Space of modular forms of level 5054, weight 2, and trivial character

• Label: 5054.2.a
• Level: $5054$
• Weight: $2$
• Character orbit: 5054.a
• Rep. character: $\chi_{5054}(1,\cdot)$
• Character field: $\Q$
• Dimension: $170$
• Newform subspaces: $39$
• Sturm bound: $1520$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 39 \)
Sturm bound:			\(1520\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\), \(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5054))\).

	Total	New	Old
Modular forms	800	170	630
Cusp forms	721	170	551
Eisenstein series	79	0	79

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

\(2\)	\(7\)	\(19\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(90\)	\(18\)	\(72\)		\(81\)	\(18\)	\(63\)		\(9\)	\(0\)	\(9\)
\(+\)	\(+\)	\(-\)	\(-\)		\(109\)	\(25\)	\(84\)		\(99\)	\(25\)	\(74\)		\(10\)	\(0\)	\(10\)
\(+\)	\(-\)	\(+\)	\(-\)		\(110\)	\(26\)	\(84\)		\(100\)	\(26\)	\(74\)		\(10\)	\(0\)	\(10\)
\(+\)	\(-\)	\(-\)	\(+\)		\(91\)	\(16\)	\(75\)		\(81\)	\(16\)	\(65\)		\(10\)	\(0\)	\(10\)
\(-\)	\(+\)	\(+\)	\(-\)		\(100\)	\(22\)	\(78\)		\(90\)	\(22\)	\(68\)		\(10\)	\(0\)	\(10\)
\(-\)	\(+\)	\(-\)	\(+\)		\(101\)	\(20\)	\(81\)		\(91\)	\(20\)	\(71\)		\(10\)	\(0\)	\(10\)
\(-\)	\(-\)	\(+\)	\(+\)		\(100\)	\(14\)	\(86\)		\(90\)	\(14\)	\(76\)		\(10\)	\(0\)	\(10\)
\(-\)	\(-\)	\(-\)	\(-\)		\(99\)	\(29\)	\(70\)		\(89\)	\(29\)	\(60\)		\(10\)	\(0\)	\(10\)
Plus space			\(+\)		\(382\)	\(68\)	\(314\)		\(343\)	\(68\)	\(275\)		\(39\)	\(0\)	\(39\)
Minus space			\(-\)		\(418\)	\(102\)	\(316\)		\(378\)	\(102\)	\(276\)		\(40\)	\(0\)	\(40\)

Trace form

170 * q - 2 * q^3 + 170 * q^4 - 6 * q^5 + 2 * q^6 + 162 * q^9 - 6 * q^10 - 8 * q^11 - 2 * q^12 - 2 * q^13 + 2 * q^14 + 170 * q^16 + 4 * q^18 - 6 * q^20 - 2 * q^21 + 12 * q^22 + 8 * q^23 + 2 * q^24 + 166 * q^25 - 2 * q^26 + 4 * q^27 + 16 * q^29 + 16 * q^30 - 28 * q^31 + 24 * q^33 - 12 * q^34 + 2 * q^35 + 162 * q^36 - 16 * q^37 + 16 * q^39 - 6 * q^40 + 8 * q^41 - 2 * q^42 - 8 * q^44 + 18 * q^45 + 36 * q^47 - 2 * q^48 + 170 * q^49 + 12 * q^50 + 44 * q^51 - 2 * q^52 + 20 * q^53 + 44 * q^54 + 32 * q^55 + 2 * q^56 + 26 * q^59 - 6 * q^61 + 20 * q^62 + 12 * q^63 + 170 * q^64 + 52 * q^65 + 32 * q^66 + 8 * q^67 + 32 * q^69 + 6 * q^70 + 4 * q^72 - 4 * q^73 - 14 * q^75 + 4 * q^77 - 40 * q^79 - 6 * q^80 + 174 * q^81 + 12 * q^82 + 26 * q^83 - 2 * q^84 - 4 * q^85 + 20 * q^86 + 36 * q^87 + 12 * q^88 - 28 * q^89 - 6 * q^90 - 14 * q^91 + 8 * q^92 + 8 * q^93 - 20 * q^94 + 2 * q^96 - 32 * q^97 - 56 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5054))\) 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	19
5054.2.a.a	$5054$	$2$	5054.a	1.a	$1$	$1$	$1$	$40.356$	\(\Q\)	None	✓				266.2.f.a	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-3q^{9}+\cdots\)
5054.2.a.b	$5054$	$2$	5054.a	1.a	$1$	$1$	$1$	$40.356$	\(\Q\)	None	✓				266.2.f.a	$1$	$1$	\(1\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}-3q^{9}+\cdots\)
5054.2.a.c	$5054$	$2$	5054.a	1.a	$1$	$1$	$1$	$40.356$	\(\Q\)	None	✓				14.2.a.a	$1$	$0$	\(1\)	\(2\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{7}+q^{8}+\cdots\)
5054.2.a.d	$5054$	$2$	5054.a	1.a	$1$	$2$	$2$	$40.356$	\(\Q(\sqrt{5}) \)	None	✓	✓			5054.2.a.d	$1$	$1$	\(-2\)	\(-1\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta q^{3}+q^{4}+(1-3\beta )q^{5}+\beta q^{6}+\cdots\)
5054.2.a.e	$5054$	$2$	5054.a	1.a	$1$	$2$	$2$	$40.356$	\(\Q(\sqrt{13}) \)	None	✓				266.2.a.c	$1$	$1$	\(-2\)	\(-1\)	\(1\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta q^{3}+q^{4}+(1-\beta )q^{5}+\beta q^{6}+\cdots\)
5054.2.a.f	$5054$	$2$	5054.a	1.a	$1$	$2$	$2$	$40.356$	\(\Q(\sqrt{5}) \)	None	✓	✓			5054.2.a.f	$1$	$0$	\(-2\)	\(-1\)	\(2\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}-q^{7}+\cdots\)
5054.2.a.g	$5054$	$2$	5054.a	1.a	$1$	$2$	$2$	$40.356$	\(\Q(\sqrt{5}) \)	None	✓	✓			5054.2.a.g	$1$	$0$	\(-2\)	\(1\)	\(-3\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta q^{3}+q^{4}+(-1-\beta )q^{5}-\beta q^{6}+\cdots\)
5054.2.a.h	$5054$	$2$	5054.a	1.a	$1$	$2$	$2$	$40.356$	\(\Q(\sqrt{17}) \)	None	✓				266.2.f.b	$1$	$1$	\(-2\)	\(1\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta q^{3}+q^{4}+(-1+\beta )q^{5}-\beta q^{6}+\cdots\)
5054.2.a.i	$5054$	$2$	5054.a	1.a	$1$	$2$	$2$	$40.356$	\(\Q(\sqrt{5}) \)	None	✓	✓			5054.2.a.i	$1$	$0$	\(-2\)	\(3\)	\(-4\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1+\beta )q^{3}+q^{4}+(-3+2\beta )q^{5}+\cdots\)
5054.2.a.j	$5054$	$2$	5054.a	1.a	$1$	$2$	$2$	$40.356$	\(\Q(\sqrt{5}) \)	None	✓	✓			5054.2.a.i	$1$	$1$	\(2\)	\(-3\)	\(-4\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1-\beta )q^{3}+q^{4}+(-3+2\beta )q^{5}+\cdots\)
5054.2.a.k	$5054$	$2$	5054.a	1.a	$1$	$2$	$2$	$40.356$	\(\Q(\sqrt{5}) \)	None	✓				266.2.a.b	$1$	$0$	\(2\)	\(-3\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1-\beta )q^{3}+q^{4}+(2-3\beta )q^{5}+\cdots\)
5054.2.a.l	$5054$	$2$	5054.a	1.a	$1$	$2$	$2$	$40.356$	\(\Q(\sqrt{5}) \)	None	✓	✓			5054.2.a.g	$1$	$1$	\(2\)	\(-1\)	\(-3\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta q^{3}+q^{4}+(-1-\beta )q^{5}-\beta q^{6}+\cdots\)
5054.2.a.m	$5054$	$2$	5054.a	1.a	$1$	$2$	$2$	$40.356$	\(\Q(\sqrt{17}) \)	None	✓				266.2.f.b	$1$	$1$	\(2\)	\(-1\)	\(-1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta q^{3}+q^{4}+(-1+\beta )q^{5}-\beta q^{6}+\cdots\)
5054.2.a.n	$5054$	$2$	5054.a	1.a	$1$	$2$	$2$	$40.356$	\(\Q(\sqrt{29}) \)	None	✓				266.2.a.a	$1$	$1$	\(2\)	\(-1\)	\(-1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta q^{3}+q^{4}+(-1+\beta )q^{5}-\beta q^{6}+\cdots\)
5054.2.a.o	$5054$	$2$	5054.a	1.a	$1$	$2$	$2$	$40.356$	\(\Q(\sqrt{5}) \)	None	✓	✓			5054.2.a.d	$1$	$0$	\(2\)	\(1\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta q^{3}+q^{4}+(1-3\beta )q^{5}+\beta q^{6}+\cdots\)
5054.2.a.p	$5054$	$2$	5054.a	1.a	$1$	$2$	$2$	$40.356$	\(\Q(\sqrt{5}) \)	None	✓	✓			5054.2.a.f	$1$	$1$	\(2\)	\(1\)	\(2\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta q^{3}+q^{4}+q^{5}+\beta q^{6}-q^{7}+\cdots\)
5054.2.a.q	$5054$	$2$	5054.a	1.a	$1$	$3$	$3$	$40.356$	3.3.148.1	None	✓				266.2.f.c	$1$	$0$	\(-3\)	\(-2\)	\(-1\)	\(-3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
5054.2.a.r	$5054$	$2$	5054.a	1.a	$1$	$3$	$3$	$40.356$	3.3.469.1	None	✓				266.2.a.d	$1$	$0$	\(-3\)	\(1\)	\(5\)	\(-3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{2}q^{3}+q^{4}+(2-\beta _{1})q^{5}+\beta _{2}q^{6}+\cdots\)
5054.2.a.s	$5054$	$2$	5054.a	1.a	$1$	$3$	$3$	$40.356$	\(\Q(\zeta_{18})^+\)	None	✓				266.2.u.a	$1$	$1$	\(-3\)	\(3\)	\(-3\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(-1+\beta _{2})q^{5}+\cdots\)
5054.2.a.t	$5054$	$2$	5054.a	1.a	$1$	$3$	$3$	$40.356$	\(\Q(\zeta_{18})^+\)	None	✓				266.2.u.a	$1$	$1$	\(3\)	\(-3\)	\(-3\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1+\beta _{2})q^{5}+\cdots\)
5054.2.a.u	$5054$	$2$	5054.a	1.a	$1$	$3$	$3$	$40.356$	3.3.148.1	None	✓				266.2.f.c	$1$	$0$	\(3\)	\(2\)	\(-1\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
5054.2.a.v	$5054$	$2$	5054.a	1.a	$1$	$4$	$4$	$40.356$	\(\Q(\zeta_{20})^+\)	None	✓	✓			5054.2.a.v	$1$	$1$	\(-4\)	\(-4\)	\(2\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
5054.2.a.w	$5054$	$2$	5054.a	1.a	$1$	$4$	$4$	$40.356$	4.4.151572.1	None	✓				266.2.f.d	$1$	$0$	\(-4\)	\(-1\)	\(1\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)
5054.2.a.x	$5054$	$2$	5054.a	1.a	$1$	$4$	$4$	$40.356$	4.4.151572.1	None	✓				266.2.f.d	$1$	$0$	\(4\)	\(1\)	\(1\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)
5054.2.a.y	$5054$	$2$	5054.a	1.a	$1$	$4$	$4$	$40.356$	\(\Q(\zeta_{20})^+\)	None	✓	✓			5054.2.a.v	$1$	$0$	\(4\)	\(4\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1+\beta _{1})q^{3}+q^{4}+(-\beta _{2}-\beta _{3})q^{5}+\cdots\)
5054.2.a.z	$5054$	$2$	5054.a	1.a	$1$	$6$	$6$	$40.356$	6.6.36538000.1	None	✓	✓	✓		5054.2.a.z	$1$	$1$	\(-6\)	\(0\)	\(-1\)	\(6\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{4}q^{5}-\beta _{1}q^{6}+\cdots\)
5054.2.a.ba	$5054$	$2$	5054.a	1.a	$1$	$6$	$6$	$40.356$	6.6.48952000.1	None	✓	✓			5054.2.a.ba	$1$	$0$	\(-6\)	\(2\)	\(-5\)	\(-6\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots\)
5054.2.a.bb	$5054$	$2$	5054.a	1.a	$1$	$6$	$6$	$40.356$	6.6.1528713.1	None	✓				266.2.u.b	$1$	$1$	\(-6\)	\(3\)	\(-3\)	\(-6\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{3}q^{3}+q^{4}+(-\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
5054.2.a.bc	$5054$	$2$	5054.a	1.a	$1$	$6$	$6$	$40.356$	6.6.1528713.1	None	✓				266.2.u.b	$1$	$1$	\(6\)	\(-3\)	\(-3\)	\(-6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{3}q^{3}+q^{4}+(-\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
5054.2.a.bd	$5054$	$2$	5054.a	1.a	$1$	$6$	$6$	$40.356$	6.6.48952000.1	None	✓	✓			5054.2.a.ba	$1$	$1$	\(6\)	\(-2\)	\(-5\)	\(-6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots\)
5054.2.a.be	$5054$	$2$	5054.a	1.a	$1$	$6$	$6$	$40.356$	6.6.36538000.1	None	✓	✓			5054.2.a.z	$1$	$0$	\(6\)	\(0\)	\(-1\)	\(6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{4}q^{5}-\beta _{1}q^{6}+\cdots\)
5054.2.a.bf	$5054$	$2$	5054.a	1.a	$1$	$8$	$8$	$40.356$	8.8.\(\cdots\).1	None	✓	✓	✓		5054.2.a.bf	$1$	$1$	\(-8\)	\(-4\)	\(6\)	\(-8\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1-\beta _{5}+\beta _{7})q^{3}+q^{4}+(1+\cdots)q^{5}+\cdots\)
5054.2.a.bg	$5054$	$2$	5054.a	1.a	$1$	$8$	$8$	$40.356$	8.8.\(\cdots\).1	None	✓	✓			5054.2.a.bg	$1$	$0$	\(-8\)	\(4\)	\(-2\)	\(8\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1+\beta _{2}+\beta _{5})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
5054.2.a.bh	$5054$	$2$	5054.a	1.a	$1$	$8$	$8$	$40.356$	8.8.\(\cdots\).1	None	✓	✓	✓		5054.2.a.bg	$1$	$1$	\(8\)	\(-4\)	\(-2\)	\(8\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1-\beta _{2}-\beta _{5})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
5054.2.a.bi	$5054$	$2$	5054.a	1.a	$1$	$8$	$8$	$40.356$	8.8.\(\cdots\).1	None	✓	✓			5054.2.a.bf	$1$	$0$	\(8\)	\(4\)	\(6\)	\(-8\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1+\beta _{5}-\beta _{7})q^{3}+q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
5054.2.a.bj	$5054$	$2$	5054.a	1.a	$1$	$9$	$9$	$40.356$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓		✓		266.2.u.c	$1$	$0$	\(-9\)	\(-3\)	\(3\)	\(-9\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{6}q^{5}+\beta _{1}q^{6}+\cdots\)
5054.2.a.bk	$5054$	$2$	5054.a	1.a	$1$	$9$	$9$	$40.356$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓		✓		266.2.u.c	$1$	$0$	\(9\)	\(3\)	\(3\)	\(-9\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{6}q^{5}+\beta _{1}q^{6}+\cdots\)
5054.2.a.bl	$5054$	$2$	5054.a	1.a	$1$	$12$	$12$	$40.356$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		266.2.u.d	$1$	$0$	\(-12\)	\(-3\)	\(3\)	\(12\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}+(\beta _{2}-\beta _{5})q^{5}+\cdots\)
5054.2.a.bm	$5054$	$2$	5054.a	1.a	$1$	$12$	$12$	$40.356$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		266.2.u.d	$1$	$0$	\(12\)	\(3\)	\(3\)	\(12\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{2}-\beta _{5})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5054))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5054)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(266))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(722))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2527))\)\(^{\oplus 2}\)