Space of modular forms of level 4950, weight 2, and trivial character

• Label: 4950.2.a
• Level: $4950$
• Weight: $2$
• Character orbit: 4950.a
• Rep. character: $\chi_{4950}(1,\cdot)$
• Character field: $\Q$
• Dimension: $81$
• Newform subspaces: $62$
• Sturm bound: $2160$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 4950 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4950.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 62 \)
Sturm bound:			\(2160\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(7\), \(13\), \(17\), \(19\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4950))\).

	Total	New	Old
Modular forms	1128	81	1047
Cusp forms	1033	81	952
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.

\(2\)	\(3\)	\(5\)	\(11\)	Fricke		Total				Cusp				Eisenstein
						All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)		\(63\)	\(2\)	\(61\)		\(58\)	\(2\)	\(56\)		\(5\)	\(0\)	\(5\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)		\(75\)	\(5\)	\(70\)		\(69\)	\(5\)	\(64\)		\(6\)	\(0\)	\(6\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)		\(75\)	\(6\)	\(69\)		\(69\)	\(6\)	\(63\)		\(6\)	\(0\)	\(6\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)		\(69\)	\(4\)	\(65\)		\(63\)	\(4\)	\(59\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)		\(72\)	\(6\)	\(66\)		\(66\)	\(6\)	\(60\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)		\(69\)	\(5\)	\(64\)		\(63\)	\(5\)	\(58\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)		\(69\)	\(6\)	\(63\)		\(63\)	\(6\)	\(57\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)		\(72\)	\(6\)	\(66\)		\(66\)	\(6\)	\(60\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)		\(69\)	\(5\)	\(64\)		\(63\)	\(5\)	\(58\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)		\(75\)	\(2\)	\(73\)		\(69\)	\(2\)	\(67\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)		\(69\)	\(4\)	\(65\)		\(63\)	\(4\)	\(59\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)		\(69\)	\(6\)	\(63\)		\(63\)	\(6\)	\(57\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)		\(69\)	\(5\)	\(64\)		\(63\)	\(5\)	\(58\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)		\(72\)	\(7\)	\(65\)		\(66\)	\(7\)	\(59\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)		\(72\)	\(7\)	\(65\)		\(66\)	\(7\)	\(59\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)		\(69\)	\(5\)	\(64\)		\(63\)	\(5\)	\(58\)		\(6\)	\(0\)	\(6\)
Plus space				\(+\)		\(552\)	\(33\)	\(519\)		\(505\)	\(33\)	\(472\)		\(47\)	\(0\)	\(47\)
Minus space				\(-\)		\(576\)	\(48\)	\(528\)		\(528\)	\(48\)	\(480\)		\(48\)	\(0\)	\(48\)

Trace form

81 * q + q^2 + 81 * q^4 + q^8 - q^11 + 2 * q^13 - 8 * q^14 + 81 * q^16 - 14 * q^17 + 12 * q^19 - q^22 - 8 * q^23 - 22 * q^26 - 6 * q^29 + 28 * q^31 + q^32 - 6 * q^34 + 14 * q^37 + 8 * q^38 - 34 * q^41 + 28 * q^43 - q^44 + 16 * q^46 - 24 * q^47 + 129 * q^49 + 2 * q^52 + 26 * q^53 - 8 * q^56 + 18 * q^58 - 12 * q^59 + 6 * q^61 - 8 * q^62 + 81 * q^64 - 14 * q^68 + 48 * q^71 - 42 * q^73 + 10 * q^74 + 12 * q^76 + 48 * q^79 + 14 * q^82 - 12 * q^83 - 12 * q^86 - q^88 + 38 * q^89 + 8 * q^91 - 8 * q^92 + 8 * q^94 + 18 * q^97 - 23 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4950))\) 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	5	11
4950.2.a.a	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				110.2.a.a	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(-5\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-5q^{7}-q^{8}-q^{11}-2q^{13}+\cdots\)
4950.2.a.b	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				990.2.c.a	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-4q^{7}-q^{8}+q^{11}+4q^{14}+\cdots\)
4950.2.a.c	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				1650.2.a.j	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{7}-q^{8}-q^{11}-5q^{13}+\cdots\)
4950.2.a.d	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				198.2.a.b	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{7}-q^{8}-q^{11}-2q^{13}+\cdots\)
4950.2.a.e	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				1650.2.a.d	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{7}-q^{8}-q^{11}-q^{13}+\cdots\)
4950.2.a.f	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				1650.2.a.i	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{7}-q^{8}+q^{11}-q^{13}+\cdots\)
4950.2.a.g	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				66.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{7}-q^{8}+q^{11}+4q^{13}+\cdots\)
4950.2.a.h	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				110.2.b.c	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{7}-q^{8}+q^{11}+q^{14}+\cdots\)
4950.2.a.i	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓	✓			4950.2.a.i	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(-1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{7}-q^{8}+q^{11}+2q^{13}+\cdots\)
4950.2.a.j	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				110.2.b.b	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{8}-q^{11}-2q^{13}+q^{16}+\cdots\)
4950.2.a.k	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				330.2.a.a	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{8}-q^{11}-2q^{13}+q^{16}+\cdots\)
4950.2.a.l	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				550.2.a.b	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{8}-q^{11}+3q^{13}+q^{16}+\cdots\)
4950.2.a.m	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				990.2.a.a	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{8}+q^{11}+q^{16}-2q^{17}+\cdots\)
4950.2.a.n	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓	✓			4950.2.a.i	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{7}-q^{8}-q^{11}-2q^{13}+\cdots\)
4950.2.a.o	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				1650.2.a.g	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{7}-q^{8}+q^{11}+4q^{13}+\cdots\)
4950.2.a.p	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				1650.2.a.f	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(3\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{7}-q^{8}-q^{11}-3q^{14}+\cdots\)
4950.2.a.q	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				110.2.b.a	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(3\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{7}-q^{8}-q^{11}+4q^{13}+\cdots\)
4950.2.a.r	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				1650.2.a.a	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(3\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{7}-q^{8}-q^{11}+4q^{13}+\cdots\)
4950.2.a.s	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				990.2.c.a	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+4q^{7}-q^{8}-q^{11}-4q^{14}+\cdots\)
4950.2.a.t	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				330.2.a.b	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+4q^{7}-q^{8}-q^{11}+2q^{13}+\cdots\)
4950.2.a.u	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				550.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+4q^{7}-q^{8}+q^{11}-5q^{13}+\cdots\)
4950.2.a.v	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				990.2.a.e	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+4q^{7}-q^{8}+q^{11}+4q^{13}+\cdots\)
4950.2.a.w	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				990.2.c.a	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-4q^{7}+q^{8}-q^{11}-4q^{14}+\cdots\)
4950.2.a.x	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				330.2.a.c	$1$	$0$	\(1\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-4q^{7}+q^{8}+q^{11}-2q^{13}+\cdots\)
4950.2.a.y	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				550.2.a.a	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-4q^{7}+q^{8}+q^{11}+5q^{13}+\cdots\)
4950.2.a.z	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				1650.2.a.a	$1$	$0$	\(1\)	\(0\)	\(0\)	\(-3\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{7}+q^{8}-q^{11}-4q^{13}+\cdots\)
4950.2.a.ba	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				110.2.b.a	$1$	$0$	\(1\)	\(0\)	\(0\)	\(-3\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{7}+q^{8}-q^{11}-4q^{13}+\cdots\)
4950.2.a.bb	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				1650.2.a.f	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-3\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{7}+q^{8}-q^{11}-3q^{14}+\cdots\)
4950.2.a.bc	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				110.2.a.b	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-3\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{7}+q^{8}-q^{11}+6q^{13}+\cdots\)
4950.2.a.bd	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				198.2.a.b	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{7}+q^{8}+q^{11}-2q^{13}+\cdots\)
4950.2.a.be	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓	✓			4950.2.a.i	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{7}+q^{8}-q^{11}+2q^{13}+\cdots\)
4950.2.a.bf	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				1650.2.a.g	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{7}+q^{8}+q^{11}-4q^{13}+\cdots\)
4950.2.a.bg	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				330.2.a.d	$1$	$1$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{8}-q^{11}-6q^{13}+q^{16}+\cdots\)
4950.2.a.bh	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				550.2.a.b	$1$	$1$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{8}-q^{11}-3q^{13}+q^{16}+\cdots\)
4950.2.a.bi	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				990.2.a.a	$1$	$0$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{8}-q^{11}+q^{16}+2q^{17}+\cdots\)
4950.2.a.bj	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				110.2.b.b	$1$	$0$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{8}-q^{11}+2q^{13}+q^{16}+\cdots\)
4950.2.a.bk	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				330.2.a.e	$1$	$0$	\(1\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{8}+q^{11}+2q^{13}+q^{16}+\cdots\)
4950.2.a.bl	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓	✓			4950.2.a.i	$1$	$1$	\(1\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{7}+q^{8}+q^{11}-2q^{13}+\cdots\)
4950.2.a.bm	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				110.2.a.c	$1$	$0$	\(1\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{7}+q^{8}+q^{11}-2q^{13}+\cdots\)
4950.2.a.bn	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				110.2.b.c	$1$	$1$	\(1\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{7}+q^{8}+q^{11}+q^{14}+\cdots\)
4950.2.a.bo	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				66.2.a.c	$1$	$1$	\(1\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{7}+q^{8}-q^{11}-4q^{13}+\cdots\)
4950.2.a.bp	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				1650.2.a.d	$1$	$0$	\(1\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{7}+q^{8}-q^{11}+q^{13}+\cdots\)
4950.2.a.bq	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				1650.2.a.j	$1$	$0$	\(1\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{7}+q^{8}-q^{11}+5q^{13}+\cdots\)
4950.2.a.br	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				1650.2.a.i	$1$	$0$	\(1\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{7}+q^{8}+q^{11}+q^{13}+\cdots\)
4950.2.a.bs	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				990.2.a.e	$1$	$0$	\(1\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+4q^{7}+q^{8}-q^{11}+4q^{13}+\cdots\)
4950.2.a.bt	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				990.2.c.a	$1$	$0$	\(1\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+4q^{7}+q^{8}+q^{11}+4q^{14}+\cdots\)
4950.2.a.bu	$4950$	$2$	4950.a	1.a	$1$	$1$	$1$	$39.526$	\(\Q\)	None	✓				66.2.a.b	$1$	$0$	\(1\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+4q^{7}+q^{8}+q^{11}+6q^{13}+\cdots\)
4950.2.a.bv	$4950$	$2$	4950.a	1.a	$1$	$2$	$2$	$39.526$	\(\Q(\sqrt{10}) \)	None	✓		✓		330.2.c.a	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-2+\beta )q^{7}-q^{8}-q^{11}+\cdots\)
4950.2.a.bw	$4950$	$2$	4950.a	1.a	$1$	$2$	$2$	$39.526$	\(\Q(\sqrt{33}) \)	None	✓		✓		110.2.a.d	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-\beta q^{7}-q^{8}+q^{11}-2q^{13}+\cdots\)
4950.2.a.bx	$4950$	$2$	4950.a	1.a	$1$	$2$	$2$	$39.526$	\(\Q(\sqrt{73}) \)	None	✓				1650.2.a.v	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-\beta q^{7}-q^{8}+q^{11}+(1+\cdots)q^{13}+\cdots\)
4950.2.a.by	$4950$	$2$	4950.a	1.a	$1$	$2$	$2$	$39.526$	\(\Q(\sqrt{6}) \)	None	✓				990.2.c.f	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta q^{7}-q^{8}-q^{11}+(4+\cdots)q^{13}+\cdots\)
4950.2.a.bz	$4950$	$2$	4950.a	1.a	$1$	$2$	$2$	$39.526$	\(\Q(\sqrt{6}) \)	None	✓		✓		990.2.c.f	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta q^{7}-q^{8}+q^{11}+(-4+\cdots)q^{13}+\cdots\)
4950.2.a.ca	$4950$	$2$	4950.a	1.a	$1$	$2$	$2$	$39.526$	\(\Q(\sqrt{2}) \)	None	✓				330.2.c.b	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(2+\beta )q^{7}-q^{8}+q^{11}+\cdots\)
4950.2.a.cb	$4950$	$2$	4950.a	1.a	$1$	$2$	$2$	$39.526$	\(\Q(\sqrt{2}) \)	None	✓		✓		330.2.c.b	$1$	$1$	\(2\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-2+\beta )q^{7}+q^{8}+q^{11}+\cdots\)
4950.2.a.cc	$4950$	$2$	4950.a	1.a	$1$	$2$	$2$	$39.526$	\(\Q(\sqrt{6}) \)	None	✓		✓		990.2.c.f	$1$	$1$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta q^{7}+q^{8}-q^{11}+(-4+\cdots)q^{13}+\cdots\)
4950.2.a.cd	$4950$	$2$	4950.a	1.a	$1$	$2$	$2$	$39.526$	\(\Q(\sqrt{6}) \)	None	✓				990.2.c.f	$1$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta q^{7}+q^{8}+q^{11}+(4+\cdots)q^{13}+\cdots\)
4950.2.a.ce	$4950$	$2$	4950.a	1.a	$1$	$2$	$2$	$39.526$	\(\Q(\sqrt{73}) \)	None	✓		✓		1650.2.a.v	$1$	$0$	\(2\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta q^{7}+q^{8}+q^{11}+(-1+\cdots)q^{13}+\cdots\)
4950.2.a.cf	$4950$	$2$	4950.a	1.a	$1$	$2$	$2$	$39.526$	\(\Q(\sqrt{10}) \)	None	✓		✓		330.2.c.a	$1$	$0$	\(2\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(2+\beta )q^{7}+q^{8}-q^{11}+\cdots\)
4950.2.a.cg	$4950$	$2$	4950.a	1.a	$1$	$3$	$3$	$39.526$	3.3.8220.1	None	✓	✓	✓		4950.2.a.cg	$1$	$0$	\(-3\)	\(0\)	\(0\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-\beta _{1}q^{7}-q^{8}+q^{11}+(1+\cdots)q^{13}+\cdots\)
4950.2.a.ch	$4950$	$2$	4950.a	1.a	$1$	$3$	$3$	$39.526$	3.3.8220.1	None	✓	✓	✓		4950.2.a.cg	$1$	$0$	\(-3\)	\(0\)	\(0\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta _{1}q^{7}-q^{8}-q^{11}+(-1+\cdots)q^{13}+\cdots\)
4950.2.a.ci	$4950$	$2$	4950.a	1.a	$1$	$3$	$3$	$39.526$	3.3.8220.1	None	✓	✓	✓		4950.2.a.cg	$1$	$0$	\(3\)	\(0\)	\(0\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-\beta _{1}q^{7}+q^{8}-q^{11}+(1+\cdots)q^{13}+\cdots\)
4950.2.a.cj	$4950$	$2$	4950.a	1.a	$1$	$3$	$3$	$39.526$	3.3.8220.1	None	✓	✓	✓		4950.2.a.cg	$1$	$0$	\(3\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta _{1}q^{7}+q^{8}+q^{11}+(-1+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4950))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4950)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(275))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(330))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(450))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(495))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(550))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(825))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(990))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1650))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2475))\)\(^{\oplus 2}\)