Space of modular forms of level 5952, weight 2, and trivial character

• Label: 5952.2.a
• Level: $5952$
• Weight: $2$
• Character orbit: 5952.a
• Rep. character: $\chi_{5952}(1,\cdot)$
• Character field: $\Q$
• Dimension: $120$
• Newform subspaces: $64$
• Sturm bound: $2048$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 5952 = 2^{6} \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5952.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 64 \)
Sturm bound:			\(2048\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5952))\).

	Total	New	Old
Modular forms	1048	120	928
Cusp forms	1001	120	881
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.

\(2\)	\(3\)	\(31\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(128\)	\(15\)	\(113\)		\(123\)	\(15\)	\(108\)		\(5\)	\(0\)	\(5\)
\(+\)	\(+\)	\(-\)	\(-\)		\(132\)	\(14\)	\(118\)		\(126\)	\(14\)	\(112\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)		\(134\)	\(17\)	\(117\)		\(128\)	\(17\)	\(111\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)		\(130\)	\(12\)	\(118\)		\(124\)	\(12\)	\(112\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)		\(134\)	\(15\)	\(119\)		\(128\)	\(15\)	\(113\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)		\(130\)	\(16\)	\(114\)		\(124\)	\(16\)	\(108\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)		\(128\)	\(13\)	\(115\)		\(122\)	\(13\)	\(109\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)		\(132\)	\(18\)	\(114\)		\(126\)	\(18\)	\(108\)		\(6\)	\(0\)	\(6\)
Plus space			\(+\)		\(516\)	\(56\)	\(460\)		\(493\)	\(56\)	\(437\)		\(23\)	\(0\)	\(23\)
Minus space			\(-\)		\(532\)	\(64\)	\(468\)		\(508\)	\(64\)	\(444\)		\(24\)	\(0\)	\(24\)

Trace form

\( 120 q + 120 q^{9} + 16 q^{17} + 136 q^{25} + 32 q^{29} + 32 q^{37} + 16 q^{41} + 120 q^{49} + 32 q^{53} - 16 q^{73} - 64 q^{77} + 120 q^{81} - 96 q^{85} - 16 q^{89} + 16 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5952))\) 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	31
5952.2.a.a	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				744.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(-5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}-5q^{7}+q^{9}+4q^{11}+\cdots\)
5952.2.a.b	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				186.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}-2q^{7}+q^{9}-5q^{11}+\cdots\)
5952.2.a.c	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				372.2.a.d	$1$	$0$	\(0\)	\(-1\)	\(-3\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}-q^{7}+q^{9}-2q^{13}+3q^{15}+\cdots\)
5952.2.a.d	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				186.2.a.c	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{7}+q^{9}+3q^{11}+q^{13}+\cdots\)
5952.2.a.e	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				744.2.a.c	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+3q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots\)
5952.2.a.f	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				744.2.a.g	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-3q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
5952.2.a.g	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				186.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{7}+q^{9}+3q^{11}-3q^{13}+\cdots\)
5952.2.a.h	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				744.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}+6q^{13}-q^{15}+\cdots\)
5952.2.a.i	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				372.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}+6q^{13}-q^{15}+\cdots\)
5952.2.a.j	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				2976.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+2q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
5952.2.a.k	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				2976.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-4q^{7}+q^{9}-6q^{13}+\cdots\)
5952.2.a.l	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				744.2.a.f	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
5952.2.a.m	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				372.2.a.c	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+4q^{7}+q^{9}-2q^{13}+\cdots\)
5952.2.a.n	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				372.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(-5\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}-5q^{7}+q^{9}-2q^{11}+\cdots\)
5952.2.a.o	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				744.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}-2q^{7}+q^{9}-5q^{11}+\cdots\)
5952.2.a.p	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				744.2.a.e	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}+q^{7}+q^{9}+6q^{11}-3q^{15}+\cdots\)
5952.2.a.q	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				2976.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}+2q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
5952.2.a.r	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				372.2.a.d	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}+q^{7}+q^{9}-2q^{13}-3q^{15}+\cdots\)
5952.2.a.s	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				186.2.a.b	$1$	$0$	\(0\)	\(1\)	\(-3\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}+2q^{7}+q^{9}+5q^{11}+\cdots\)
5952.2.a.t	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				744.2.a.d	$1$	$0$	\(0\)	\(1\)	\(-3\)	\(5\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}+5q^{7}+q^{9}-4q^{11}+\cdots\)
5952.2.a.u	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				744.2.a.c	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-3q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots\)
5952.2.a.v	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				186.2.a.c	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+2q^{7}+q^{9}-3q^{11}+q^{13}+\cdots\)
5952.2.a.w	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				2976.2.a.c	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
5952.2.a.x	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				372.2.a.a	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}+6q^{13}+q^{15}+\cdots\)
5952.2.a.y	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				744.2.a.b	$1$	$0$	\(0\)	\(1\)	\(1\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}+6q^{13}+q^{15}+\cdots\)
5952.2.a.z	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				186.2.a.a	$1$	$1$	\(0\)	\(1\)	\(1\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+2q^{7}+q^{9}-3q^{11}-3q^{13}+\cdots\)
5952.2.a.ba	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				744.2.a.g	$1$	$0$	\(0\)	\(1\)	\(1\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+3q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
5952.2.a.bb	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				372.2.a.c	$1$	$1$	\(0\)	\(1\)	\(2\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-4q^{7}+q^{9}-2q^{13}+\cdots\)
5952.2.a.bc	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				744.2.a.f	$1$	$0$	\(0\)	\(1\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
5952.2.a.bd	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				2976.2.a.b	$1$	$0$	\(0\)	\(1\)	\(2\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+4q^{7}+q^{9}-6q^{13}+\cdots\)
5952.2.a.be	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				2976.2.a.a	$1$	$0$	\(0\)	\(1\)	\(3\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}-2q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
5952.2.a.bf	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				744.2.a.e	$1$	$1$	\(0\)	\(1\)	\(3\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}-q^{7}+q^{9}-6q^{11}+3q^{15}+\cdots\)
5952.2.a.bg	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				744.2.a.a	$1$	$0$	\(0\)	\(1\)	\(3\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}+2q^{7}+q^{9}+5q^{11}+\cdots\)
5952.2.a.bh	$5952$	$2$	5952.a	1.a	$1$	$1$	$1$	$47.527$	\(\Q\)	None	✓				372.2.a.b	$1$	$0$	\(0\)	\(1\)	\(3\)	\(5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}+5q^{7}+q^{9}+2q^{11}+\cdots\)
5952.2.a.bi	$5952$	$2$	5952.a	1.a	$1$	$2$	$2$	$47.527$	\(\Q(\sqrt{41}) \)	None	✓				744.2.a.i	$1$	$1$	\(0\)	\(-2\)	\(-6\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+(-1+\beta )q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)
5952.2.a.bj	$5952$	$2$	5952.a	1.a	$1$	$2$	$2$	$47.527$	\(\Q(\sqrt{3}) \)	None	✓				2976.2.a.h	$1$	$1$	\(0\)	\(-2\)	\(-4\)	\(4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-2+\beta )q^{5}+(2-\beta )q^{7}+q^{9}+\cdots\)
5952.2.a.bk	$5952$	$2$	5952.a	1.a	$1$	$2$	$2$	$47.527$	\(\Q(\sqrt{17}) \)	None	✓				186.2.a.d	$1$	$1$	\(0\)	\(-2\)	\(-3\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta )q^{5}+(-2+2\beta )q^{7}+\cdots\)
5952.2.a.bl	$5952$	$2$	5952.a	1.a	$1$	$2$	$2$	$47.527$	\(\Q(\sqrt{17}) \)	None	✓				372.2.a.e	$1$	$1$	\(0\)	\(-2\)	\(-3\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta )q^{5}+(1-\beta )q^{7}+q^{9}+\cdots\)
5952.2.a.bm	$5952$	$2$	5952.a	1.a	$1$	$2$	$2$	$47.527$	\(\Q(\sqrt{17}) \)	None	✓				744.2.a.h	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+(1+\beta )q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
5952.2.a.bn	$5952$	$2$	5952.a	1.a	$1$	$2$	$2$	$47.527$	\(\Q(\sqrt{2}) \)	None	✓				2976.2.a.g	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}+(1+\beta )q^{7}+q^{9}+\cdots\)
5952.2.a.bo	$5952$	$2$	5952.a	1.a	$1$	$2$	$2$	$47.527$	\(\Q(\sqrt{5}) \)	None	✓				93.2.a.a	$1$	$1$	\(0\)	\(-2\)	\(4\)	\(4\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(2+\beta )q^{5}+(2-\beta )q^{7}+q^{9}+\cdots\)
5952.2.a.bp	$5952$	$2$	5952.a	1.a	$1$	$2$	$2$	$47.527$	\(\Q(\sqrt{41}) \)	None	✓				744.2.a.i	$1$	$0$	\(0\)	\(2\)	\(-6\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}+\beta q^{7}+q^{9}+(-1-\beta )q^{11}+\cdots\)
5952.2.a.bq	$5952$	$2$	5952.a	1.a	$1$	$2$	$2$	$47.527$	\(\Q(\sqrt{3}) \)	None	✓				2976.2.a.h	$1$	$1$	\(0\)	\(2\)	\(-4\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-2+\beta )q^{5}+(-2+\beta )q^{7}+\cdots\)
5952.2.a.br	$5952$	$2$	5952.a	1.a	$1$	$2$	$2$	$47.527$	\(\Q(\sqrt{17}) \)	None	✓				372.2.a.e	$1$	$0$	\(0\)	\(2\)	\(-3\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
5952.2.a.bs	$5952$	$2$	5952.a	1.a	$1$	$2$	$2$	$47.527$	\(\Q(\sqrt{17}) \)	None	✓				186.2.a.d	$1$	$0$	\(0\)	\(2\)	\(-3\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta )q^{5}+(2-2\beta )q^{7}+q^{9}+\cdots\)
5952.2.a.bt	$5952$	$2$	5952.a	1.a	$1$	$2$	$2$	$47.527$	\(\Q(\sqrt{17}) \)	None	✓				744.2.a.h	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+(-1-\beta )q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)
5952.2.a.bu	$5952$	$2$	5952.a	1.a	$1$	$2$	$2$	$47.527$	\(\Q(\sqrt{2}) \)	None	✓				2976.2.a.g	$1$	$1$	\(0\)	\(2\)	\(2\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{5}+(-1-\beta )q^{7}+q^{9}+\cdots\)
5952.2.a.bv	$5952$	$2$	5952.a	1.a	$1$	$2$	$2$	$47.527$	\(\Q(\sqrt{5}) \)	None	✓				93.2.a.a	$1$	$0$	\(0\)	\(2\)	\(4\)	\(-4\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(2+\beta )q^{5}+(-2+\beta )q^{7}+q^{9}+\cdots\)
5952.2.a.bw	$5952$	$2$	5952.a	1.a	$1$	$3$	$3$	$47.527$	3.3.1708.1	None	✓				2976.2.a.n	$1$	$0$	\(0\)	\(-3\)	\(-2\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta _{1})q^{5}+(-1-\beta _{1})q^{7}+\cdots\)
5952.2.a.bx	$5952$	$2$	5952.a	1.a	$1$	$3$	$3$	$47.527$	3.3.1849.1	None	✓				744.2.a.j	$1$	$0$	\(0\)	\(-3\)	\(-2\)	\(5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta _{1})q^{5}+(2+\beta _{2})q^{7}+\cdots\)
5952.2.a.by	$5952$	$2$	5952.a	1.a	$1$	$3$	$3$	$47.527$	3.3.316.1	None	✓				2976.2.a.m	$1$	$1$	\(0\)	\(-3\)	\(1\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(\beta _{1}-\beta _{2})q^{5}+(-1+\beta _{1})q^{7}+\cdots\)
5952.2.a.bz	$5952$	$2$	5952.a	1.a	$1$	$3$	$3$	$47.527$	3.3.229.1	None	✓				93.2.a.b	$1$	$1$	\(0\)	\(-3\)	\(2\)	\(4\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta _{2})q^{5}+(1-\beta _{2})q^{7}+q^{9}+\cdots\)
5952.2.a.ca	$5952$	$2$	5952.a	1.a	$1$	$3$	$3$	$47.527$	3.3.892.1	None	✓				2976.2.a.l	$1$	$0$	\(0\)	\(-3\)	\(3\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{2})q^{5}+(1-\beta _{1})q^{7}+q^{9}+\cdots\)
5952.2.a.cb	$5952$	$2$	5952.a	1.a	$1$	$3$	$3$	$47.527$	3.3.568.1	None	✓				2976.2.a.k	$1$	$0$	\(0\)	\(-3\)	\(4\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta _{1})q^{5}+(-1+\beta _{1})q^{7}+\cdots\)
5952.2.a.cc	$5952$	$2$	5952.a	1.a	$1$	$3$	$3$	$47.527$	3.3.1849.1	None	✓				744.2.a.j	$1$	$1$	\(0\)	\(3\)	\(-2\)	\(-5\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta _{1})q^{5}+(-2-\beta _{2})q^{7}+\cdots\)
5952.2.a.cd	$5952$	$2$	5952.a	1.a	$1$	$3$	$3$	$47.527$	3.3.1708.1	None	✓				2976.2.a.n	$1$	$0$	\(0\)	\(3\)	\(-2\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+\beta _{1})q^{5}+(1+\beta _{1})q^{7}+\cdots\)
5952.2.a.ce	$5952$	$2$	5952.a	1.a	$1$	$3$	$3$	$47.527$	3.3.316.1	None	✓				2976.2.a.m	$1$	$1$	\(0\)	\(3\)	\(1\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(\beta _{1}-\beta _{2})q^{5}+(1-\beta _{1})q^{7}+q^{9}+\cdots\)
5952.2.a.cf	$5952$	$2$	5952.a	1.a	$1$	$3$	$3$	$47.527$	3.3.229.1	None	✓				93.2.a.b	$1$	$0$	\(0\)	\(3\)	\(2\)	\(-4\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta _{2})q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
5952.2.a.cg	$5952$	$2$	5952.a	1.a	$1$	$3$	$3$	$47.527$	3.3.892.1	None	✓				2976.2.a.l	$1$	$0$	\(0\)	\(3\)	\(3\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-\beta _{2})q^{5}+(-1+\beta _{1})q^{7}+\cdots\)
5952.2.a.ch	$5952$	$2$	5952.a	1.a	$1$	$3$	$3$	$47.527$	3.3.568.1	None	✓				2976.2.a.k	$1$	$0$	\(0\)	\(3\)	\(4\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta _{1})q^{5}+(1-\beta _{1})q^{7}+q^{9}+\cdots\)
5952.2.a.ci	$5952$	$2$	5952.a	1.a	$1$	$5$	$5$	$47.527$	5.5.2245192.1	None	✓		✓		2976.2.a.s	$1$	$1$	\(0\)	\(-5\)	\(-6\)	\(2\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta _{3})q^{5}-\beta _{4}q^{7}+q^{9}+\cdots\)
5952.2.a.cj	$5952$	$2$	5952.a	1.a	$1$	$5$	$5$	$47.527$	5.5.2245192.1	None	✓		✓		2976.2.a.s	$1$	$1$	\(0\)	\(5\)	\(-6\)	\(-2\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta _{3})q^{5}+\beta _{4}q^{7}+q^{9}+\cdots\)
5952.2.a.ck	$5952$	$2$	5952.a	1.a	$1$	$6$	$6$	$47.527$	6.6.803803840.1	None	✓		✓		2976.2.a.u	$1$	$0$	\(0\)	\(-6\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{4}q^{5}+\beta _{1}q^{7}+q^{9}+\beta _{2}q^{11}+\cdots\)
5952.2.a.cl	$5952$	$2$	5952.a	1.a	$1$	$6$	$6$	$47.527$	6.6.803803840.1	None	✓		✓		2976.2.a.u	$1$	$0$	\(0\)	\(6\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{4}q^{5}-\beta _{1}q^{7}+q^{9}-\beta _{2}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5952))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5952)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(62))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(93))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(124))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(186))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(248))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(372))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(496))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(744))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(992))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1488))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1984))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2976))\)\(^{\oplus 2}\)