Space of modular forms of level 7650, weight 2, and trivial character

• Label: 7650.2.a
• Level: $7650$
• Weight: $2$
• Character orbit: 7650.a
• Rep. character: $\chi_{7650}(1,\cdot)$
• Character field: $\Q$
• Dimension: $128$
• Newform subspaces: $94$
• Sturm bound: $3240$
• Trace bound: $29$

Defining parameters

Level:	\( N \)	\(=\)	\( 7650 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7650.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 94 \)
Sturm bound:			\(3240\)
Trace bound:			\(29\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(19\), \(23\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7650))\).

	Total	New	Old
Modular forms	1668	128	1540
Cusp forms	1573	128	1445
Eisenstein series	95	0	95

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

\(2\)	\(3\)	\(5\)	\(17\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(5\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(7\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(9\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(5\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(8\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(10\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(10\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(10\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(7\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(5\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(5\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(9\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(7\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(11\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(12\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(8\)
Plus space				\(+\)	\(55\)
Minus space				\(-\)	\(73\)

Trace form

\( 128 q + 128 q^{4} - 4 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7650))\) 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	5	17
7650.2.a.a	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓	✓			7650.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-5\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-5q^{7}-q^{8}-5q^{11}+5q^{14}+\cdots\)
7650.2.a.b	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				2550.2.a.g	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-5\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-5q^{7}-q^{8}+q^{11}+2q^{13}+\cdots\)
7650.2.a.c	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				2550.2.a.q	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-4q^{7}-q^{8}-2q^{11}-2q^{13}+\cdots\)
7650.2.a.d	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				2550.2.a.p	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-4q^{7}-q^{8}+2q^{11}-6q^{13}+\cdots\)
7650.2.a.e	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				510.2.d.a	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-4q^{7}-q^{8}+2q^{11}+4q^{13}+\cdots\)
7650.2.a.f	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				2550.2.a.f	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-3\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-3q^{7}-q^{8}+5q^{11}-4q^{13}+\cdots\)
7650.2.a.g	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				170.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{7}-q^{8}-6q^{11}-2q^{13}+\cdots\)
7650.2.a.h	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓	✓			7650.2.a.h	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{7}-q^{8}-2q^{11}+2q^{14}+\cdots\)
7650.2.a.i	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				170.2.a.c	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{7}-q^{8}-5q^{13}+2q^{14}+\cdots\)
7650.2.a.j	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				102.2.a.b	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{7}-q^{8}-2q^{13}+2q^{14}+\cdots\)
7650.2.a.k	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				510.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{7}-q^{8}+4q^{11}-4q^{13}+\cdots\)
7650.2.a.l	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				170.2.a.d	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{7}-q^{8}+4q^{11}+3q^{13}+\cdots\)
7650.2.a.m	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓	✓			7650.2.a.m	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{7}-q^{8}+6q^{11}+4q^{13}+\cdots\)
7650.2.a.n	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓	✓			7650.2.a.n	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{7}-q^{8}+3q^{11}-4q^{13}+\cdots\)
7650.2.a.o	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				2550.2.a.m	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{7}-q^{8}+3q^{11}+4q^{13}+\cdots\)
7650.2.a.p	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				2550.2.a.e	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{8}-6q^{11}-2q^{13}+\cdots\)
7650.2.a.q	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				1530.2.d.a	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{8}+q^{16}+q^{17}-4q^{19}+\cdots\)
7650.2.a.r	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				1530.2.d.a	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{8}+q^{16}+q^{17}-4q^{19}+\cdots\)
7650.2.a.s	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				170.2.c.a	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{8}+6q^{11}-3q^{13}+\cdots\)
7650.2.a.t	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				2550.2.a.k	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{7}-q^{8}-3q^{11}+4q^{13}+\cdots\)
7650.2.a.u	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓	✓			7650.2.a.n	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{7}-q^{8}-3q^{11}+4q^{13}+\cdots\)
7650.2.a.v	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				2550.2.a.j	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{7}-q^{8}+3q^{11}-2q^{13}+\cdots\)
7650.2.a.w	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				850.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{7}-q^{8}+4q^{11}-3q^{13}+\cdots\)
7650.2.a.x	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓	✓			7650.2.a.m	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{7}-q^{8}-6q^{11}-4q^{13}+\cdots\)
7650.2.a.y	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				510.2.a.b	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{7}-q^{8}-4q^{11}-2q^{14}+\cdots\)
7650.2.a.z	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				102.2.a.a	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{7}-q^{8}+6q^{13}-2q^{14}+\cdots\)
7650.2.a.ba	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓	✓			7650.2.a.h	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{7}-q^{8}+2q^{11}-2q^{14}+\cdots\)
7650.2.a.bb	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				1530.2.a.e	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{7}-q^{8}+2q^{11}-2q^{14}+\cdots\)
7650.2.a.bc	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				170.2.a.b	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{7}-q^{8}+2q^{11}+6q^{13}+\cdots\)
7650.2.a.bd	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				2550.2.a.a	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(3\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{7}-q^{8}+3q^{11}+4q^{13}+\cdots\)
7650.2.a.be	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				2550.2.a.h	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(3\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{7}-q^{8}+5q^{11}-2q^{13}+\cdots\)
7650.2.a.bf	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				1530.2.a.a	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+4q^{7}-q^{8}-2q^{11}+6q^{13}+\cdots\)
7650.2.a.bg	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				850.2.a.c	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(5\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+5q^{7}-q^{8}-4q^{11}-3q^{13}+\cdots\)
7650.2.a.bh	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓	✓			7650.2.a.a	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(5\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+5q^{7}-q^{8}+5q^{11}-5q^{14}+\cdots\)
7650.2.a.bi	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				850.2.a.c	$1$	$0$	\(1\)	\(0\)	\(0\)	\(-5\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-5q^{7}+q^{8}-4q^{11}+3q^{13}+\cdots\)
7650.2.a.bj	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓	✓			7650.2.a.a	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-5\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-5q^{7}+q^{8}+5q^{11}-5q^{14}+\cdots\)
7650.2.a.bk	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				2550.2.a.a	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-3\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{7}+q^{8}+3q^{11}-4q^{13}+\cdots\)
7650.2.a.bl	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				2550.2.a.h	$1$	$0$	\(1\)	\(0\)	\(0\)	\(-3\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{7}+q^{8}+5q^{11}+2q^{13}+\cdots\)
7650.2.a.bm	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓	✓			7650.2.a.m	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{7}+q^{8}-6q^{11}+4q^{13}+\cdots\)
7650.2.a.bn	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				510.2.a.d	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{7}+q^{8}-4q^{13}-2q^{14}+\cdots\)
7650.2.a.bo	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				170.2.a.e	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{7}+q^{8}+q^{13}-2q^{14}+\cdots\)
7650.2.a.bp	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				510.2.a.g	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{7}+q^{8}+4q^{13}-2q^{14}+\cdots\)
7650.2.a.bq	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓	✓			7650.2.a.h	$1$	$0$	\(1\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{7}+q^{8}+2q^{11}-2q^{14}+\cdots\)
7650.2.a.br	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				2550.2.a.k	$1$	$0$	\(1\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{11}-4q^{13}+\cdots\)
7650.2.a.bs	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓	✓			7650.2.a.n	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{11}-4q^{13}+\cdots\)
7650.2.a.bt	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				2550.2.a.j	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{7}+q^{8}+3q^{11}+2q^{13}+\cdots\)
7650.2.a.bu	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				850.2.a.a	$1$	$0$	\(1\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{7}+q^{8}+4q^{11}+3q^{13}+\cdots\)
7650.2.a.bv	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				2550.2.a.e	$1$	$1$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{8}-6q^{11}+2q^{13}+\cdots\)
7650.2.a.bw	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				510.2.a.f	$1$	$0$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{8}-4q^{11}-2q^{13}+\cdots\)
7650.2.a.bx	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				510.2.a.e	$1$	$0$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{8}-4q^{11}+2q^{13}+\cdots\)
7650.2.a.by	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				1530.2.d.a	$1$	$1$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{8}+q^{16}-q^{17}-4q^{19}+\cdots\)
7650.2.a.bz	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				1530.2.d.a	$1$	$1$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{8}+q^{16}-q^{17}-4q^{19}+\cdots\)
7650.2.a.ca	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				102.2.a.c	$1$	$0$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{8}+4q^{11}+2q^{13}+\cdots\)
7650.2.a.cb	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				170.2.c.a	$1$	$0$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{8}+6q^{11}+3q^{13}+\cdots\)
7650.2.a.cc	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				2550.2.a.m	$1$	$1$	\(1\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{7}+q^{8}+3q^{11}-4q^{13}+\cdots\)
7650.2.a.cd	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓	✓			7650.2.a.n	$1$	$0$	\(1\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{7}+q^{8}+3q^{11}+4q^{13}+\cdots\)
7650.2.a.ce	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓	✓			7650.2.a.h	$1$	$1$	\(1\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{7}+q^{8}-2q^{11}+2q^{14}+\cdots\)
7650.2.a.cf	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				1530.2.a.e	$1$	$0$	\(1\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{7}+q^{8}-2q^{11}+2q^{14}+\cdots\)
7650.2.a.cg	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓	✓			7650.2.a.m	$1$	$0$	\(1\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{7}+q^{8}+6q^{11}-4q^{13}+\cdots\)
7650.2.a.ch	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				2550.2.a.f	$1$	$0$	\(1\)	\(0\)	\(0\)	\(3\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+3q^{7}+q^{8}+5q^{11}+4q^{13}+\cdots\)
7650.2.a.ci	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				34.2.a.a	$1$	$1$	\(1\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+4q^{7}+q^{8}-6q^{11}-2q^{13}+\cdots\)
7650.2.a.cj	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				2550.2.a.q	$1$	$0$	\(1\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+4q^{7}+q^{8}-2q^{11}+2q^{13}+\cdots\)
7650.2.a.ck	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				510.2.d.a	$1$	$0$	\(1\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+4q^{7}+q^{8}+2q^{11}-4q^{13}+\cdots\)
7650.2.a.cl	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				1530.2.a.a	$1$	$0$	\(1\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+4q^{7}+q^{8}+2q^{11}+6q^{13}+\cdots\)
7650.2.a.cm	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				2550.2.a.p	$1$	$0$	\(1\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+4q^{7}+q^{8}+2q^{11}+6q^{13}+\cdots\)
7650.2.a.cn	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				510.2.a.c	$1$	$0$	\(1\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+4q^{7}+q^{8}+4q^{11}+2q^{13}+\cdots\)
7650.2.a.co	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓	✓			7650.2.a.a	$1$	$0$	\(1\)	\(0\)	\(0\)	\(5\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+5q^{7}+q^{8}-5q^{11}+5q^{14}+\cdots\)
7650.2.a.cp	$7650$	$2$	7650.a	1.a	$1$	$1$	$1$	$61.086$	\(\Q\)	None	✓				2550.2.a.g	$1$	$0$	\(1\)	\(0\)	\(0\)	\(5\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+5q^{7}+q^{8}+q^{11}-2q^{13}+\cdots\)
7650.2.a.cq	$7650$	$2$	7650.a	1.a	$1$	$2$	$2$	$61.086$	\(\Q(\sqrt{6}) \)	None	✓		✓		306.2.a.e	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-2+\beta )q^{7}-q^{8}-2\beta q^{11}+\cdots\)
7650.2.a.cr	$7650$	$2$	7650.a	1.a	$1$	$2$	$2$	$61.086$	\(\Q(\sqrt{2}) \)	None	✓	✓			7650.2.a.cr	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-1+\beta )q^{7}-q^{8}-q^{11}+\cdots\)
7650.2.a.cs	$7650$	$2$	7650.a	1.a	$1$	$2$	$2$	$61.086$	\(\Q(\sqrt{5}) \)	None	✓				1530.2.a.q	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-1-\beta )q^{7}-q^{8}+2q^{11}+\cdots\)
7650.2.a.ct	$7650$	$2$	7650.a	1.a	$1$	$2$	$2$	$61.086$	\(\Q(\sqrt{6}) \)	None	✓				510.2.d.c	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta q^{7}-q^{8}+2\beta q^{11}+\cdots\)
7650.2.a.cu	$7650$	$2$	7650.a	1.a	$1$	$2$	$2$	$61.086$	\(\Q(\sqrt{6}) \)	None	✓		✓		510.2.a.h	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta q^{7}-q^{8}+(-2-\beta )q^{13}+\cdots\)
7650.2.a.cv	$7650$	$2$	7650.a	1.a	$1$	$2$	$2$	$61.086$	\(\Q(\sqrt{33}) \)	None	✓				2550.2.a.bg	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta q^{7}-q^{8}+(-2+\beta )q^{11}+\cdots\)
7650.2.a.cw	$7650$	$2$	7650.a	1.a	$1$	$2$	$2$	$61.086$	\(\Q(\sqrt{2}) \)	None	✓				850.2.a.m	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(1+\beta )q^{7}-q^{8}-2q^{11}+\cdots\)
7650.2.a.cx	$7650$	$2$	7650.a	1.a	$1$	$2$	$2$	$61.086$	\(\Q(\sqrt{5}) \)	None	✓				510.2.d.b	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(1+\beta )q^{7}-q^{8}-2q^{11}+\cdots\)
7650.2.a.cy	$7650$	$2$	7650.a	1.a	$1$	$2$	$2$	$61.086$	\(\Q(\sqrt{2}) \)	None	✓	✓			7650.2.a.cr	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(1+\beta )q^{7}-q^{8}+q^{11}+\cdots\)
7650.2.a.cz	$7650$	$2$	7650.a	1.a	$1$	$2$	$2$	$61.086$	\(\Q(\sqrt{6}) \)	None	✓		✓		306.2.a.e	$1$	$0$	\(2\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-2+\beta )q^{7}+q^{8}+2\beta q^{11}+\cdots\)
7650.2.a.da	$7650$	$2$	7650.a	1.a	$1$	$2$	$2$	$61.086$	\(\Q(\sqrt{5}) \)	None	✓				510.2.d.b	$1$	$1$	\(2\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-1-\beta )q^{7}+q^{8}-2q^{11}+\cdots\)
7650.2.a.db	$7650$	$2$	7650.a	1.a	$1$	$2$	$2$	$61.086$	\(\Q(\sqrt{5}) \)	None	✓				1530.2.a.q	$1$	$1$	\(2\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-1-\beta )q^{7}+q^{8}-2q^{11}+\cdots\)
7650.2.a.dc	$7650$	$2$	7650.a	1.a	$1$	$2$	$2$	$61.086$	\(\Q(\sqrt{2}) \)	None	✓				850.2.a.m	$1$	$0$	\(2\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-1+\beta )q^{7}+q^{8}-2q^{11}+\cdots\)
7650.2.a.dd	$7650$	$2$	7650.a	1.a	$1$	$2$	$2$	$61.086$	\(\Q(\sqrt{2}) \)	None	✓	✓			7650.2.a.cr	$1$	$1$	\(2\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-1+\beta )q^{7}+q^{8}+q^{11}+\cdots\)
7650.2.a.de	$7650$	$2$	7650.a	1.a	$1$	$2$	$2$	$61.086$	\(\Q(\sqrt{17}) \)	None	✓				170.2.a.f	$1$	$0$	\(2\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2\beta q^{7}+q^{8}+4q^{11}+\cdots\)
7650.2.a.df	$7650$	$2$	7650.a	1.a	$1$	$2$	$2$	$61.086$	\(\Q(\sqrt{33}) \)	None	✓		✓		2550.2.a.bg	$1$	$1$	\(2\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-\beta q^{7}+q^{8}+(-2+\beta )q^{11}+\cdots\)
7650.2.a.dg	$7650$	$2$	7650.a	1.a	$1$	$2$	$2$	$61.086$	\(\Q(\sqrt{6}) \)	None	✓				510.2.d.c	$1$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta q^{7}+q^{8}-2\beta q^{11}+\cdots\)
7650.2.a.dh	$7650$	$2$	7650.a	1.a	$1$	$2$	$2$	$61.086$	\(\Q(\sqrt{2}) \)	None	✓	✓			7650.2.a.cr	$1$	$0$	\(2\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(1+\beta )q^{7}+q^{8}-q^{11}+\cdots\)
7650.2.a.di	$7650$	$2$	7650.a	1.a	$1$	$3$	$3$	$61.086$	3.3.148.1	None	✓				1530.2.d.h	$1$	$0$	\(-3\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta _{2}q^{7}-q^{8}-4q^{11}+\cdots\)
7650.2.a.dj	$7650$	$2$	7650.a	1.a	$1$	$3$	$3$	$61.086$	3.3.568.1	None	✓		✓		170.2.c.b	$1$	$1$	\(-3\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(\beta _{1}+\beta _{2})q^{7}-q^{8}-2q^{11}+\cdots\)
7650.2.a.dk	$7650$	$2$	7650.a	1.a	$1$	$3$	$3$	$61.086$	3.3.148.1	None	✓				1530.2.d.h	$1$	$0$	\(-3\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-\beta _{2}q^{7}-q^{8}+4q^{11}+\cdots\)
7650.2.a.dl	$7650$	$2$	7650.a	1.a	$1$	$3$	$3$	$61.086$	3.3.568.1	None	✓		✓		510.2.d.d	$1$	$0$	\(-3\)	\(0\)	\(0\)	\(6\)		$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(2+\beta _{1})q^{7}-q^{8}+(-1+\cdots)q^{11}+\cdots\)
7650.2.a.dm	$7650$	$2$	7650.a	1.a	$1$	$3$	$3$	$61.086$	3.3.568.1	None	✓		✓		510.2.d.d	$1$	$0$	\(3\)	\(0\)	\(0\)	\(-6\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-2-\beta _{1})q^{7}+q^{8}+(-1+\cdots)q^{11}+\cdots\)
7650.2.a.dn	$7650$	$2$	7650.a	1.a	$1$	$3$	$3$	$61.086$	3.3.148.1	None	✓				1530.2.d.h	$1$	$0$	\(3\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-\beta _{2}q^{7}+q^{8}-4q^{11}+\cdots\)
7650.2.a.do	$7650$	$2$	7650.a	1.a	$1$	$3$	$3$	$61.086$	3.3.568.1	None	✓		✓		170.2.c.b	$1$	$1$	\(3\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-\beta _{1}-\beta _{2})q^{7}+q^{8}+\cdots\)
7650.2.a.dp	$7650$	$2$	7650.a	1.a	$1$	$3$	$3$	$61.086$	3.3.148.1	None	✓				1530.2.d.h	$1$	$0$	\(3\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta _{2}q^{7}+q^{8}+4q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7650))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7650)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(153))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(170))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(255))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(306))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(425))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(450))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(510))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(765))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(850))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1275))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1530))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2550))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3825))\)\(^{\oplus 2}\)