$	$37.945$	3.3.564.1	None	✓				2376.2.a.k	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+\cdots\)
4752.2.a.bk	$4752$	$2$	4752.a	1.a	$1$	$3$	$3$	$37.945$	3.3.7032.1	None	✓				2376.2.a.n	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{5}+(1-\beta _{1})q^{7}+q^{11}+(-1+\cdots)q^{13}+\cdots\)
4752.2.a.bl	$4752$	$2$	4752.a	1.a	$1$	$3$	$3$	$37.945$	3.3.3124.1	None	✓		✓		1188.2.a.g	$1$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{5}+\beta _{2}q^{7}-q^{11}+(2-\beta _{1})q^{13}+\cdots\)
4752.2.a.bm	$4752$	$2$	4752.a	1.a	$1$	$3$	$3$	$37.945$	3.3.3124.1	None	✓		✓		1188.2.a.g	$1$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}+\beta _{2}q^{7}+q^{11}+(2-\beta _{1})q^{13}+\cdots\)
4752.2.a.bn	$4752$	$2$	4752.a	1.a	$1$	$3$	$3$	$37.945$	3.3.7032.1	None	✓		✓		2376.2.a.n	$1$	$1$	\(0\)	\(0\)	\(1\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}+(1-\beta _{1})q^{7}-q^{11}+(-1+\cdots)q^{13}+\cdots\)
4752.2.a.bo	$4752$	$2$	4752.a	1.a	$1$	$3$	$3$	$37.945$	3.3.564.1	None	✓		✓		297.2.a.g	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-7\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{5}+(-2-\beta _{1})q^{7}-q^{11}+\cdots\)
4752.2.a.bp	$4752$	$2$	4752.a	1.a	$1$	$3$	$3$	$37.945$	3.3.788.1	None	✓				2376.2.a.l	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{2})q^{5}-\beta _{1}q^{7}-q^{11}+(1-2\beta _{1}+\cdots)q^{13}+\cdots\)
4752.2.a.bq	$4752$	$2$	4752.a	1.a	$1$	$3$	$3$	$37.945$	3.3.1016.1	None	✓				2376.2.a.m	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{5}+(-\beta _{1}-\beta _{2})q^{7}-q^{11}+\cdots\)
4752.2.a.br	$4752$	$2$	4752.a	1.a	$1$	$3$	$3$	$37.945$	3.3.564.1	None	✓				2376.2.a.k	$1$	$0$	\(0\)	\(0\)	\(2\)	\(3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4752))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4752)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(216))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(297))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(396))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(432))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(528))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(594))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(792))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1188))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1584))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2376))\)\(^{\oplus 2}\)