Space of modular forms of level 9968, weight 2, and trivial character

• Label: 9968.2.a
• Level: $9968$
• Weight: $2$
• Character orbit: 9968.a
• Rep. character: $\chi_{9968}(1,\cdot)$
• Character field: $\Q$
• Dimension: $264$
• Newform subspaces: $43$
• Sturm bound: $2880$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 9968 = 2^{4} \cdot 7 \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9968.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 43 \)
Sturm bound:			\(2880\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9968))\).

	Total	New	Old
Modular forms	1452	264	1188
Cusp forms	1429	264	1165
Eisenstein series	23	0	23

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

\(2\)	\(7\)	\(89\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(33\)
\(+\)	\(+\)	\(-\)	\(-\)	\(33\)
\(+\)	\(-\)	\(+\)	\(-\)	\(33\)
\(+\)	\(-\)	\(-\)	\(+\)	\(33\)
\(-\)	\(+\)	\(+\)	\(-\)	\(38\)
\(-\)	\(+\)	\(-\)	\(+\)	\(27\)
\(-\)	\(-\)	\(+\)	\(+\)	\(28\)
\(-\)	\(-\)	\(-\)	\(-\)	\(39\)
Plus space			\(+\)	\(121\)
Minus space			\(-\)	\(143\)

Trace form

\( 264 q + 2 q^{7} + 264 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9968))\) 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	7	89
9968.2.a.a	$9968$	$2$	9968.a	1.a	$1$	$1$	$1$	$79.595$	\(\Q\)	None	✓				4984.2.a.c	$1$	$1$	\(0\)	\(-3\)	\(-1\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-q^{5}+q^{7}+6q^{9}-2q^{11}+\cdots\)
9968.2.a.b	$9968$	$2$	9968.a	1.a	$1$	$1$	$1$	$79.595$	\(\Q\)	None	✓				4984.2.a.d	$1$	$1$	\(0\)	\(-3\)	\(3\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+3q^{5}+q^{7}+6q^{9}-4q^{11}+\cdots\)
9968.2.a.c	$9968$	$2$	9968.a	1.a	$1$	$1$	$1$	$79.595$	\(\Q\)	None	✓				1246.2.a.f	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{5}-q^{7}+q^{9}-4q^{13}+\cdots\)
9968.2.a.d	$9968$	$2$	9968.a	1.a	$1$	$1$	$1$	$79.595$	\(\Q\)	None	✓				1246.2.a.g	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+2q^{5}+q^{7}+q^{9}+4q^{13}+\cdots\)
9968.2.a.e	$9968$	$2$	9968.a	1.a	$1$	$1$	$1$	$79.595$	\(\Q\)	None	✓				4984.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}-2q^{9}+4q^{13}+q^{15}+\cdots\)
9968.2.a.f	$9968$	$2$	9968.a	1.a	$1$	$1$	$1$	$79.595$	\(\Q\)	None	✓				1246.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}-2q^{9}+6q^{11}+4q^{13}+\cdots\)
9968.2.a.g	$9968$	$2$	9968.a	1.a	$1$	$1$	$1$	$79.595$	\(\Q\)	None	✓				2492.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}-q^{7}-2q^{9}-4q^{13}+\cdots\)
9968.2.a.h	$9968$	$2$	9968.a	1.a	$1$	$1$	$1$	$79.595$	\(\Q\)	None	✓				1246.2.a.i	$1$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-3q^{9}+4q^{11}-2q^{13}-2q^{17}+\cdots\)
9968.2.a.i	$9968$	$2$	9968.a	1.a	$1$	$1$	$1$	$79.595$	\(\Q\)	None	✓				2492.2.a.b	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}+q^{7}-2q^{9}+6q^{11}+\cdots\)
9968.2.a.j	$9968$	$2$	9968.a	1.a	$1$	$1$	$1$	$79.595$	\(\Q\)	None	✓				1246.2.a.c	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}-2q^{9}-6q^{11}+4q^{13}+\cdots\)
9968.2.a.k	$9968$	$2$	9968.a	1.a	$1$	$1$	$1$	$79.595$	\(\Q\)	None	✓				1246.2.a.h	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}-2q^{9}+4q^{13}-q^{15}+\cdots\)
9968.2.a.l	$9968$	$2$	9968.a	1.a	$1$	$1$	$1$	$79.595$	\(\Q\)	None	✓				1246.2.a.d	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}-2q^{9}+2q^{13}+q^{15}+\cdots\)
9968.2.a.m	$9968$	$2$	9968.a	1.a	$1$	$1$	$1$	$79.595$	\(\Q\)	None	✓				623.2.a.a	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}-2q^{9}+4q^{11}+2q^{13}+\cdots\)
9968.2.a.n	$9968$	$2$	9968.a	1.a	$1$	$1$	$1$	$79.595$	\(\Q\)	None	✓				4984.2.a.a	$1$	$1$	\(0\)	\(1\)	\(3\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}+q^{7}-2q^{9}-2q^{11}+\cdots\)
9968.2.a.o	$9968$	$2$	9968.a	1.a	$1$	$1$	$1$	$79.595$	\(\Q\)	None	✓				1246.2.a.b	$1$	$1$	\(0\)	\(2\)	\(-4\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-4q^{5}-q^{7}+q^{9}+4q^{13}+\cdots\)
9968.2.a.p	$9968$	$2$	9968.a	1.a	$1$	$1$	$1$	$79.595$	\(\Q\)	None	✓				1246.2.a.a	$1$	$0$	\(0\)	\(3\)	\(-3\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-3q^{5}+q^{7}+6q^{9}-6q^{13}+\cdots\)
9968.2.a.q	$9968$	$2$	9968.a	1.a	$1$	$1$	$1$	$79.595$	\(\Q\)	None	✓				2492.2.a.a	$1$	$0$	\(0\)	\(3\)	\(3\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+3q^{5}+q^{7}+6q^{9}+4q^{11}+\cdots\)
9968.2.a.r	$9968$	$2$	9968.a	1.a	$1$	$2$	$2$	$79.595$	\(\Q(\sqrt{5}) \)	None	✓				4984.2.a.e	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta q^{5}-q^{7}-2q^{9}+(-2-2\beta )q^{11}+\cdots\)
9968.2.a.s	$9968$	$2$	9968.a	1.a	$1$	$2$	$2$	$79.595$	\(\Q(\sqrt{5}) \)	None	✓				1246.2.a.j	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+q^{7}-2q^{9}+(1+\beta )q^{11}+\cdots\)
9968.2.a.t	$9968$	$2$	9968.a	1.a	$1$	$2$	$2$	$79.595$	\(\Q(\sqrt{5}) \)	None	✓				623.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(2\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-q^{5}+q^{7}+2q^{9}+2\beta q^{11}+\cdots\)
9968.2.a.u	$9968$	$2$	9968.a	1.a	$1$	$2$	$2$	$79.595$	\(\Q(\sqrt{17}) \)	None	✓				1246.2.a.k	$1$	$0$	\(0\)	\(1\)	\(-3\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-2+\beta )q^{5}+q^{7}+(1+\beta )q^{9}+\cdots\)
9968.2.a.v	$9968$	$2$	9968.a	1.a	$1$	$3$	$3$	$79.595$	3.3.404.1	None	✓				1246.2.a.l	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{2})q^{3}+(-1+\beta _{1})q^{5}+q^{7}+\cdots\)
9968.2.a.w	$9968$	$2$	9968.a	1.a	$1$	$4$	$4$	$79.595$	4.4.725.1	None	✓				623.2.a.c	$1$	$1$	\(0\)	\(2\)	\(0\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}+(-\beta _{2}+\beta _{3})q^{5}+q^{7}+(-2+\cdots)q^{9}+\cdots\)
9968.2.a.x	$9968$	$2$	9968.a	1.a	$1$	$4$	$4$	$79.595$	4.4.11344.1	None	✓				1246.2.a.m	$1$	$0$	\(0\)	\(2\)	\(4\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}+(1-\beta _{1}-\beta _{3})q^{5}+q^{7}+(1+\cdots)q^{9}+\cdots\)
9968.2.a.y	$9968$	$2$	9968.a	1.a	$1$	$5$	$5$	$79.595$	5.5.81589.1	None	✓				623.2.a.d	$1$	$1$	\(0\)	\(3\)	\(-5\)	\(-5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(-1+\beta _{3}+\cdots)q^{5}+\cdots\)
9968.2.a.z	$9968$	$2$	9968.a	1.a	$1$	$5$	$5$	$79.595$	5.5.135076.1	None	✓				1246.2.a.n	$1$	$0$	\(0\)	\(6\)	\(-10\)	\(-5\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{4})q^{3}+(-2+\beta _{2})q^{5}-q^{7}+\cdots\)
9968.2.a.ba	$9968$	$2$	9968.a	1.a	$1$	$6$	$6$	$79.595$	6.6.17756288.1	None	✓				1246.2.a.q	$1$	$1$	\(0\)	\(-4\)	\(6\)	\(-6\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+(1-\beta _{4})q^{5}-q^{7}+\cdots\)
9968.2.a.bb	$9968$	$2$	9968.a	1.a	$1$	$6$	$6$	$79.595$	6.6.14378816.1	None	✓				1246.2.a.o	$1$	$0$	\(0\)	\(-2\)	\(6\)	\(-6\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}+(1+\beta _{2}-\beta _{4})q^{5}-q^{7}+(1+\cdots)q^{9}+\cdots\)
9968.2.a.bc	$9968$	$2$	9968.a	1.a	$1$	$6$	$6$	$79.595$	6.6.88017152.1	None	✓				1246.2.a.p	$1$	$1$	\(0\)	\(0\)	\(2\)	\(6\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{4}q^{5}+q^{7}+(1-\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots\)
9968.2.a.bd	$9968$	$2$	9968.a	1.a	$1$	$10$	$10$	$79.595$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		2492.2.a.f	$1$	$1$	\(0\)	\(-6\)	\(3\)	\(10\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+\beta _{2}q^{5}+q^{7}+(-\beta _{2}+\cdots)q^{9}+\cdots\)
9968.2.a.be	$9968$	$2$	9968.a	1.a	$1$	$10$	$10$	$79.595$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		2492.2.a.e	$1$	$1$	\(0\)	\(-4\)	\(3\)	\(-10\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{5}q^{5}-q^{7}+(1+\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
9968.2.a.bf	$9968$	$2$	9968.a	1.a	$1$	$10$	$10$	$79.595$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓				2492.2.a.d	$1$	$0$	\(0\)	\(0\)	\(-5\)	\(10\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{7}q^{5}+q^{7}+(\beta _{5}+\beta _{6})q^{9}+\cdots\)
9968.2.a.bg	$9968$	$2$	9968.a	1.a	$1$	$11$	$11$	$79.595$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓				2492.2.a.g	$1$	$0$	\(0\)	\(7\)	\(-4\)	\(-11\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}-\beta _{4}q^{5}-q^{7}+(1-\beta _{3}+\cdots)q^{9}+\cdots\)
9968.2.a.bh	$9968$	$2$	9968.a	1.a	$1$	$13$	$13$	$79.595$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓				4984.2.a.f	$1$	$1$	\(0\)	\(-3\)	\(-12\)	\(13\)		$+$	$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1+\beta _{6})q^{5}+q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
9968.2.a.bi	$9968$	$2$	9968.a	1.a	$1$	$14$	$14$	$79.595$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓				4984.2.a.h	$1$	$1$	\(0\)	\(5\)	\(-10\)	\(-14\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1+\beta _{6})q^{5}-q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
9968.2.a.bj	$9968$	$2$	9968.a	1.a	$1$	$14$	$14$	$79.595$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓				4984.2.a.g	$1$	$0$	\(0\)	\(6\)	\(-3\)	\(-14\)		$+$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{3}q^{5}-q^{7}+(\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{9}+\cdots\)
9968.2.a.bk	$9968$	$2$	9968.a	1.a	$1$	$16$	$16$	$79.595$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓		✓		623.2.a.e	$1$	$0$	\(0\)	\(-6\)	\(6\)	\(-16\)		$-$	$+$	$+$	$-$	$2^{6}$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}-\beta _{10}q^{5}-q^{7}+(1+\beta _{8})q^{9}+\cdots\)
9968.2.a.bl	$9968$	$2$	9968.a	1.a	$1$	$16$	$16$	$79.595$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓				4984.2.a.i	$1$	$0$	\(0\)	\(3\)	\(2\)	\(16\)		$+$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{15}q^{5}+q^{7}+(1+\beta _{2})q^{9}+\cdots\)
9968.2.a.bm	$9968$	$2$	9968.a	1.a	$1$	$17$	$17$	$79.595$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓		✓		4984.2.a.l	$1$	$1$	\(0\)	\(-5\)	\(6\)	\(-17\)		$+$	$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{5}q^{5}-q^{7}+(1+\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots\)
9968.2.a.bn	$9968$	$2$	9968.a	1.a	$1$	$17$	$17$	$79.595$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓		✓		623.2.a.f	$1$	$0$	\(0\)	\(-4\)	\(6\)	\(17\)		$-$	$-$	$-$	$-$	$2^{6}$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}+\beta _{14}q^{5}+q^{7}+(2-\beta _{8})q^{9}+\cdots\)
9968.2.a.bo	$9968$	$2$	9968.a	1.a	$1$	$17$	$17$	$79.595$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓		✓		4984.2.a.k	$1$	$1$	\(0\)	\(0\)	\(-7\)	\(17\)		$+$	$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{9}q^{5}+q^{7}+(1+\beta _{2})q^{9}+\cdots\)
9968.2.a.bp	$9968$	$2$	9968.a	1.a	$1$	$17$	$17$	$79.595$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓		✓		4984.2.a.j	$1$	$0$	\(0\)	\(5\)	\(6\)	\(17\)		$+$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{7}q^{5}+q^{7}+(1+\beta _{2})q^{9}+\cdots\)
9968.2.a.bq	$9968$	$2$	9968.a	1.a	$1$	$18$	$18$	$79.595$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓		✓		4984.2.a.m	$1$	$0$	\(0\)	\(-3\)	\(14\)	\(-18\)		$+$	$+$	$-$	$-$	$2^{7}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(1+\beta _{3})q^{5}-q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9968))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9968)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(89))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(178))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(356))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(623))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(712))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1246))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1424))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2492))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4984))\)\(^{\oplus 2}\)