Space of modular forms of level 7200, weight 2, and trivial character

• Label: 7200.2.a
• Level: $7200$
• Weight: $2$
• Character orbit: 7200.a
• Rep. character: $\chi_{7200}(1,\cdot)$
• Character field: $\Q$
• Dimension: $95$
• Newform subspaces: $72$
• Sturm bound: $2880$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 7200 = 2^{5} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7200.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 72 \)
Sturm bound:			\(2880\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(17\), \(19\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7200))\).

	Total	New	Old
Modular forms	1536	95	1441
Cusp forms	1345	95	1250
Eisenstein series	191	0	191

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

\(2\)	\(3\)	\(5\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(186\)	\(9\)	\(177\)		\(163\)	\(9\)	\(154\)		\(23\)	\(0\)	\(23\)
\(+\)	\(+\)	\(-\)	\(-\)		\(198\)	\(10\)	\(188\)		\(174\)	\(10\)	\(164\)		\(24\)	\(0\)	\(24\)
\(+\)	\(-\)	\(+\)	\(-\)		\(192\)	\(15\)	\(177\)		\(168\)	\(15\)	\(153\)		\(24\)	\(0\)	\(24\)
\(+\)	\(-\)	\(-\)	\(+\)		\(192\)	\(14\)	\(178\)		\(168\)	\(14\)	\(154\)		\(24\)	\(0\)	\(24\)
\(-\)	\(+\)	\(+\)	\(-\)		\(198\)	\(9\)	\(189\)		\(174\)	\(9\)	\(165\)		\(24\)	\(0\)	\(24\)
\(-\)	\(+\)	\(-\)	\(+\)		\(186\)	\(10\)	\(176\)		\(162\)	\(10\)	\(152\)		\(24\)	\(0\)	\(24\)
\(-\)	\(-\)	\(+\)	\(+\)		\(192\)	\(12\)	\(180\)		\(168\)	\(12\)	\(156\)		\(24\)	\(0\)	\(24\)
\(-\)	\(-\)	\(-\)	\(-\)		\(192\)	\(16\)	\(176\)		\(168\)	\(16\)	\(152\)		\(24\)	\(0\)	\(24\)
Plus space			\(+\)		\(756\)	\(45\)	\(711\)		\(661\)	\(45\)	\(616\)		\(95\)	\(0\)	\(95\)
Minus space			\(-\)		\(780\)	\(50\)	\(730\)		\(684\)	\(50\)	\(634\)		\(96\)	\(0\)	\(96\)

Trace form

\( 95 q - 6 q^{13} - 2 q^{17} - 6 q^{29} - 6 q^{37} - 10 q^{41} + 87 q^{49} + 18 q^{53} - 14 q^{61} - 34 q^{73} - 16 q^{77} + 22 q^{89} - 10 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7200))\) 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
7200.2.a.a	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				480.2.f.c	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}-4q^{13}+8q^{19}-4q^{23}+6q^{29}+\cdots\)
7200.2.a.b	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				480.2.a.c	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}+2q^{13}-6q^{17}+4q^{23}+2q^{29}+\cdots\)
7200.2.a.c	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				480.2.f.c	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}+4q^{13}-8q^{19}-4q^{23}+6q^{29}+\cdots\)
7200.2.a.d	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				480.2.a.a	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}+4q^{11}-6q^{13}+2q^{17}-4q^{19}+\cdots\)
7200.2.a.e	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				96.2.a.a	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}+4q^{11}+2q^{13}-6q^{17}+4q^{19}+\cdots\)
7200.2.a.f	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				2400.2.a.k	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{7}-4q^{11}-7q^{13}-4q^{17}-q^{19}+\cdots\)
7200.2.a.g	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				2400.2.a.l	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{7}-5q^{13}+5q^{19}-4q^{23}-4q^{29}+\cdots\)
7200.2.a.h	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				2400.2.a.l	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{7}+5q^{13}-5q^{19}-4q^{23}-4q^{29}+\cdots\)
7200.2.a.i	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				2400.2.a.k	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{7}+4q^{11}+7q^{13}+4q^{17}+q^{19}+\cdots\)
7200.2.a.j	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				480.2.f.a	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-6q^{11}-2q^{13}+6q^{17}-4q^{19}+\cdots\)
7200.2.a.k	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				800.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-5q^{11}-5q^{17}+5q^{19}-6q^{23}+\cdots\)
7200.2.a.l	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				160.2.a.a	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-4q^{11}+6q^{13}+2q^{17}-8q^{19}+\cdots\)
7200.2.a.m	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				1440.2.a.b	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-2q^{11}-2q^{17}+4q^{19}-2q^{29}+\cdots\)
7200.2.a.n	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				1440.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+2q^{11}+2q^{17}+4q^{19}+2q^{29}+\cdots\)
7200.2.a.o	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				800.2.a.b	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+5q^{11}+5q^{17}-5q^{19}-6q^{23}+\cdots\)
7200.2.a.p	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				480.2.f.a	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+6q^{11}+2q^{13}-6q^{17}+4q^{19}+\cdots\)
7200.2.a.q	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				2400.2.a.e	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}-4q^{11}-3q^{13}+4q^{17}+q^{19}+\cdots\)
7200.2.a.r	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				2400.2.a.f	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}-q^{13}+3q^{19}+4q^{23}-4q^{29}+\cdots\)
7200.2.a.s	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				2400.2.a.f	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}+q^{13}-3q^{19}+4q^{23}-4q^{29}+\cdots\)
7200.2.a.t	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				2400.2.a.e	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}+4q^{11}+3q^{13}-4q^{17}-q^{19}+\cdots\)
7200.2.a.u	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				480.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{11}-2q^{13}-2q^{17}+8q^{19}+\cdots\)
7200.2.a.v	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓				32.2.a.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-6q^{13}+2q^{17}+10q^{29}+2q^{37}+\cdots\)
7200.2.a.w	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓				1440.2.f.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-4q^{13}-2q^{17}+4q^{29}+12q^{37}+\cdots\)
7200.2.a.x	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓				1440.2.f.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-4q^{13}+2q^{17}-4q^{29}+12q^{37}+\cdots\)
7200.2.a.y	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓				160.2.c.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-4q^{13}+8q^{17}-10q^{29}-12q^{37}+\cdots\)
7200.2.a.z	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				480.2.a.d	$1$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{13}+6q^{17}-4q^{19}+8q^{23}+\cdots\)
7200.2.a.ba	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				480.2.a.d	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{13}+6q^{17}+4q^{19}-8q^{23}+\cdots\)
7200.2.a.bb	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓				160.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+4q^{13}-8q^{17}-10q^{29}+12q^{37}+\cdots\)
7200.2.a.bc	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓				1440.2.f.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	\(q+4q^{13}-2q^{17}-4q^{29}-12q^{37}+\cdots\)
7200.2.a.bd	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓				1440.2.f.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+4q^{13}+2q^{17}+4q^{29}-12q^{37}+\cdots\)
7200.2.a.be	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓				288.2.a.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q+6q^{13}-8q^{17}-4q^{29}+2q^{37}+\cdots\)
7200.2.a.bf	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓				288.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+6q^{13}+8q^{17}+4q^{29}+2q^{37}+\cdots\)
7200.2.a.bg	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				480.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{11}-2q^{13}-2q^{17}-8q^{19}+\cdots\)
7200.2.a.bh	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				2400.2.a.e	$1$	$1$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-4q^{11}+3q^{13}-4q^{17}+q^{19}+\cdots\)
7200.2.a.bi	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				2400.2.a.f	$1$	$1$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-q^{13}-3q^{19}-4q^{23}-4q^{29}+\cdots\)
7200.2.a.bj	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				2400.2.a.f	$1$	$1$	\(0\)	\(0\)	\(0\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}+q^{13}+3q^{19}-4q^{23}-4q^{29}+\cdots\)
7200.2.a.bk	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				2400.2.a.e	$1$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}+4q^{11}-3q^{13}+4q^{17}-q^{19}+\cdots\)
7200.2.a.bl	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				480.2.f.a	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-6q^{11}+2q^{13}-6q^{17}-4q^{19}+\cdots\)
7200.2.a.bm	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				800.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-5q^{11}+5q^{17}+5q^{19}+6q^{23}+\cdots\)
7200.2.a.bn	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				1440.2.a.b	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-2q^{11}+2q^{17}-4q^{19}+2q^{29}+\cdots\)
7200.2.a.bo	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				1440.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}+2q^{11}-2q^{17}-4q^{19}-2q^{29}+\cdots\)
7200.2.a.bp	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				160.2.a.a	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}+4q^{11}+6q^{13}+2q^{17}+8q^{19}+\cdots\)
7200.2.a.bq	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				800.2.a.b	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}+5q^{11}-5q^{17}-5q^{19}+6q^{23}+\cdots\)
7200.2.a.br	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				480.2.f.a	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}+6q^{11}-2q^{13}+6q^{17}+4q^{19}+\cdots\)
7200.2.a.bs	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				2400.2.a.k	$1$	$0$	\(0\)	\(0\)	\(0\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{7}-4q^{11}+7q^{13}+4q^{17}-q^{19}+\cdots\)
7200.2.a.bt	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				2400.2.a.l	$1$	$1$	\(0\)	\(0\)	\(0\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{7}-5q^{13}-5q^{19}+4q^{23}-4q^{29}+\cdots\)
7200.2.a.bu	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				2400.2.a.l	$1$	$0$	\(0\)	\(0\)	\(0\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{7}+5q^{13}+5q^{19}+4q^{23}-4q^{29}+\cdots\)
7200.2.a.bv	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				2400.2.a.k	$1$	$0$	\(0\)	\(0\)	\(0\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{7}+4q^{11}-7q^{13}-4q^{17}+q^{19}+\cdots\)
7200.2.a.bw	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				480.2.a.a	$1$	$1$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}-4q^{11}-6q^{13}+2q^{17}+4q^{19}+\cdots\)
7200.2.a.bx	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				96.2.a.a	$1$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}-4q^{11}+2q^{13}-6q^{17}-4q^{19}+\cdots\)
7200.2.a.by	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				480.2.f.c	$1$	$1$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}-4q^{13}-8q^{19}+4q^{23}+6q^{29}+\cdots\)
7200.2.a.bz	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				480.2.a.c	$1$	$1$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}+2q^{13}-6q^{17}-4q^{23}+2q^{29}+\cdots\)
7200.2.a.ca	$7200$	$2$	7200.a	1.a	$1$	$1$	$1$	$57.492$	\(\Q\)	None	✓				480.2.f.c	$1$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}+4q^{13}+8q^{19}+4q^{23}+6q^{29}+\cdots\)
7200.2.a.cb	$7200$	$2$	7200.a	1.a	$1$	$2$	$2$	$57.492$	\(\Q(\sqrt{5}) \)	\(\Q(\sqrt{-5}) \)	✓				160.2.c.b	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-6\)		$+$	$-$	$-$	$+$	$2$	$N(\mathrm{U}(1))$	\(q+(-3-\beta )q^{7}+(1+3\beta )q^{23}+6q^{29}+\cdots\)
7200.2.a.cc	$7200$	$2$	7200.a	1.a	$1$	$2$	$2$	$57.492$	\(\Q(\sqrt{5}) \)	None	✓				480.2.f.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-2q^{7}-\beta q^{11}-\beta q^{13}-\beta q^{17}+4q^{23}+\cdots\)
7200.2.a.cd	$7200$	$2$	7200.a	1.a	$1$	$2$	$2$	$57.492$	\(\Q(\sqrt{13}) \)	None	✓	✓			7200.2.a.cd	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{7}-2q^{11}-3q^{13}+2\beta q^{17}+\cdots\)
7200.2.a.ce	$7200$	$2$	7200.a	1.a	$1$	$2$	$2$	$57.492$	\(\Q(\sqrt{13}) \)	None	✓	✓			7200.2.a.cd	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{7}-2q^{11}+3q^{13}+2\beta q^{17}+\cdots\)
7200.2.a.cf	$7200$	$2$	7200.a	1.a	$1$	$2$	$2$	$57.492$	\(\Q(\sqrt{5}) \)	None	✓				800.2.a.k	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-2\beta q^{7}-\beta q^{11}-4q^{13}-7q^{17}+\cdots\)
7200.2.a.cg	$7200$	$2$	7200.a	1.a	$1$	$2$	$2$	$57.492$	\(\Q(\sqrt{5}) \)	None	✓				1440.2.a.p	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta q^{7}-\beta q^{11}-4q^{13}-2q^{17}-2\beta q^{23}+\cdots\)
7200.2.a.ch	$7200$	$2$	7200.a	1.a	$1$	$2$	$2$	$57.492$	\(\Q(\sqrt{5}) \)	None	✓				1440.2.a.p	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta q^{7}+\beta q^{11}-4q^{13}+2q^{17}+2\beta q^{23}+\cdots\)
7200.2.a.ci	$7200$	$2$	7200.a	1.a	$1$	$2$	$2$	$57.492$	\(\Q(\sqrt{5}) \)	None	✓	✓			7200.2.a.ci	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{7}+2\beta q^{11}-q^{13}-2q^{17}+3\beta q^{19}+\cdots\)
7200.2.a.cj	$7200$	$2$	7200.a	1.a	$1$	$2$	$2$	$57.492$	\(\Q(\sqrt{5}) \)	None	✓	✓			7200.2.a.ci	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{7}-2\beta q^{11}-q^{13}+2q^{17}+3\beta q^{19}+\cdots\)
7200.2.a.ck	$7200$	$2$	7200.a	1.a	$1$	$2$	$2$	$57.492$	\(\Q(\sqrt{5}) \)	None	✓	✓			7200.2.a.ci	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{7}+2\beta q^{11}+q^{13}-2q^{17}-3\beta q^{19}+\cdots\)
7200.2.a.cl	$7200$	$2$	7200.a	1.a	$1$	$2$	$2$	$57.492$	\(\Q(\sqrt{5}) \)	None	✓	✓			7200.2.a.ci	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{7}-2\beta q^{11}+q^{13}+2q^{17}-3\beta q^{19}+\cdots\)
7200.2.a.cm	$7200$	$2$	7200.a	1.a	$1$	$2$	$2$	$57.492$	\(\Q(\sqrt{2}) \)	None	✓				160.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{7}+2\beta q^{11}+2q^{13}+2q^{17}+\cdots\)
7200.2.a.cn	$7200$	$2$	7200.a	1.a	$1$	$2$	$2$	$57.492$	\(\Q(\sqrt{5}) \)	None	✓				800.2.a.k	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-2\beta q^{7}+\beta q^{11}+4q^{13}+7q^{17}+\cdots\)
7200.2.a.co	$7200$	$2$	7200.a	1.a	$1$	$2$	$2$	$57.492$	\(\Q(\sqrt{13}) \)	None	✓	✓			7200.2.a.cd	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{7}+2q^{11}-3q^{13}-2\beta q^{17}+\cdots\)
7200.2.a.cp	$7200$	$2$	7200.a	1.a	$1$	$2$	$2$	$57.492$	\(\Q(\sqrt{13}) \)	None	✓	✓			7200.2.a.cd	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{7}+2q^{11}+3q^{13}-2\beta q^{17}+\cdots\)
7200.2.a.cq	$7200$	$2$	7200.a	1.a	$1$	$2$	$2$	$57.492$	\(\Q(\sqrt{5}) \)	None	✓				480.2.f.e	$2$	$1$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+2q^{7}+\beta q^{11}-\beta q^{13}-\beta q^{17}-4q^{23}+\cdots\)
7200.2.a.cr	$7200$	$2$	7200.a	1.a	$1$	$2$	$2$	$57.492$	\(\Q(\sqrt{5}) \)	\(\Q(\sqrt{-5}) \)	✓				160.2.c.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)		$-$	$-$	$-$	$-$	$2$	$N(\mathrm{U}(1))$	\(q+(3+\beta )q^{7}+(-1-3\beta )q^{23}+6q^{29}+\cdots\)
7200.2.a.cs	$7200$	$2$	7200.a	1.a	$1$	$4$	$4$	$57.492$	\(\Q(\zeta_{24})^+\)	None	✓		✓		1440.2.f.j	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{7}-\beta _{2}q^{11}+\beta _{2}q^{13}+\beta _{3}q^{17}+\cdots\)
7200.2.a.ct	$7200$	$2$	7200.a	1.a	$1$	$4$	$4$	$57.492$	\(\Q(\zeta_{24})^+\)	None	✓		✓		1440.2.f.j	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{7}+\beta _{2}q^{11}+\beta _{2}q^{13}-\beta _{3}q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7200))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7200)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(300))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(400))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(450))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(480))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(600))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(720))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(800))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(900))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1440))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1800))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2400))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3600))\)\(^{\oplus 2}\)