Space of modular forms of level 7644, weight 2, and trivial character

• Label: 7644.2.a
• Level: $7644$
• Weight: $2$
• Character orbit: 7644.a
• Rep. character: $\chi_{7644}(1,\cdot)$
• Character field: $\Q$
• Dimension: $82$
• Newform subspaces: $32$
• Sturm bound: $3136$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 7644 = 2^{2} \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7644.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 32 \)
Sturm bound:			\(3136\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7644))\).

	Total	New	Old
Modular forms	1616	82	1534
Cusp forms	1521	82	1439
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.

\(2\)	\(3\)	\(7\)	\(13\)	Fricke		Total				Cusp				Eisenstein
						All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)		\(92\)	\(0\)	\(92\)		\(85\)	\(0\)	\(85\)		\(7\)	\(0\)	\(7\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)		\(108\)	\(0\)	\(108\)		\(100\)	\(0\)	\(100\)		\(8\)	\(0\)	\(8\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)		\(111\)	\(0\)	\(111\)		\(103\)	\(0\)	\(103\)		\(8\)	\(0\)	\(8\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)		\(95\)	\(0\)	\(95\)		\(87\)	\(0\)	\(87\)		\(8\)	\(0\)	\(8\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)		\(112\)	\(0\)	\(112\)		\(104\)	\(0\)	\(104\)		\(8\)	\(0\)	\(8\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)		\(96\)	\(0\)	\(96\)		\(88\)	\(0\)	\(88\)		\(8\)	\(0\)	\(8\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)		\(93\)	\(0\)	\(93\)		\(85\)	\(0\)	\(85\)		\(8\)	\(0\)	\(8\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)		\(109\)	\(0\)	\(109\)		\(101\)	\(0\)	\(101\)		\(8\)	\(0\)	\(8\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)		\(96\)	\(9\)	\(87\)		\(92\)	\(9\)	\(83\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)		\(104\)	\(11\)	\(93\)		\(100\)	\(11\)	\(89\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)		\(104\)	\(12\)	\(92\)		\(100\)	\(12\)	\(88\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)		\(96\)	\(9\)	\(87\)		\(92\)	\(9\)	\(83\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)		\(104\)	\(9\)	\(95\)		\(100\)	\(9\)	\(91\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)		\(96\)	\(11\)	\(85\)		\(92\)	\(11\)	\(81\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)		\(96\)	\(12\)	\(84\)		\(92\)	\(12\)	\(80\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)		\(104\)	\(9\)	\(95\)		\(100\)	\(9\)	\(91\)		\(4\)	\(0\)	\(4\)
Plus space				\(+\)		\(792\)	\(41\)	\(751\)		\(745\)	\(41\)	\(704\)		\(47\)	\(0\)	\(47\)
Minus space				\(-\)		\(824\)	\(41\)	\(783\)		\(776\)	\(41\)	\(735\)		\(48\)	\(0\)	\(48\)

Trace form

82 * q + 4 * q^5 + 82 * q^9 + 4 * q^11 - 2 * q^13 - 4 * q^15 - 4 * q^17 - 8 * q^19 - 8 * q^23 + 78 * q^25 + 4 * q^29 - 12 * q^33 - 20 * q^37 + 12 * q^41 - 16 * q^43 + 4 * q^45 + 20 * q^47 + 12 * q^53 - 12 * q^57 + 4 * q^59 - 4 * q^61 + 4 * q^65 + 8 * q^67 - 8 * q^69 + 12 * q^71 - 12 * q^73 - 16 * q^75 - 8 * q^79 + 82 * q^81 - 12 * q^83 - 32 * q^85 - 8 * q^87 + 4 * q^89 - 4 * q^93 - 24 * q^95 - 28 * q^97 + 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7644))\) 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	7	13
7644.2.a.a	$7644$	$2$	7644.a	1.a	$1$	$1$	$1$	$61.038$	\(\Q\)	None	✓				156.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}-q^{13}+6q^{17}-2q^{19}+\cdots\)
7644.2.a.b	$7644$	$2$	7644.a	1.a	$1$	$1$	$1$	$61.038$	\(\Q\)	None	✓	✓			7644.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}+2q^{11}-q^{13}-q^{15}+\cdots\)
7644.2.a.c	$7644$	$2$	7644.a	1.a	$1$	$1$	$1$	$61.038$	\(\Q\)	None	✓				1092.2.a.e	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{9}+q^{13}-2q^{15}+\cdots\)
7644.2.a.d	$7644$	$2$	7644.a	1.a	$1$	$1$	$1$	$61.038$	\(\Q\)	None	✓	✓			7644.2.a.d	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}+q^{9}+2q^{11}+q^{13}+\cdots\)
7644.2.a.e	$7644$	$2$	7644.a	1.a	$1$	$1$	$1$	$61.038$	\(\Q\)	None	✓	✓			7644.2.a.d	$1$	$0$	\(0\)	\(1\)	\(-3\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}+q^{9}+2q^{11}-q^{13}+\cdots\)
7644.2.a.f	$7644$	$2$	7644.a	1.a	$1$	$1$	$1$	$61.038$	\(\Q\)	None	✓				1092.2.a.d	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}-6q^{11}+q^{13}-q^{15}+\cdots\)
7644.2.a.g	$7644$	$2$	7644.a	1.a	$1$	$1$	$1$	$61.038$	\(\Q\)	None	✓	✓			7644.2.a.b	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}+2q^{11}+q^{13}-q^{15}+\cdots\)
7644.2.a.h	$7644$	$2$	7644.a	1.a	$1$	$1$	$1$	$61.038$	\(\Q\)	None	✓				1092.2.a.c	$1$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}-2q^{11}+q^{13}-4q^{17}+\cdots\)
7644.2.a.i	$7644$	$2$	7644.a	1.a	$1$	$1$	$1$	$61.038$	\(\Q\)	None	✓				1092.2.a.b	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}+2q^{11}-q^{13}+q^{15}+\cdots\)
7644.2.a.j	$7644$	$2$	7644.a	1.a	$1$	$1$	$1$	$61.038$	\(\Q\)	None	✓				1092.2.a.a	$1$	$1$	\(0\)	\(1\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}+q^{13}+2q^{15}+\cdots\)
7644.2.a.k	$7644$	$2$	7644.a	1.a	$1$	$1$	$1$	$61.038$	\(\Q\)	None	✓				156.2.a.a	$1$	$0$	\(0\)	\(1\)	\(4\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{5}+q^{9}-4q^{11}-q^{13}+\cdots\)
7644.2.a.l	$7644$	$2$	7644.a	1.a	$1$	$2$	$2$	$61.038$	\(\Q(\sqrt{7}) \)	None	✓	✓			7644.2.a.l	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta )q^{5}+q^{9}+(-3+\beta )q^{11}+\cdots\)
7644.2.a.m	$7644$	$2$	7644.a	1.a	$1$	$2$	$2$	$61.038$	\(\Q(\sqrt{3}) \)	None	✓	✓			7644.2.a.m	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta )q^{5}+q^{9}+(1-3\beta )q^{11}+\cdots\)
7644.2.a.n	$7644$	$2$	7644.a	1.a	$1$	$2$	$2$	$61.038$	\(\Q(\sqrt{33}) \)	None	✓				1092.2.a.g	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta q^{5}+q^{9}+2q^{11}+q^{13}+\cdots\)
7644.2.a.o	$7644$	$2$	7644.a	1.a	$1$	$2$	$2$	$61.038$	\(\Q(\sqrt{2}) \)	None	✓				1092.2.q.a	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2\beta q^{5}+q^{9}+(-1-\beta )q^{11}+\cdots\)
7644.2.a.p	$7644$	$2$	7644.a	1.a	$1$	$2$	$2$	$61.038$	\(\Q(\sqrt{5}) \)	None	✓				1092.2.a.f	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta )q^{5}+q^{9}+(1-\beta )q^{11}+\cdots\)
7644.2.a.q	$7644$	$2$	7644.a	1.a	$1$	$2$	$2$	$61.038$	\(\Q(\sqrt{2}) \)	None	✓				1092.2.q.a	$1$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2\beta q^{5}+q^{9}+(-1+\beta )q^{11}+\cdots\)
7644.2.a.r	$7644$	$2$	7644.a	1.a	$1$	$2$	$2$	$61.038$	\(\Q(\sqrt{7}) \)	None	✓	✓			7644.2.a.l	$1$	$1$	\(0\)	\(2\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{5}+q^{9}+(-3-\beta )q^{11}+\cdots\)
7644.2.a.s	$7644$	$2$	7644.a	1.a	$1$	$2$	$2$	$61.038$	\(\Q(\sqrt{3}) \)	None	✓	✓			7644.2.a.m	$1$	$0$	\(0\)	\(2\)	\(2\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{5}+q^{9}+(1+3\beta )q^{11}+\cdots\)
7644.2.a.t	$7644$	$2$	7644.a	1.a	$1$	$3$	$3$	$61.038$	3.3.1373.1	None	✓				1092.2.a.h	$1$	$1$	\(0\)	\(-3\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{2}q^{5}+q^{9}+\beta _{1}q^{11}-q^{13}+\cdots\)
7644.2.a.u	$7644$	$2$	7644.a	1.a	$1$	$3$	$3$	$61.038$	3.3.321.1	None	✓				1092.2.q.b	$1$	$1$	\(0\)	\(-3\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$3$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{2}q^{5}+q^{9}+(1+\beta _{1}-\beta _{2})q^{11}+\cdots\)
7644.2.a.v	$7644$	$2$	7644.a	1.a	$1$	$3$	$3$	$61.038$	3.3.321.1	None	✓		✓		1092.2.q.c	$1$	$0$	\(0\)	\(-3\)	\(1\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{1}q^{5}+q^{9}+(2\beta _{1}+\beta _{2})q^{11}+\cdots\)
7644.2.a.w	$7644$	$2$	7644.a	1.a	$1$	$3$	$3$	$61.038$	3.3.321.1	None	✓				1092.2.q.d	$1$	$0$	\(0\)	\(-3\)	\(5\)	\(0\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(2-\beta _{1})q^{5}+q^{9}-\beta _{2}q^{11}+\cdots\)
7644.2.a.x	$7644$	$2$	7644.a	1.a	$1$	$3$	$3$	$61.038$	3.3.321.1	None	✓		✓		1092.2.q.d	$1$	$1$	\(0\)	\(3\)	\(-5\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-2+\beta _{1})q^{5}+q^{9}-\beta _{2}q^{11}+\cdots\)
7644.2.a.y	$7644$	$2$	7644.a	1.a	$1$	$3$	$3$	$61.038$	3.3.321.1	None	✓				1092.2.q.c	$1$	$1$	\(0\)	\(3\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{1}q^{5}+q^{9}+(2\beta _{1}+\beta _{2})q^{11}+\cdots\)
7644.2.a.z	$7644$	$2$	7644.a	1.a	$1$	$3$	$3$	$61.038$	3.3.321.1	None	✓				1092.2.q.b	$1$	$0$	\(0\)	\(3\)	\(1\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$3$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{2}q^{5}+q^{9}+(1+\beta _{1}-\beta _{2})q^{11}+\cdots\)
7644.2.a.ba	$7644$	$2$	7644.a	1.a	$1$	$5$	$5$	$61.038$	5.5.20094696.1	None	✓				1092.2.q.e	$1$	$1$	\(0\)	\(-5\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{1}q^{5}+q^{9}+(\beta _{1}-\beta _{4})q^{11}+\cdots\)
7644.2.a.bb	$7644$	$2$	7644.a	1.a	$1$	$5$	$5$	$61.038$	5.5.20094696.1	None	✓		✓		1092.2.q.e	$1$	$0$	\(0\)	\(5\)	\(1\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{5}+q^{9}+(\beta _{1}-\beta _{4})q^{11}+\cdots\)
7644.2.a.bc	$7644$	$2$	7644.a	1.a	$1$	$6$	$6$	$61.038$	6.6.566222848.1	None	✓	✓	✓		7644.2.a.bc	$1$	$0$	\(0\)	\(-6\)	\(-2\)	\(0\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{1}q^{5}+q^{9}+(2-\beta _{1}+\beta _{3}+\cdots)q^{11}+\cdots\)
7644.2.a.bd	$7644$	$2$	7644.a	1.a	$1$	$6$	$6$	$61.038$	6.6.71950336.1	None	✓	✓	✓		7644.2.a.bd	$1$	$1$	\(0\)	\(-6\)	\(2\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{3}q^{5}+q^{9}+(-2-\beta _{2}-\beta _{3}+\cdots)q^{11}+\cdots\)
7644.2.a.be	$7644$	$2$	7644.a	1.a	$1$	$6$	$6$	$61.038$	6.6.71950336.1	None	✓	✓	✓		7644.2.a.bd	$1$	$1$	\(0\)	\(6\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{3}q^{5}+q^{9}+(-2-\beta _{2}-\beta _{3}+\cdots)q^{11}+\cdots\)
7644.2.a.bf	$7644$	$2$	7644.a	1.a	$1$	$6$	$6$	$61.038$	6.6.566222848.1	None	✓	✓	✓		7644.2.a.bc	$1$	$0$	\(0\)	\(6\)	\(2\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{5}+q^{9}+(2-\beta _{1}+\beta _{3}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7644))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7644)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(273))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(364))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(546))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(588))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(637))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1092))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1274))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1911))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2548))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3822))\)\(^{\oplus 2}\)