Space of modular forms of level 7488, weight 2, and trivial character

• Label: 7488.2.a
• Level: $7488$
• Weight: $2$
• Character orbit: 7488.a
• Rep. character: $\chi_{7488}(1,\cdot)$
• Character field: $\Q$
• Dimension: $120$
• Newform subspaces: $82$
• Sturm bound: $2688$
• Trace bound: $29$

Defining parameters

Level:	\( N \)	\(=\)	\( 7488 = 2^{6} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7488.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 82 \)
Sturm bound:			\(2688\)
Trace bound:			\(29\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(17\), \(19\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7488))\).

	Total	New	Old
Modular forms	1392	120	1272
Cusp forms	1297	120	1177
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.

\(2\)	\(3\)	\(13\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(168\)	\(10\)	\(158\)		\(157\)	\(10\)	\(147\)		\(11\)	\(0\)	\(11\)
\(+\)	\(+\)	\(-\)	\(-\)		\(176\)	\(14\)	\(162\)		\(164\)	\(14\)	\(150\)		\(12\)	\(0\)	\(12\)
\(+\)	\(-\)	\(+\)	\(-\)		\(180\)	\(19\)	\(161\)		\(168\)	\(19\)	\(149\)		\(12\)	\(0\)	\(12\)
\(+\)	\(-\)	\(-\)	\(+\)		\(172\)	\(17\)	\(155\)		\(160\)	\(17\)	\(143\)		\(12\)	\(0\)	\(12\)
\(-\)	\(+\)	\(+\)	\(-\)		\(180\)	\(14\)	\(166\)		\(168\)	\(14\)	\(154\)		\(12\)	\(0\)	\(12\)
\(-\)	\(+\)	\(-\)	\(+\)		\(172\)	\(10\)	\(162\)		\(160\)	\(10\)	\(150\)		\(12\)	\(0\)	\(12\)
\(-\)	\(-\)	\(+\)	\(+\)		\(168\)	\(17\)	\(151\)		\(156\)	\(17\)	\(139\)		\(12\)	\(0\)	\(12\)
\(-\)	\(-\)	\(-\)	\(-\)		\(176\)	\(19\)	\(157\)		\(164\)	\(19\)	\(145\)		\(12\)	\(0\)	\(12\)
Plus space			\(+\)		\(680\)	\(54\)	\(626\)		\(633\)	\(54\)	\(579\)		\(47\)	\(0\)	\(47\)
Minus space			\(-\)		\(712\)	\(66\)	\(646\)		\(664\)	\(66\)	\(598\)		\(48\)	\(0\)	\(48\)

Trace form

\( 120 q + 120 q^{25} - 16 q^{29} - 16 q^{37} + 16 q^{41} + 120 q^{49} - 64 q^{53} + 32 q^{61} + 32 q^{77} + 80 q^{85} + 32 q^{89} + 32 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7488))\) 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	13
7488.2.a.a	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				468.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}-4q^{7}-4q^{11}+q^{13}+8q^{23}+\cdots\)
7488.2.a.b	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				312.2.a.d	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}-4q^{7}-2q^{11}+q^{13}+6q^{17}+\cdots\)
7488.2.a.c	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				156.2.a.a	$1$	$2$	\(0\)	\(0\)	\(-4\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}-2q^{7}-4q^{11}-q^{13}-2q^{17}+\cdots\)
7488.2.a.d	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				156.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}+2q^{7}+4q^{11}-q^{13}-2q^{17}+\cdots\)
7488.2.a.e	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				312.2.a.d	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}+4q^{7}+2q^{11}+q^{13}+6q^{17}+\cdots\)
7488.2.a.f	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				468.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}+4q^{7}+4q^{11}+q^{13}-8q^{23}+\cdots\)
7488.2.a.g	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				26.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-q^{7}+6q^{11}-q^{13}+3q^{17}+\cdots\)
7488.2.a.h	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				26.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+q^{7}-6q^{11}-q^{13}+3q^{17}+\cdots\)
7488.2.a.i	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				312.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-4q^{7}-q^{13}-2q^{17}+8q^{19}+\cdots\)
7488.2.a.j	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				234.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-2q^{7}-4q^{11}+q^{13}+6q^{19}+\cdots\)
7488.2.a.k	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				936.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-2q^{7}+4q^{11}+q^{13}-2q^{19}+\cdots\)
7488.2.a.l	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				1248.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-2q^{7}+6q^{11}+q^{13}+2q^{17}+\cdots\)
7488.2.a.m	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				1248.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-4q^{11}-q^{13}+6q^{17}-8q^{19}+\cdots\)
7488.2.a.n	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				3744.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-2q^{11}-q^{13}-4q^{19}+4q^{23}+\cdots\)
7488.2.a.o	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				3744.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+2q^{11}-q^{13}+4q^{19}-4q^{23}+\cdots\)
7488.2.a.p	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				1248.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+4q^{11}-q^{13}+6q^{17}+8q^{19}+\cdots\)
7488.2.a.q	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				1248.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+2q^{7}-6q^{11}+q^{13}+2q^{17}+\cdots\)
7488.2.a.r	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				936.2.a.c	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+2q^{7}-4q^{11}+q^{13}+2q^{19}+\cdots\)
7488.2.a.s	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				234.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+2q^{7}+4q^{11}+q^{13}-6q^{19}+\cdots\)
7488.2.a.t	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				312.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+4q^{7}-q^{13}-2q^{17}-8q^{19}+\cdots\)
7488.2.a.u	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				104.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-5q^{7}+2q^{11}+q^{13}+3q^{17}+\cdots\)
7488.2.a.v	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				26.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}+2q^{11}+q^{13}+3q^{17}+\cdots\)
7488.2.a.w	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				26.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}-2q^{11}+q^{13}+3q^{17}+\cdots\)
7488.2.a.x	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				104.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(5\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+5q^{7}-2q^{11}+q^{13}+3q^{17}+\cdots\)
7488.2.a.y	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				312.2.a.b	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}-2q^{11}+q^{13}+6q^{17}+4q^{19}+\cdots\)
7488.2.a.z	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				1248.2.a.d	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-4q^{11}-q^{13}+6q^{17}+6q^{19}+\cdots\)
7488.2.a.ba	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				1248.2.a.c	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-q^{13}-2q^{17}-2q^{19}+8q^{23}+\cdots\)
7488.2.a.bb	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				156.2.a.b	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-q^{13}+6q^{17}+2q^{19}-5q^{25}+\cdots\)
7488.2.a.bc	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				312.2.a.e	$1$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-6q^{11}+q^{13}-2q^{17}+4q^{23}-5q^{25}+\cdots\)
7488.2.a.bd	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				312.2.a.e	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+6q^{11}+q^{13}-2q^{17}-4q^{23}-5q^{25}+\cdots\)
7488.2.a.be	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				1248.2.a.c	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-q^{13}-2q^{17}+2q^{19}-8q^{23}+\cdots\)
7488.2.a.bf	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				156.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-q^{13}+6q^{17}-2q^{19}-5q^{25}+\cdots\)
7488.2.a.bg	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				1248.2.a.d	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}+4q^{11}-q^{13}+6q^{17}-6q^{19}+\cdots\)
7488.2.a.bh	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				312.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}+2q^{11}+q^{13}+6q^{17}-4q^{19}+\cdots\)
7488.2.a.bi	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				416.2.a.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-3q^{7}-2q^{11}-q^{13}+3q^{17}+\cdots\)
7488.2.a.bj	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				416.2.a.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+3q^{7}+2q^{11}-q^{13}+3q^{17}+\cdots\)
7488.2.a.bk	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				78.2.a.a	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-4q^{7}+4q^{11}-q^{13}-2q^{17}+\cdots\)
7488.2.a.bl	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				39.2.a.a	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-4q^{7}+4q^{11}-q^{13}-2q^{17}+\cdots\)
7488.2.a.bm	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				936.2.a.c	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-2q^{7}-4q^{11}+q^{13}-2q^{19}+\cdots\)
7488.2.a.bn	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				52.2.a.a	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-2q^{7}-2q^{11}+q^{13}-6q^{17}+\cdots\)
7488.2.a.bo	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				1248.2.a.e	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-2q^{7}+2q^{11}+q^{13}-6q^{17}+\cdots\)
7488.2.a.bp	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				234.2.a.a	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-2q^{7}+4q^{11}+q^{13}+6q^{19}+\cdots\)
7488.2.a.bq	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				3744.2.a.b	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-2q^{11}-q^{13}+4q^{19}+4q^{23}+\cdots\)
7488.2.a.br	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				312.2.a.f	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-q^{13}-2q^{17}-4q^{19}-q^{25}+\cdots\)
7488.2.a.bs	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				312.2.a.f	$1$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-q^{13}-2q^{17}+4q^{19}-q^{25}+\cdots\)
7488.2.a.bt	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				3744.2.a.b	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+2q^{11}-q^{13}-4q^{19}-4q^{23}+\cdots\)
7488.2.a.bu	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				234.2.a.a	$1$	$1$	\(0\)	\(0\)	\(2\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+2q^{7}-4q^{11}+q^{13}-6q^{19}+\cdots\)
7488.2.a.bv	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				1248.2.a.e	$1$	$1$	\(0\)	\(0\)	\(2\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+2q^{7}-2q^{11}+q^{13}-6q^{17}+\cdots\)
7488.2.a.bw	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				52.2.a.a	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+2q^{7}+2q^{11}+q^{13}-6q^{17}+\cdots\)
7488.2.a.bx	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				936.2.a.c	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+2q^{7}+4q^{11}+q^{13}+2q^{19}+\cdots\)
7488.2.a.by	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				39.2.a.a	$1$	$1$	\(0\)	\(0\)	\(2\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+4q^{7}-4q^{11}-q^{13}-2q^{17}+\cdots\)
7488.2.a.bz	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				78.2.a.a	$1$	$0$	\(0\)	\(0\)	\(2\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+4q^{7}-4q^{11}-q^{13}-2q^{17}+\cdots\)
7488.2.a.ca	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				468.2.a.a	$1$	$1$	\(0\)	\(0\)	\(4\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}-4q^{7}+4q^{11}+q^{13}-8q^{23}+\cdots\)
7488.2.a.cb	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				312.2.a.c	$1$	$1$	\(0\)	\(0\)	\(4\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}-2q^{11}+q^{13}-2q^{17}-8q^{19}+\cdots\)
7488.2.a.cc	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				312.2.a.c	$1$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}+2q^{11}+q^{13}-2q^{17}+8q^{19}+\cdots\)
7488.2.a.cd	$7488$	$2$	7488.a	1.a	$1$	$1$	$1$	$59.792$	\(\Q\)	None	✓				468.2.a.a	$1$	$0$	\(0\)	\(0\)	\(4\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}+4q^{7}-4q^{11}+q^{13}+8q^{23}+\cdots\)
7488.2.a.ce	$7488$	$2$	7488.a	1.a	$1$	$2$	$2$	$59.792$	\(\Q(\sqrt{17}) \)	None	✓				416.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{5}+(-1-\beta )q^{7}-2q^{11}+\cdots\)
7488.2.a.cf	$7488$	$2$	7488.a	1.a	$1$	$2$	$2$	$59.792$	\(\Q(\sqrt{17}) \)	None	✓				416.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{5}+(1+\beta )q^{7}+2q^{11}+\cdots\)
7488.2.a.cg	$7488$	$2$	7488.a	1.a	$1$	$2$	$2$	$59.792$	\(\Q(\sqrt{5}) \)	None	✓				1248.2.a.k	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-6\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{5}+(-3+\beta )q^{7}+2\beta q^{11}+\cdots\)
7488.2.a.ch	$7488$	$2$	7488.a	1.a	$1$	$2$	$2$	$59.792$	\(\Q(\sqrt{5}) \)	None	✓				1248.2.a.k	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(6\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{5}+(3-\beta )q^{7}-2\beta q^{11}+\cdots\)
7488.2.a.ci	$7488$	$2$	7488.a	1.a	$1$	$2$	$2$	$59.792$	\(\Q(\sqrt{2}) \)	None	✓				936.2.a.k	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(-2-\beta )q^{7}+(-2-\beta )q^{11}+\cdots\)
7488.2.a.cj	$7488$	$2$	7488.a	1.a	$1$	$2$	$2$	$59.792$	\(\Q(\sqrt{3}) \)	None	✓				117.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-2q^{7}-\beta q^{11}-q^{13}-2\beta q^{17}+2q^{19}+\cdots\)
7488.2.a.ck	$7488$	$2$	7488.a	1.a	$1$	$2$	$2$	$59.792$	\(\Q(\sqrt{2}) \)	None	✓				936.2.a.k	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(-2+\beta )q^{7}+(2-\beta )q^{11}+\cdots\)
7488.2.a.cl	$7488$	$2$	7488.a	1.a	$1$	$2$	$2$	$59.792$	\(\Q(\sqrt{2}) \)	None	✓				39.2.a.b	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-\beta q^{7}-2q^{11}+q^{13}+(-2+\cdots)q^{17}+\cdots\)
7488.2.a.cm	$7488$	$2$	7488.a	1.a	$1$	$2$	$2$	$59.792$	\(\Q(\sqrt{2}) \)	None	✓				3744.2.a.t	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{7}+\beta q^{11}+q^{13}+\beta q^{19}-2\beta q^{23}+\cdots\)
7488.2.a.cn	$7488$	$2$	7488.a	1.a	$1$	$2$	$2$	$59.792$	\(\Q(\sqrt{2}) \)	None	✓				3744.2.a.t	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{7}+\beta q^{11}+q^{13}-\beta q^{19}-2\beta q^{23}+\cdots\)
7488.2.a.co	$7488$	$2$	7488.a	1.a	$1$	$2$	$2$	$59.792$	\(\Q(\sqrt{2}) \)	None	✓				39.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+\beta q^{7}+2q^{11}+q^{13}+(-2+\cdots)q^{17}+\cdots\)
7488.2.a.cp	$7488$	$2$	7488.a	1.a	$1$	$2$	$2$	$59.792$	\(\Q(\sqrt{2}) \)	None	✓				936.2.a.k	$1$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(2-\beta )q^{7}+(-2+\beta )q^{11}+\cdots\)
7488.2.a.cq	$7488$	$2$	7488.a	1.a	$1$	$2$	$2$	$59.792$	\(\Q(\sqrt{3}) \)	None	✓				117.2.a.b	$2$	$1$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+2q^{7}-\beta q^{11}-q^{13}+2\beta q^{17}-2q^{19}+\cdots\)
7488.2.a.cr	$7488$	$2$	7488.a	1.a	$1$	$2$	$2$	$59.792$	\(\Q(\sqrt{2}) \)	None	✓				936.2.a.k	$1$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(2+\beta )q^{7}+(2+\beta )q^{11}-q^{13}+\cdots\)
7488.2.a.cs	$7488$	$2$	7488.a	1.a	$1$	$2$	$2$	$59.792$	\(\Q(\sqrt{5}) \)	None	✓				1248.2.a.l	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}+(-1-\beta )q^{7}-2q^{11}+\cdots\)
7488.2.a.ct	$7488$	$2$	7488.a	1.a	$1$	$2$	$2$	$59.792$	\(\Q(\sqrt{5}) \)	None	✓				1248.2.a.l	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}+(1+\beta )q^{7}+2q^{11}+q^{13}+\cdots\)
7488.2.a.cu	$7488$	$2$	7488.a	1.a	$1$	$2$	$2$	$59.792$	\(\Q(\sqrt{17}) \)	None	✓				104.2.a.b	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}+(-1+\beta )q^{7}+(-2+2\beta )q^{11}+\cdots\)
7488.2.a.cv	$7488$	$2$	7488.a	1.a	$1$	$2$	$2$	$59.792$	\(\Q(\sqrt{17}) \)	None	✓				104.2.a.b	$1$	$1$	\(0\)	\(0\)	\(3\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}+(1-\beta )q^{7}+(2-2\beta )q^{11}+\cdots\)
7488.2.a.cw	$7488$	$2$	7488.a	1.a	$1$	$2$	$2$	$59.792$	\(\Q(\sqrt{5}) \)	None	✓				416.2.a.d	$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+3q^{5}+\beta q^{7}-2\beta q^{11}+q^{13}+3q^{17}+\cdots\)
7488.2.a.cx	$7488$	$2$	7488.a	1.a	$1$	$3$	$3$	$59.792$	3.3.148.1	None	✓				1248.2.a.o	$1$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{5}+\beta _{2}q^{7}+(-1+\beta _{1}+\beta _{2})q^{11}+\cdots\)
7488.2.a.cy	$7488$	$2$	7488.a	1.a	$1$	$3$	$3$	$59.792$	3.3.148.1	None	✓				1248.2.a.o	$1$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{5}-\beta _{2}q^{7}+(1-\beta _{1}-\beta _{2})q^{11}+\cdots\)
7488.2.a.cz	$7488$	$2$	7488.a	1.a	$1$	$4$	$4$	$59.792$	\(\Q(\zeta_{20})^+\)	None	✓				3744.2.a.bb	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{3})q^{5}-\beta _{2}q^{7}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
7488.2.a.da	$7488$	$2$	7488.a	1.a	$1$	$4$	$4$	$59.792$	4.4.13448.1	None	✓		✓		416.2.a.f	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\beta _{1}q^{11}+\cdots\)
7488.2.a.db	$7488$	$2$	7488.a	1.a	$1$	$4$	$4$	$59.792$	\(\Q(\zeta_{24})^+\)	None	✓				3744.2.a.bc	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}+\beta _{3}q^{7}+(-2-\beta _{2})q^{11}+\cdots\)
7488.2.a.dc	$7488$	$2$	7488.a	1.a	$1$	$4$	$4$	$59.792$	\(\Q(\zeta_{24})^+\)	None	✓				3744.2.a.bc	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}-\beta _{3}q^{7}+(2+\beta _{2})q^{11}+q^{13}+\cdots\)
7488.2.a.dd	$7488$	$2$	7488.a	1.a	$1$	$4$	$4$	$59.792$	\(\Q(\zeta_{20})^+\)	None	✓				3744.2.a.bb	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$-$	$+$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{3})q^{5}-\beta _{2}q^{7}+(-\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7488))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7488)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(234))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(416))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(468))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(576))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(624))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(832))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(936))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1248))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1872))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2496))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3744))\)\(^{\oplus 2}\)