Space of modular forms of level 4704, weight 2, and trivial character

• Label: 4704.2.a
• Level: $4704$
• Weight: $2$
• Character orbit: 4704.a
• Rep. character: $\chi_{4704}(1,\cdot)$
• Character field: $\Q$
• Dimension: $82$
• Newform subspaces: $52$
• Sturm bound: $1792$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 4704 = 2^{5} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4704.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 52 \)
Sturm bound:			\(1792\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\), \(19\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4704))\).

	Total	New	Old
Modular forms	960	82	878
Cusp forms	833	82	751
Eisenstein series	127	0	127

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

\(2\)	\(3\)	\(7\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(112\)	\(9\)	\(103\)		\(97\)	\(9\)	\(88\)		\(15\)	\(0\)	\(15\)
\(+\)	\(+\)	\(-\)	\(-\)		\(126\)	\(12\)	\(114\)		\(110\)	\(12\)	\(98\)		\(16\)	\(0\)	\(16\)
\(+\)	\(-\)	\(+\)	\(-\)		\(120\)	\(11\)	\(109\)		\(104\)	\(11\)	\(93\)		\(16\)	\(0\)	\(16\)
\(+\)	\(-\)	\(-\)	\(+\)		\(122\)	\(9\)	\(113\)		\(106\)	\(9\)	\(97\)		\(16\)	\(0\)	\(16\)
\(-\)	\(+\)	\(+\)	\(-\)		\(128\)	\(11\)	\(117\)		\(112\)	\(11\)	\(101\)		\(16\)	\(0\)	\(16\)
\(-\)	\(+\)	\(-\)	\(+\)		\(114\)	\(9\)	\(105\)		\(98\)	\(9\)	\(89\)		\(16\)	\(0\)	\(16\)
\(-\)	\(-\)	\(+\)	\(+\)		\(120\)	\(9\)	\(111\)		\(104\)	\(9\)	\(95\)		\(16\)	\(0\)	\(16\)
\(-\)	\(-\)	\(-\)	\(-\)		\(118\)	\(12\)	\(106\)		\(102\)	\(12\)	\(90\)		\(16\)	\(0\)	\(16\)
Plus space			\(+\)		\(468\)	\(36\)	\(432\)		\(405\)	\(36\)	\(369\)		\(63\)	\(0\)	\(63\)
Minus space			\(-\)		\(492\)	\(46\)	\(446\)		\(428\)	\(46\)	\(382\)		\(64\)	\(0\)	\(64\)

Trace form

82 * q + 4 * q^5 + 82 * q^9 + 12 * q^13 - 12 * q^17 + 62 * q^25 + 4 * q^29 - 8 * q^33 + 12 * q^37 - 28 * q^41 + 4 * q^45 - 12 * q^53 + 8 * q^57 - 4 * q^61 - 40 * q^65 - 12 * q^73 + 82 * q^81 + 40 * q^85 - 12 * q^89 - 8 * q^93 + 36 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4704))\) 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
4704.2.a.a	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓				672.2.q.e	$1$	$0$	\(0\)	\(-1\)	\(-4\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}+q^{9}+6q^{11}+5q^{13}+\cdots\)
4704.2.a.b	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓				672.2.q.a	$1$	$0$	\(0\)	\(-1\)	\(-3\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+q^{9}-q^{11}+4q^{13}+\cdots\)
4704.2.a.c	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓				672.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}-2q^{13}+2q^{15}+\cdots\)
4704.2.a.d	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓	✓			4704.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}+2q^{11}+2q^{15}+\cdots\)
4704.2.a.e	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓				96.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
4704.2.a.f	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓				672.2.q.b	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}-q^{11}+q^{15}+8q^{17}+\cdots\)
4704.2.a.g	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓				672.2.q.d	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}-2q^{11}+q^{13}-2q^{17}+\cdots\)
4704.2.a.h	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓				672.2.q.c	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}-2q^{11}+5q^{13}-2q^{17}+\cdots\)
4704.2.a.i	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓				672.2.q.c	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}+2q^{11}-5q^{13}+2q^{17}+\cdots\)
4704.2.a.j	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓				672.2.q.d	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}+2q^{11}-q^{13}+2q^{17}+\cdots\)
4704.2.a.k	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓				672.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}+2q^{11}+2q^{13}-4q^{17}+\cdots\)
4704.2.a.l	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓				672.2.q.b	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}+q^{11}-q^{15}-8q^{17}+\cdots\)
4704.2.a.m	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓				672.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{9}-4q^{11}+6q^{13}+\cdots\)
4704.2.a.n	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓	✓			4704.2.a.d	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{9}-2q^{11}-2q^{15}+\cdots\)
4704.2.a.o	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓				672.2.q.a	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}+q^{9}+q^{11}-4q^{13}+\cdots\)
4704.2.a.p	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓				672.2.q.e	$1$	$1$	\(0\)	\(-1\)	\(4\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}+q^{9}-6q^{11}-5q^{13}+\cdots\)
4704.2.a.q	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓				672.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}+q^{9}-2q^{11}+2q^{13}+\cdots\)
4704.2.a.r	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓				672.2.q.e	$1$	$1$	\(0\)	\(1\)	\(-4\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{5}+q^{9}-6q^{11}+5q^{13}+\cdots\)
4704.2.a.s	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓				672.2.q.a	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}+q^{9}+q^{11}+4q^{13}+\cdots\)
4704.2.a.t	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓				96.2.a.a	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
4704.2.a.u	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓	✓			4704.2.a.d	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}-2q^{11}-2q^{15}+\cdots\)
4704.2.a.v	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓				672.2.a.d	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}-2q^{13}-2q^{15}+\cdots\)
4704.2.a.w	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓				672.2.q.b	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}+q^{11}-q^{15}+8q^{17}+\cdots\)
4704.2.a.x	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓				672.2.q.c	$1$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}-2q^{11}-5q^{13}+2q^{17}+\cdots\)
4704.2.a.y	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓				672.2.q.d	$1$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}-2q^{11}-q^{13}+2q^{17}+\cdots\)
4704.2.a.z	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓				672.2.a.c	$1$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}-2q^{11}+2q^{13}-4q^{17}+\cdots\)
4704.2.a.ba	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓				672.2.q.d	$1$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}+2q^{11}+q^{13}-2q^{17}+\cdots\)
4704.2.a.bb	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓				672.2.q.c	$1$	$0$	\(0\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}+2q^{11}+5q^{13}-2q^{17}+\cdots\)
4704.2.a.bc	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓				672.2.q.b	$1$	$1$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}-q^{11}+q^{15}-8q^{17}+\cdots\)
4704.2.a.bd	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓	✓			4704.2.a.d	$1$	$0$	\(0\)	\(1\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}+2q^{11}+2q^{15}+\cdots\)
4704.2.a.be	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓				672.2.a.b	$1$	$0$	\(0\)	\(1\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots\)
4704.2.a.bf	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓				672.2.q.a	$1$	$0$	\(0\)	\(1\)	\(3\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}+q^{9}-q^{11}-4q^{13}+\cdots\)
4704.2.a.bg	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓				672.2.a.a	$1$	$0$	\(0\)	\(1\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{5}+q^{9}+2q^{11}+2q^{13}+\cdots\)
4704.2.a.bh	$4704$	$2$	4704.a	1.a	$1$	$1$	$1$	$37.562$	\(\Q\)	None	✓				672.2.q.e	$1$	$0$	\(0\)	\(1\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{5}+q^{9}+6q^{11}-5q^{13}+\cdots\)
4704.2.a.bi	$4704$	$2$	4704.a	1.a	$1$	$2$	$2$	$37.562$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓		4704.2.a.bi	$2$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+q^{9}+\beta q^{11}-\beta q^{15}+\cdots\)
4704.2.a.bj	$4704$	$2$	4704.a	1.a	$1$	$2$	$2$	$37.562$	\(\Q(\sqrt{2}) \)	None	✓	✓			4704.2.a.bj	$2$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+q^{9}-2\beta q^{11}+\beta q^{13}+\cdots\)
4704.2.a.bk	$4704$	$2$	4704.a	1.a	$1$	$2$	$2$	$37.562$	\(\Q(\sqrt{2}) \)	None	✓	✓			4704.2.a.bk	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{9}+\beta q^{11}+\beta q^{13}+\beta q^{17}+\cdots\)
4704.2.a.bl	$4704$	$2$	4704.a	1.a	$1$	$2$	$2$	$37.562$	\(\Q(\sqrt{2}) \)	None	✓	✓			4704.2.a.bl	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+q^{9}+2\beta q^{11}-3\beta q^{13}+\cdots\)
4704.2.a.bm	$4704$	$2$	4704.a	1.a	$1$	$2$	$2$	$37.562$	\(\Q(\sqrt{3}) \)	None	✓				672.2.a.i	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+q^{9}+(2+\beta )q^{11}-2q^{13}+\cdots\)
4704.2.a.bn	$4704$	$2$	4704.a	1.a	$1$	$2$	$2$	$37.562$	\(\Q(\sqrt{3}) \)	None	✓				672.2.a.i	$1$	$1$	\(0\)	\(2\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+q^{9}+(-2-\beta )q^{11}+\cdots\)
4704.2.a.bo	$4704$	$2$	4704.a	1.a	$1$	$2$	$2$	$37.562$	\(\Q(\sqrt{2}) \)	None	✓	✓			4704.2.a.bl	$2$	$1$	\(0\)	\(2\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+q^{9}-2\beta q^{11}-3\beta q^{13}+\cdots\)
4704.2.a.bp	$4704$	$2$	4704.a	1.a	$1$	$2$	$2$	$37.562$	\(\Q(\sqrt{2}) \)	None	✓	✓			4704.2.a.bk	$2$	$1$	\(0\)	\(2\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}-\beta q^{11}+\beta q^{13}+\beta q^{17}+\cdots\)
4704.2.a.bq	$4704$	$2$	4704.a	1.a	$1$	$2$	$2$	$37.562$	\(\Q(\sqrt{2}) \)	None	✓	✓			4704.2.a.bj	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+q^{9}+2\beta q^{11}+\beta q^{13}+\cdots\)
4704.2.a.br	$4704$	$2$	4704.a	1.a	$1$	$2$	$2$	$37.562$	\(\Q(\sqrt{2}) \)	None	✓	✓			4704.2.a.bi	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+q^{9}-\beta q^{11}+\beta q^{15}+\cdots\)
4704.2.a.bs	$4704$	$2$	4704.a	1.a	$1$	$3$	$3$	$37.562$	3.3.621.1	None	✓				672.2.q.k	$1$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{2}q^{5}+q^{9}+(\beta _{1}+\beta _{2})q^{11}+\cdots\)
4704.2.a.bt	$4704$	$2$	4704.a	1.a	$1$	$3$	$3$	$37.562$	3.3.621.1	None	✓		✓		672.2.q.k	$1$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{2}q^{5}+q^{9}+(-\beta _{1}-\beta _{2})q^{11}+\cdots\)
4704.2.a.bu	$4704$	$2$	4704.a	1.a	$1$	$3$	$3$	$37.562$	3.3.621.1	None	✓				672.2.q.k	$1$	$0$	\(0\)	\(3\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{2}q^{5}+q^{9}+(-\beta _{1}-\beta _{2})q^{11}+\cdots\)
4704.2.a.bv	$4704$	$2$	4704.a	1.a	$1$	$3$	$3$	$37.562$	3.3.621.1	None	✓		✓		672.2.q.k	$1$	$0$	\(0\)	\(3\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{2}q^{5}+q^{9}+(\beta _{1}+\beta _{2})q^{11}+\cdots\)
4704.2.a.bw	$4704$	$2$	4704.a	1.a	$1$	$4$	$4$	$37.562$	4.4.2624.1	None	✓	✓	✓		4704.2.a.bw	$1$	$1$	\(0\)	\(-4\)	\(-4\)	\(0\)		$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta _{3})q^{5}+q^{9}+(1-\beta _{2}+\cdots)q^{11}+\cdots\)
4704.2.a.bx	$4704$	$2$	4704.a	1.a	$1$	$4$	$4$	$37.562$	4.4.2624.1	None	✓	✓	✓		4704.2.a.bw	$1$	$0$	\(0\)	\(-4\)	\(4\)	\(0\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta _{3})q^{5}+q^{9}+(-1-\beta _{2}+\cdots)q^{11}+\cdots\)
4704.2.a.by	$4704$	$2$	4704.a	1.a	$1$	$4$	$4$	$37.562$	4.4.2624.1	None	✓	✓	✓		4704.2.a.bw	$1$	$1$	\(0\)	\(4\)	\(-4\)	\(0\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta _{3})q^{5}+q^{9}+(-1+\beta _{2}+\cdots)q^{11}+\cdots\)
4704.2.a.bz	$4704$	$2$	4704.a	1.a	$1$	$4$	$4$	$37.562$	4.4.2624.1	None	✓	✓	✓		4704.2.a.bw	$1$	$0$	\(0\)	\(4\)	\(4\)	\(0\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta _{3})q^{5}+q^{9}+(1+\beta _{2})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4704))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4704)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(588))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(672))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(784))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1176))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1568))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2352))\)\(^{\oplus 2}\)