Space of modular forms of level 3776, weight 2, and trivial character

• Label: 3776.2.a
• Level: $3776$
• Weight: $2$
• Character orbit: 3776.a
• Rep. character: $\chi_{3776}(1,\cdot)$
• Character field: $\Q$
• Dimension: $116$
• Newform subspaces: $46$
• Sturm bound: $960$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 3776 = 2^{6} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3776.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 46 \)
Sturm bound:			\(960\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3776))\).

	Total	New	Old
Modular forms	492	116	376
Cusp forms	469	116	353
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.

\(2\)	\(59\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(114\)	\(25\)	\(89\)		\(109\)	\(25\)	\(84\)		\(5\)	\(0\)	\(5\)
\(+\)	\(-\)	\(-\)		\(132\)	\(34\)	\(98\)		\(126\)	\(34\)	\(92\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)		\(132\)	\(33\)	\(99\)		\(126\)	\(33\)	\(93\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)		\(114\)	\(24\)	\(90\)		\(108\)	\(24\)	\(84\)		\(6\)	\(0\)	\(6\)
Plus space		\(+\)		\(228\)	\(49\)	\(179\)		\(217\)	\(49\)	\(168\)		\(11\)	\(0\)	\(11\)
Minus space		\(-\)		\(264\)	\(67\)	\(197\)		\(252\)	\(67\)	\(185\)		\(12\)	\(0\)	\(12\)

Trace form

116 * q + 116 * q^9 + 16 * q^13 - 8 * q^17 + 16 * q^21 + 108 * q^25 - 16 * q^29 - 8 * q^41 + 116 * q^49 - 16 * q^53 - 16 * q^61 - 32 * q^69 + 8 * q^73 + 32 * q^77 + 84 * q^81 + 16 * q^85 - 24 * q^89 + 16 * q^93 - 8 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3776))\) 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	59
3776.2.a.a	$3776$	$2$	3776.a	1.a	$1$	$1$	$1$	$30.152$	\(\Q\)	None	✓				1888.2.a.a	$1$	$1$	\(0\)	\(-3\)	\(-1\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-q^{5}+3q^{7}+6q^{9}+3q^{15}+\cdots\)
3776.2.a.b	$3776$	$2$	3776.a	1.a	$1$	$1$	$1$	$30.152$	\(\Q\)	None	✓				472.2.a.a	$1$	$2$	\(0\)	\(-3\)	\(1\)	\(-3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+q^{5}-3q^{7}+6q^{9}-4q^{11}+\cdots\)
3776.2.a.c	$3776$	$2$	3776.a	1.a	$1$	$1$	$1$	$30.152$	\(\Q\)	None	✓				472.2.a.e	$1$	$0$	\(0\)	\(-3\)	\(3\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+3q^{5}+3q^{7}+6q^{9}-6q^{11}+\cdots\)
3776.2.a.d	$3776$	$2$	3776.a	1.a	$1$	$1$	$1$	$30.152$	\(\Q\)	None	✓				118.2.a.b	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{5}-3q^{7}+q^{9}-q^{11}+\cdots\)
3776.2.a.e	$3776$	$2$	3776.a	1.a	$1$	$1$	$1$	$30.152$	\(\Q\)	None	✓				472.2.a.d	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{5}+q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
3776.2.a.f	$3776$	$2$	3776.a	1.a	$1$	$1$	$1$	$30.152$	\(\Q\)	None	✓				118.2.a.d	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(-3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+2q^{5}-3q^{7}+q^{9}+q^{11}+\cdots\)
3776.2.a.g	$3776$	$2$	3776.a	1.a	$1$	$1$	$1$	$30.152$	\(\Q\)	None	✓				236.2.a.b	$1$	$2$	\(0\)	\(-1\)	\(-3\)	\(-1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}-q^{7}-2q^{9}-6q^{11}+\cdots\)
3776.2.a.h	$3776$	$2$	3776.a	1.a	$1$	$1$	$1$	$30.152$	\(\Q\)	None	✓				118.2.a.c	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-3q^{7}-2q^{9}+2q^{11}+\cdots\)
3776.2.a.i	$3776$	$2$	3776.a	1.a	$1$	$1$	$1$	$30.152$	\(\Q\)	None	✓				472.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}-2q^{9}+2q^{13}-q^{15}+\cdots\)
3776.2.a.j	$3776$	$2$	3776.a	1.a	$1$	$1$	$1$	$30.152$	\(\Q\)	None	✓				472.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}-2q^{9}+4q^{11}-2q^{13}+\cdots\)
3776.2.a.k	$3776$	$2$	3776.a	1.a	$1$	$1$	$1$	$30.152$	\(\Q\)	None	✓				236.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+3q^{7}-2q^{9}-2q^{11}+\cdots\)
3776.2.a.l	$3776$	$2$	3776.a	1.a	$1$	$1$	$1$	$30.152$	\(\Q\)	None	✓				118.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}+q^{7}-2q^{9}-2q^{11}+\cdots\)
3776.2.a.m	$3776$	$2$	3776.a	1.a	$1$	$1$	$1$	$30.152$	\(\Q\)	None	✓				1888.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(5\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}+5q^{7}-2q^{9}+4q^{13}+\cdots\)
3776.2.a.n	$3776$	$2$	3776.a	1.a	$1$	$1$	$1$	$30.152$	\(\Q\)	None	✓				236.2.a.b	$1$	$0$	\(0\)	\(1\)	\(-3\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}+q^{7}-2q^{9}+6q^{11}+\cdots\)
3776.2.a.o	$3776$	$2$	3776.a	1.a	$1$	$1$	$1$	$30.152$	\(\Q\)	None	✓				118.2.a.c	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+3q^{7}-2q^{9}-2q^{11}+\cdots\)
3776.2.a.p	$3776$	$2$	3776.a	1.a	$1$	$1$	$1$	$30.152$	\(\Q\)	None	✓				236.2.a.a	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-3q^{7}-2q^{9}+2q^{11}+\cdots\)
3776.2.a.q	$3776$	$2$	3776.a	1.a	$1$	$1$	$1$	$30.152$	\(\Q\)	None	✓				472.2.a.c	$1$	$1$	\(0\)	\(1\)	\(1\)	\(1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}-2q^{9}-4q^{11}-2q^{13}+\cdots\)
3776.2.a.r	$3776$	$2$	3776.a	1.a	$1$	$1$	$1$	$30.152$	\(\Q\)	None	✓				472.2.a.b	$1$	$1$	\(0\)	\(1\)	\(1\)	\(1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}-2q^{9}+2q^{13}+q^{15}+\cdots\)
3776.2.a.s	$3776$	$2$	3776.a	1.a	$1$	$1$	$1$	$30.152$	\(\Q\)	None	✓				1888.2.a.b	$1$	$1$	\(0\)	\(1\)	\(3\)	\(-5\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}-5q^{7}-2q^{9}+4q^{13}+\cdots\)
3776.2.a.t	$3776$	$2$	3776.a	1.a	$1$	$1$	$1$	$30.152$	\(\Q\)	None	✓				118.2.a.a	$1$	$0$	\(0\)	\(1\)	\(3\)	\(-1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}-q^{7}-2q^{9}+2q^{11}+\cdots\)
3776.2.a.u	$3776$	$2$	3776.a	1.a	$1$	$1$	$1$	$30.152$	\(\Q\)	None	✓				472.2.a.d	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(-1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-2q^{5}-q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
3776.2.a.v	$3776$	$2$	3776.a	1.a	$1$	$1$	$1$	$30.152$	\(\Q\)	None	✓				118.2.a.b	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-2q^{5}+3q^{7}+q^{9}+q^{11}+\cdots\)
3776.2.a.w	$3776$	$2$	3776.a	1.a	$1$	$1$	$1$	$30.152$	\(\Q\)	None	✓				118.2.a.d	$1$	$0$	\(0\)	\(2\)	\(2\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+2q^{5}+3q^{7}+q^{9}-q^{11}+\cdots\)
3776.2.a.x	$3776$	$2$	3776.a	1.a	$1$	$1$	$1$	$30.152$	\(\Q\)	None	✓				1888.2.a.a	$1$	$0$	\(0\)	\(3\)	\(-1\)	\(-3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-q^{5}-3q^{7}+6q^{9}-3q^{15}+\cdots\)
3776.2.a.y	$3776$	$2$	3776.a	1.a	$1$	$1$	$1$	$30.152$	\(\Q\)	None	✓				472.2.a.a	$1$	$0$	\(0\)	\(3\)	\(1\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+q^{5}+3q^{7}+6q^{9}+4q^{11}+\cdots\)
3776.2.a.z	$3776$	$2$	3776.a	1.a	$1$	$1$	$1$	$30.152$	\(\Q\)	None	✓				472.2.a.e	$1$	$0$	\(0\)	\(3\)	\(3\)	\(-3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+3q^{5}-3q^{7}+6q^{9}+6q^{11}+\cdots\)
3776.2.a.ba	$3776$	$2$	3776.a	1.a	$1$	$3$	$3$	$30.152$	\(\Q(\zeta_{14})^+\)	None	✓				1888.2.a.e	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+(1-\beta _{1}+2\beta _{2})q^{5}+\cdots\)
3776.2.a.bb	$3776$	$2$	3776.a	1.a	$1$	$3$	$3$	$30.152$	3.3.321.1	None	✓				236.2.a.c	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-8\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{2})q^{3}+(1+\beta _{1})q^{5}+(-3+\cdots)q^{7}+\cdots\)
3776.2.a.bc	$3776$	$2$	3776.a	1.a	$1$	$3$	$3$	$30.152$	3.3.321.1	None	✓				236.2.a.c	$1$	$0$	\(0\)	\(0\)	\(4\)	\(8\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{2})q^{3}+(1+\beta _{1})q^{5}+(3+\beta _{2})q^{7}+\cdots\)
3776.2.a.bd	$3776$	$2$	3776.a	1.a	$1$	$3$	$3$	$30.152$	\(\Q(\zeta_{14})^+\)	None	✓				1888.2.a.e	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(-3+\cdots)q^{7}+\cdots\)
3776.2.a.be	$3776$	$2$	3776.a	1.a	$1$	$4$	$4$	$30.152$	4.4.2777.1	None	✓				1888.2.a.g	$1$	$1$	\(0\)	\(-3\)	\(-5\)	\(3\)		$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{2})q^{3}+(-1-\beta _{2})q^{5}+(1+\cdots)q^{7}+\cdots\)
3776.2.a.bf	$3776$	$2$	3776.a	1.a	$1$	$4$	$4$	$30.152$	4.4.8468.1	None	✓				1888.2.a.h	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(4\)		$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}-\beta _{2}q^{5}+q^{7}+(3-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
3776.2.a.bg	$3776$	$2$	3776.a	1.a	$1$	$4$	$4$	$30.152$	4.4.6809.1	None	✓				472.2.a.f	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(9\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+(2+2\beta _{1}+\cdots)q^{7}+\cdots\)
3776.2.a.bh	$3776$	$2$	3776.a	1.a	$1$	$4$	$4$	$30.152$	4.4.8468.1	None	✓				1888.2.a.h	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-4\)		$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}-\beta _{2}q^{5}-q^{7}+(3-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
3776.2.a.bi	$3776$	$2$	3776.a	1.a	$1$	$4$	$4$	$30.152$	4.4.6809.1	None	✓				472.2.a.f	$1$	$0$	\(0\)	\(1\)	\(3\)	\(-9\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}+(1-\beta _{1}+\beta _{3})q^{5}+(-2-2\beta _{1}+\cdots)q^{7}+\cdots\)
3776.2.a.bj	$3776$	$2$	3776.a	1.a	$1$	$4$	$4$	$30.152$	4.4.2777.1	None	✓				1888.2.a.g	$1$	$0$	\(0\)	\(3\)	\(-5\)	\(-3\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{2})q^{3}+(-1-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
3776.2.a.bk	$3776$	$2$	3776.a	1.a	$1$	$5$	$5$	$30.152$	5.5.791953.1	None	✓				1888.2.a.k	$1$	$1$	\(0\)	\(-3\)	\(-3\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{4})q^{3}+(-\beta _{2}+\beta _{3}+\beta _{4})q^{5}+\cdots\)
3776.2.a.bl	$3776$	$2$	3776.a	1.a	$1$	$5$	$5$	$30.152$	5.5.138136.1	None	✓				59.2.a.a	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+\beta _{1}q^{5}+(-1+\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
3776.2.a.bm	$3776$	$2$	3776.a	1.a	$1$	$5$	$5$	$30.152$	5.5.459533.1	None	✓				1888.2.a.l	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(8\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{4}q^{3}+\beta _{2}q^{5}+(2-\beta _{1})q^{7}+(1-\beta _{2}+\cdots)q^{9}+\cdots\)
3776.2.a.bn	$3776$	$2$	3776.a	1.a	$1$	$5$	$5$	$30.152$	5.5.138136.1	None	✓				59.2.a.a	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(2\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+\beta _{1}q^{5}+(1-\beta _{2}+\beta _{3}-\beta _{4})q^{7}+\cdots\)
3776.2.a.bo	$3776$	$2$	3776.a	1.a	$1$	$5$	$5$	$30.152$	5.5.459533.1	None	✓				1888.2.a.l	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-8\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{3}+\beta _{2}q^{5}+(-2+\beta _{1})q^{7}+(1+\cdots)q^{9}+\cdots\)
3776.2.a.bp	$3776$	$2$	3776.a	1.a	$1$	$5$	$5$	$30.152$	5.5.791953.1	None	✓				1888.2.a.k	$1$	$0$	\(0\)	\(3\)	\(-3\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{4})q^{3}+(-\beta _{2}+\beta _{3}+\beta _{4})q^{5}+\cdots\)
3776.2.a.bq	$3776$	$2$	3776.a	1.a	$1$	$6$	$6$	$30.152$	6.6.921465377.1	None	✓		✓		472.2.a.g	$1$	$0$	\(0\)	\(-1\)	\(-7\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+(1+\beta _{4})q^{7}+\cdots\)
3776.2.a.br	$3776$	$2$	3776.a	1.a	$1$	$6$	$6$	$30.152$	6.6.905177.1	None	✓		✓		1888.2.a.o	$1$	$1$	\(0\)	\(-1\)	\(5\)	\(-5\)		$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(1+\beta _{3})q^{5}+(-1-\beta _{1})q^{7}+\cdots\)
3776.2.a.bs	$3776$	$2$	3776.a	1.a	$1$	$6$	$6$	$30.152$	6.6.921465377.1	None	✓				472.2.a.g	$1$	$0$	\(0\)	\(1\)	\(-7\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+(-1-\beta _{4}+\cdots)q^{7}+\cdots\)
3776.2.a.bt	$3776$	$2$	3776.a	1.a	$1$	$6$	$6$	$30.152$	6.6.905177.1	None	✓				1888.2.a.o	$1$	$0$	\(0\)	\(1\)	\(5\)	\(5\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+(1+\beta _{3})q^{5}+(1+\beta _{1})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3776))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3776)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(118))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(236))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(472))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(944))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1888))\)\(^{\oplus 2}\)