Space of modular forms of level 4114, weight 2, and trivial character

• Label: 4114.2.a
• Level: $4114$
• Weight: $2$
• Character orbit: 4114.a
• Rep. character: $\chi_{4114}(1,\cdot)$
• Character field: $\Q$
• Dimension: $144$
• Newform subspaces: $38$
• Sturm bound: $1188$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 4114 = 2 \cdot 11^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4114.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 38 \)
Sturm bound:			\(1188\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4114))\).

	Total	New	Old
Modular forms	618	144	474
Cusp forms	571	144	427
Eisenstein series	47	0	47

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

\(2\)	\(11\)	\(17\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(69\)	\(17\)	\(52\)		\(64\)	\(17\)	\(47\)		\(5\)	\(0\)	\(5\)
\(+\)	\(+\)	\(-\)	\(-\)		\(81\)	\(19\)	\(62\)		\(75\)	\(19\)	\(56\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)		\(84\)	\(18\)	\(66\)		\(78\)	\(18\)	\(60\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)		\(74\)	\(18\)	\(56\)		\(68\)	\(18\)	\(50\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)		\(78\)	\(23\)	\(55\)		\(72\)	\(23\)	\(49\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)		\(78\)	\(13\)	\(65\)		\(72\)	\(13\)	\(59\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)		\(76\)	\(13\)	\(63\)		\(70\)	\(13\)	\(57\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)		\(78\)	\(23\)	\(55\)		\(72\)	\(23\)	\(49\)		\(6\)	\(0\)	\(6\)
Plus space			\(+\)		\(297\)	\(61\)	\(236\)		\(274\)	\(61\)	\(213\)		\(23\)	\(0\)	\(23\)
Minus space			\(-\)		\(321\)	\(83\)	\(238\)		\(297\)	\(83\)	\(214\)		\(24\)	\(0\)	\(24\)

Trace form

144 * q + 2 * q^3 + 144 * q^4 + 2 * q^5 - 2 * q^6 - 4 * q^7 + 140 * q^9 + 6 * q^10 + 2 * q^12 - 4 * q^13 - 4 * q^14 + 8 * q^15 + 144 * q^16 + 2 * q^17 - 4 * q^18 - 8 * q^19 + 2 * q^20 - 16 * q^21 - 8 * q^23 - 2 * q^24 + 148 * q^25 + 12 * q^26 + 20 * q^27 - 4 * q^28 + 6 * q^29 + 4 * q^31 - 2 * q^34 + 24 * q^35 + 140 * q^36 + 6 * q^37 + 8 * q^38 + 4 * q^39 + 6 * q^40 + 12 * q^41 + 24 * q^42 - 28 * q^43 + 58 * q^45 - 8 * q^46 + 40 * q^47 + 2 * q^48 + 120 * q^49 + 12 * q^50 + 2 * q^51 - 4 * q^52 + 28 * q^53 + 4 * q^54 - 4 * q^56 + 32 * q^57 + 26 * q^58 + 28 * q^59 + 8 * q^60 - 38 * q^61 + 20 * q^62 + 36 * q^63 + 144 * q^64 + 36 * q^65 - 20 * q^67 + 2 * q^68 + 64 * q^69 + 16 * q^70 + 48 * q^71 - 4 * q^72 + 8 * q^73 + 34 * q^74 + 86 * q^75 - 8 * q^76 + 36 * q^78 - 40 * q^79 + 2 * q^80 + 180 * q^81 + 12 * q^82 + 28 * q^83 - 16 * q^84 + 6 * q^85 + 4 * q^86 + 72 * q^87 + 72 * q^89 + 78 * q^90 - 136 * q^91 - 8 * q^92 - 64 * q^93 + 48 * q^95 - 2 * q^96 - 132 * q^97 + 8 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4114))\) 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	11	17
4114.2.a.a	$4114$	$2$	4114.a	1.a	$1$	$1$	$1$	$32.850$	\(\Q\)	None	✓				34.2.a.a	$1$	$1$	\(-1\)	\(-2\)	\(0\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}+q^{4}+2q^{6}+4q^{7}-q^{8}+\cdots\)
4114.2.a.b	$4114$	$2$	4114.a	1.a	$1$	$1$	$1$	$32.850$	\(\Q\)	None	✓	✓			4114.2.a.b	$1$	$0$	\(-1\)	\(0\)	\(3\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{5}+q^{7}-q^{8}-3q^{9}+\cdots\)
4114.2.a.c	$4114$	$2$	4114.a	1.a	$1$	$1$	$1$	$32.850$	\(\Q\)	None	✓				374.2.a.a	$1$	$0$	\(1\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{7}+q^{8}-3q^{9}+2q^{13}+\cdots\)
4114.2.a.d	$4114$	$2$	4114.a	1.a	$1$	$1$	$1$	$32.850$	\(\Q\)	None	✓	✓			4114.2.a.b	$1$	$0$	\(1\)	\(0\)	\(3\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+3q^{5}-q^{7}+q^{8}-3q^{9}+\cdots\)
4114.2.a.e	$4114$	$2$	4114.a	1.a	$1$	$2$	$2$	$32.850$	\(\Q(\sqrt{5}) \)	None	✓	✓			4114.2.a.e	$1$	$1$	\(-2\)	\(-1\)	\(-1\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta q^{3}+q^{4}-\beta q^{5}+\beta q^{6}+\beta q^{7}+\cdots\)
4114.2.a.f	$4114$	$2$	4114.a	1.a	$1$	$2$	$2$	$32.850$	\(\Q(\sqrt{5}) \)	None	✓				374.2.g.c	$1$	$0$	\(-2\)	\(-1\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta q^{3}+q^{4}+(-1+2\beta )q^{5}+\cdots\)
4114.2.a.g	$4114$	$2$	4114.a	1.a	$1$	$2$	$2$	$32.850$	\(\Q(\sqrt{5}) \)	None	✓				374.2.g.b	$1$	$0$	\(-2\)	\(-1\)	\(2\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}+(2+\cdots)q^{7}+\cdots\)
4114.2.a.h	$4114$	$2$	4114.a	1.a	$1$	$2$	$2$	$32.850$	\(\Q(\sqrt{5}) \)	None	✓	✓			4114.2.a.h	$1$	$1$	\(-2\)	\(1\)	\(-1\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{5}-\beta q^{6}+(-2+\cdots)q^{7}+\cdots\)
4114.2.a.i	$4114$	$2$	4114.a	1.a	$1$	$2$	$2$	$32.850$	\(\Q(\sqrt{5}) \)	None	✓				374.2.g.a	$1$	$1$	\(-2\)	\(3\)	\(-4\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1+\beta )q^{3}+q^{4}+(-3+2\beta )q^{5}+\cdots\)
4114.2.a.j	$4114$	$2$	4114.a	1.a	$1$	$2$	$2$	$32.850$	\(\Q(\sqrt{5}) \)	None	✓	✓			4114.2.a.e	$1$	$1$	\(2\)	\(-1\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta q^{3}+q^{4}-\beta q^{5}-\beta q^{6}-\beta q^{7}+\cdots\)
4114.2.a.k	$4114$	$2$	4114.a	1.a	$1$	$2$	$2$	$32.850$	\(\Q(\sqrt{5}) \)	None	✓				374.2.g.c	$1$	$1$	\(2\)	\(-1\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta q^{3}+q^{4}+(-1+2\beta )q^{5}+\cdots\)
4114.2.a.l	$4114$	$2$	4114.a	1.a	$1$	$2$	$2$	$32.850$	\(\Q(\sqrt{5}) \)	None	✓				374.2.g.b	$1$	$1$	\(2\)	\(-1\)	\(2\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta q^{3}+q^{4}+q^{5}-\beta q^{6}+(-2+\cdots)q^{7}+\cdots\)
4114.2.a.m	$4114$	$2$	4114.a	1.a	$1$	$2$	$2$	$32.850$	\(\Q(\sqrt{5}) \)	None	✓	✓			4114.2.a.h	$1$	$1$	\(2\)	\(1\)	\(-1\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta q^{3}+q^{4}-\beta q^{5}+\beta q^{6}+(2+\cdots)q^{7}+\cdots\)
4114.2.a.n	$4114$	$2$	4114.a	1.a	$1$	$2$	$2$	$32.850$	\(\Q(\sqrt{5}) \)	None	✓				374.2.g.a	$1$	$0$	\(2\)	\(3\)	\(-4\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1+\beta )q^{3}+q^{4}+(-3+2\beta )q^{5}+\cdots\)
4114.2.a.o	$4114$	$2$	4114.a	1.a	$1$	$3$	$3$	$32.850$	3.3.321.1	None	✓	✓			4114.2.a.o	$1$	$1$	\(-3\)	\(-1\)	\(-3\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}+(-1+\beta _{1}+\beta _{2})q^{5}+\cdots\)
4114.2.a.p	$4114$	$2$	4114.a	1.a	$1$	$3$	$3$	$32.850$	3.3.257.1	None	✓				374.2.a.c	$1$	$1$	\(-3\)	\(3\)	\(-1\)	\(-7\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1+\beta _{2})q^{3}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots\)
4114.2.a.q	$4114$	$2$	4114.a	1.a	$1$	$3$	$3$	$32.850$	3.3.733.1	None	✓	✓			4114.2.a.q	$1$	$0$	\(-3\)	\(3\)	\(2\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1+\beta _{2})q^{3}+q^{4}+(1-\beta _{1})q^{5}+\cdots\)
4114.2.a.r	$4114$	$2$	4114.a	1.a	$1$	$3$	$3$	$32.850$	3.3.321.1	None	✓	✓			4114.2.a.o	$1$	$1$	\(3\)	\(-1\)	\(-3\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}+(-1+\beta _{1}+\beta _{2})q^{5}+\cdots\)
4114.2.a.s	$4114$	$2$	4114.a	1.a	$1$	$3$	$3$	$32.850$	3.3.785.1	None	✓				374.2.a.b	$1$	$1$	\(3\)	\(-1\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)
4114.2.a.t	$4114$	$2$	4114.a	1.a	$1$	$3$	$3$	$32.850$	3.3.733.1	None	✓	✓			4114.2.a.q	$1$	$0$	\(3\)	\(3\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1+\beta _{2})q^{3}+q^{4}+(1-\beta _{1})q^{5}+\cdots\)
4114.2.a.u	$4114$	$2$	4114.a	1.a	$1$	$4$	$4$	$32.850$	4.4.725.1	None	✓				374.2.g.d	$1$	$0$	\(-4\)	\(-5\)	\(-6\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-2+\beta _{1}+\beta _{2})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots\)
4114.2.a.v	$4114$	$2$	4114.a	1.a	$1$	$4$	$4$	$32.850$	4.4.2525.1	None	✓				374.2.g.e	$1$	$0$	\(-4\)	\(-1\)	\(-2\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(\beta _{2}-\beta _{3})q^{3}+q^{4}-\beta _{1}q^{5}+\cdots\)
4114.2.a.w	$4114$	$2$	4114.a	1.a	$1$	$4$	$4$	$32.850$	\(\Q(\sqrt{3}, \sqrt{7})\)	None	✓	✓			4114.2.a.w	$1$	$1$	\(-4\)	\(0\)	\(-6\)	\(4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{3}q^{3}+q^{4}+(-1+\beta _{2})q^{5}+\cdots\)
4114.2.a.x	$4114$	$2$	4114.a	1.a	$1$	$4$	$4$	$32.850$	4.4.17417.1	None	✓				374.2.a.e	$1$	$0$	\(-4\)	\(1\)	\(-1\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{3}q^{3}+q^{4}+(-1-\beta _{2}-\beta _{3})q^{5}+\cdots\)
4114.2.a.y	$4114$	$2$	4114.a	1.a	$1$	$4$	$4$	$32.850$	4.4.13676.1	None	✓	✓			4114.2.a.y	$1$	$0$	\(-4\)	\(1\)	\(5\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{3}q^{3}+q^{4}+(2-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
4114.2.a.z	$4114$	$2$	4114.a	1.a	$1$	$4$	$4$	$32.850$	4.4.725.1	None	✓				374.2.g.d	$1$	$1$	\(4\)	\(-5\)	\(-6\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-2+\beta _{1}+\beta _{2})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots\)
4114.2.a.ba	$4114$	$2$	4114.a	1.a	$1$	$4$	$4$	$32.850$	4.4.2525.1	None	✓		✓		374.2.g.e	$1$	$1$	\(4\)	\(-1\)	\(-2\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(\beta _{2}-\beta _{3})q^{3}+q^{4}-\beta _{1}q^{5}+\cdots\)
4114.2.a.bb	$4114$	$2$	4114.a	1.a	$1$	$4$	$4$	$32.850$	\(\Q(\sqrt{3}, \sqrt{7})\)	None	✓	✓			4114.2.a.w	$1$	$1$	\(4\)	\(0\)	\(-6\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{3}q^{3}+q^{4}+(-1+\beta _{2})q^{5}+\cdots\)
4114.2.a.bc	$4114$	$2$	4114.a	1.a	$1$	$4$	$4$	$32.850$	4.4.55585.1	None	✓				374.2.a.d	$1$	$0$	\(4\)	\(1\)	\(5\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{2})q^{5}+\beta _{1}q^{6}+\cdots\)
4114.2.a.bd	$4114$	$2$	4114.a	1.a	$1$	$4$	$4$	$32.850$	4.4.13676.1	None	✓	✓			4114.2.a.y	$1$	$0$	\(4\)	\(1\)	\(5\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{3}q^{3}+q^{4}+(2-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
4114.2.a.be	$4114$	$2$	4114.a	1.a	$1$	$5$	$5$	$32.850$	5.5.7679496.1	None	✓	✓			4114.2.a.be	$1$	$0$	\(-5\)	\(1\)	\(3\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{3}q^{3}+q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)
4114.2.a.bf	$4114$	$2$	4114.a	1.a	$1$	$5$	$5$	$32.850$	5.5.7679496.1	None	✓	✓			4114.2.a.be	$1$	$0$	\(5\)	\(1\)	\(3\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{3}q^{3}+q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)
4114.2.a.bg	$4114$	$2$	4114.a	1.a	$1$	$8$	$8$	$32.850$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		374.2.g.f	$1$	$1$	\(-8\)	\(-5\)	\(2\)	\(-11\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}-\beta _{6}q^{5}+\cdots\)
4114.2.a.bh	$4114$	$2$	4114.a	1.a	$1$	$8$	$8$	$32.850$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓	✓		4114.2.a.bh	$1$	$0$	\(-8\)	\(4\)	\(6\)	\(8\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{5})q^{5}+\cdots\)
4114.2.a.bi	$4114$	$2$	4114.a	1.a	$1$	$8$	$8$	$32.850$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				374.2.g.f	$1$	$0$	\(8\)	\(-5\)	\(2\)	\(11\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}-\beta _{6}q^{5}+\cdots\)
4114.2.a.bj	$4114$	$2$	4114.a	1.a	$1$	$8$	$8$	$32.850$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓			4114.2.a.bh	$1$	$0$	\(8\)	\(4\)	\(6\)	\(-8\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{5})q^{5}+\cdots\)
4114.2.a.bk	$4114$	$2$	4114.a	1.a	$1$	$10$	$10$	$32.850$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		374.2.g.g	$1$	$1$	\(-10\)	\(2\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{4}q^{5}-\beta _{1}q^{6}+\cdots\)
4114.2.a.bl	$4114$	$2$	4114.a	1.a	$1$	$10$	$10$	$32.850$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		374.2.g.g	$1$	$0$	\(10\)	\(2\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{4}q^{5}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4114))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4114)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(187))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(374))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2057))\)\(^{\oplus 2}\)