Space of modular forms of level 7360, weight 2, and trivial character

• Label: 7360.2.a
• Level: $7360$
• Weight: $2$
• Character orbit: 7360.a
• Rep. character: $\chi_{7360}(1,\cdot)$
• Character field: $\Q$
• Dimension: $176$
• Newform subspaces: $74$
• Sturm bound: $2304$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 7360 = 2^{6} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7360.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 74 \)
Sturm bound:			\(2304\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7360))\).

	Total	New	Old
Modular forms	1176	176	1000
Cusp forms	1129	176	953
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.

\(2\)	\(5\)	\(23\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(142\)	\(22\)	\(120\)		\(137\)	\(22\)	\(115\)		\(5\)	\(0\)	\(5\)
\(+\)	\(+\)	\(-\)	\(-\)		\(148\)	\(22\)	\(126\)		\(142\)	\(22\)	\(120\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)		\(152\)	\(25\)	\(127\)		\(146\)	\(25\)	\(121\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)		\(146\)	\(19\)	\(127\)		\(140\)	\(19\)	\(121\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)		\(152\)	\(22\)	\(130\)		\(146\)	\(22\)	\(124\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)		\(146\)	\(22\)	\(124\)		\(140\)	\(22\)	\(118\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)		\(142\)	\(19\)	\(123\)		\(136\)	\(19\)	\(117\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)		\(148\)	\(25\)	\(123\)		\(142\)	\(25\)	\(117\)		\(6\)	\(0\)	\(6\)
Plus space			\(+\)		\(576\)	\(82\)	\(494\)		\(553\)	\(82\)	\(471\)		\(23\)	\(0\)	\(23\)
Minus space			\(-\)		\(600\)	\(94\)	\(506\)		\(576\)	\(94\)	\(482\)		\(24\)	\(0\)	\(24\)

Trace form

\( 176 q + 176 q^{9} - 32 q^{13} - 32 q^{21} + 176 q^{25} + 32 q^{33} - 32 q^{37} + 32 q^{41} + 176 q^{49} + 32 q^{57} - 32 q^{61} + 208 q^{81} + 16 q^{93}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7360))\) 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	5	23
7360.2.a.a	$7360$	$2$	7360.a	1.a	$1$	$1$	$1$	$58.770$	\(\Q\)	None	✓				920.2.a.a	$1$	$0$	\(0\)	\(-3\)	\(-1\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-q^{5}+2q^{7}+6q^{9}-q^{13}+\cdots\)
7360.2.a.b	$7360$	$2$	7360.a	1.a	$1$	$1$	$1$	$58.770$	\(\Q\)	None	✓				460.2.a.d	$1$	$0$	\(0\)	\(-3\)	\(1\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+q^{5}+2q^{7}+6q^{9}+3q^{13}+\cdots\)
7360.2.a.c	$7360$	$2$	7360.a	1.a	$1$	$1$	$1$	$58.770$	\(\Q\)	None	✓				3680.2.a.d	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}-q^{7}+q^{9}+2q^{11}+4q^{13}+\cdots\)
7360.2.a.d	$7360$	$2$	7360.a	1.a	$1$	$1$	$1$	$58.770$	\(\Q\)	None	✓				3680.2.a.c	$1$	$0$	\(0\)	\(-2\)	\(1\)	\(-3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}-3q^{7}+q^{9}+6q^{11}+\cdots\)
7360.2.a.e	$7360$	$2$	7360.a	1.a	$1$	$1$	$1$	$58.770$	\(\Q\)	None	✓				3680.2.a.b	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}-q^{7}+q^{9}+2q^{11}-2q^{15}+\cdots\)
7360.2.a.f	$7360$	$2$	7360.a	1.a	$1$	$1$	$1$	$58.770$	\(\Q\)	None	✓				3680.2.a.a	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}+5q^{7}+q^{9}-2q^{11}+\cdots\)
7360.2.a.g	$7360$	$2$	7360.a	1.a	$1$	$1$	$1$	$58.770$	\(\Q\)	None	✓				920.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{9}+2q^{11}+5q^{13}+\cdots\)
7360.2.a.h	$7360$	$2$	7360.a	1.a	$1$	$1$	$1$	$58.770$	\(\Q\)	None	✓				460.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+2q^{7}-2q^{9}-4q^{11}+\cdots\)
7360.2.a.i	$7360$	$2$	7360.a	1.a	$1$	$1$	$1$	$58.770$	\(\Q\)	None	✓				460.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-4q^{7}-2q^{9}+6q^{11}+\cdots\)
7360.2.a.j	$7360$	$2$	7360.a	1.a	$1$	$1$	$1$	$58.770$	\(\Q\)	None	✓				920.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{7}-2q^{9}-q^{13}-q^{15}+\cdots\)
7360.2.a.k	$7360$	$2$	7360.a	1.a	$1$	$1$	$1$	$58.770$	\(\Q\)	None	✓				920.2.a.c	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}-3q^{9}-6q^{11}+2q^{13}+\cdots\)
7360.2.a.l	$7360$	$2$	7360.a	1.a	$1$	$1$	$1$	$58.770$	\(\Q\)	None	✓				920.2.a.c	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}-3q^{9}+6q^{11}+2q^{13}+\cdots\)
7360.2.a.m	$7360$	$2$	7360.a	1.a	$1$	$1$	$1$	$58.770$	\(\Q\)	None	✓				460.2.a.b	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}-3q^{9}-6q^{11}-6q^{13}+\cdots\)
7360.2.a.n	$7360$	$2$	7360.a	1.a	$1$	$1$	$1$	$58.770$	\(\Q\)	None	✓				115.2.a.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}-3q^{9}+2q^{11}+2q^{13}+\cdots\)
7360.2.a.o	$7360$	$2$	7360.a	1.a	$1$	$1$	$1$	$58.770$	\(\Q\)	None	✓				3680.2.a.e	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-3q^{9}-4q^{11}+2q^{13}+2q^{17}+\cdots\)
7360.2.a.p	$7360$	$2$	7360.a	1.a	$1$	$1$	$1$	$58.770$	\(\Q\)	None	✓				3680.2.a.e	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-3q^{9}+4q^{11}+2q^{13}+2q^{17}+\cdots\)
7360.2.a.q	$7360$	$2$	7360.a	1.a	$1$	$1$	$1$	$58.770$	\(\Q\)	None	✓				115.2.a.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-3q^{9}-2q^{11}+2q^{13}+\cdots\)
7360.2.a.r	$7360$	$2$	7360.a	1.a	$1$	$1$	$1$	$58.770$	\(\Q\)	None	✓				460.2.a.b	$1$	$0$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-3q^{9}+6q^{11}-6q^{13}+\cdots\)
7360.2.a.s	$7360$	$2$	7360.a	1.a	$1$	$1$	$1$	$58.770$	\(\Q\)	None	✓				460.2.a.a	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{7}-2q^{9}+4q^{11}+\cdots\)
7360.2.a.t	$7360$	$2$	7360.a	1.a	$1$	$1$	$1$	$58.770$	\(\Q\)	None	✓				920.2.a.b	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{9}-2q^{11}+5q^{13}+\cdots\)
7360.2.a.u	$7360$	$2$	7360.a	1.a	$1$	$1$	$1$	$58.770$	\(\Q\)	None	✓				920.2.a.d	$1$	$1$	\(0\)	\(1\)	\(1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+2q^{7}-2q^{9}-q^{13}+q^{15}+\cdots\)
7360.2.a.v	$7360$	$2$	7360.a	1.a	$1$	$1$	$1$	$58.770$	\(\Q\)	None	✓				460.2.a.c	$1$	$1$	\(0\)	\(1\)	\(1\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+4q^{7}-2q^{9}-6q^{11}+\cdots\)
7360.2.a.w	$7360$	$2$	7360.a	1.a	$1$	$1$	$1$	$58.770$	\(\Q\)	None	✓				3680.2.a.d	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+q^{7}+q^{9}-2q^{11}+4q^{13}+\cdots\)
7360.2.a.x	$7360$	$2$	7360.a	1.a	$1$	$1$	$1$	$58.770$	\(\Q\)	None	✓				3680.2.a.a	$1$	$0$	\(0\)	\(2\)	\(1\)	\(-5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}-5q^{7}+q^{9}+2q^{11}+\cdots\)
7360.2.a.y	$7360$	$2$	7360.a	1.a	$1$	$1$	$1$	$58.770$	\(\Q\)	None	✓				3680.2.a.b	$1$	$0$	\(0\)	\(2\)	\(1\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}+q^{7}+q^{9}-2q^{11}+2q^{15}+\cdots\)
7360.2.a.z	$7360$	$2$	7360.a	1.a	$1$	$1$	$1$	$58.770$	\(\Q\)	None	✓				3680.2.a.c	$1$	$1$	\(0\)	\(2\)	\(1\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}+3q^{7}+q^{9}-6q^{11}+\cdots\)
7360.2.a.ba	$7360$	$2$	7360.a	1.a	$1$	$1$	$1$	$58.770$	\(\Q\)	None	✓				920.2.a.a	$1$	$0$	\(0\)	\(3\)	\(-1\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-q^{5}-2q^{7}+6q^{9}-q^{13}+\cdots\)
7360.2.a.bb	$7360$	$2$	7360.a	1.a	$1$	$1$	$1$	$58.770$	\(\Q\)	None	✓				460.2.a.d	$1$	$0$	\(0\)	\(3\)	\(1\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+q^{5}-2q^{7}+6q^{9}+3q^{13}+\cdots\)
7360.2.a.bc	$7360$	$2$	7360.a	1.a	$1$	$2$	$2$	$58.770$	\(\Q(\sqrt{13}) \)	None	✓				230.2.a.b	$1$	$1$	\(0\)	\(-3\)	\(-2\)	\(3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}-q^{5}+(2-\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
7360.2.a.bd	$7360$	$2$	7360.a	1.a	$1$	$2$	$2$	$58.770$	\(\Q(\sqrt{13}) \)	None	✓				3680.2.a.k	$1$	$1$	\(0\)	\(-3\)	\(2\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+q^{5}+(-2+\beta )q^{7}+\cdots\)
7360.2.a.be	$7360$	$2$	7360.a	1.a	$1$	$2$	$2$	$58.770$	\(\Q(\sqrt{7}) \)	None	✓				3680.2.a.m	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+(-1-\beta )q^{7}-2q^{9}+(-1+\cdots)q^{11}+\cdots\)
7360.2.a.bf	$7360$	$2$	7360.a	1.a	$1$	$2$	$2$	$58.770$	\(\Q(\sqrt{5}) \)	None	✓				115.2.a.b	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(1+\beta )q^{7}-2q^{9}+(-1+\cdots)q^{11}+\cdots\)
7360.2.a.bg	$7360$	$2$	7360.a	1.a	$1$	$2$	$2$	$58.770$	\(\Q(\sqrt{3}) \)	None	✓				3680.2.a.l	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(1-\beta )q^{7}-2q^{9}+(1-\beta )q^{11}+\cdots\)
7360.2.a.bh	$7360$	$2$	7360.a	1.a	$1$	$2$	$2$	$58.770$	\(\Q(\sqrt{5}) \)	None	✓				230.2.a.c	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-q^{5}+(1-\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
7360.2.a.bi	$7360$	$2$	7360.a	1.a	$1$	$2$	$2$	$58.770$	\(\Q(\sqrt{17}) \)	None	✓				460.2.a.e	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-q^{5}+(1-\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
7360.2.a.bj	$7360$	$2$	7360.a	1.a	$1$	$2$	$2$	$58.770$	\(\Q(\sqrt{17}) \)	None	✓				920.2.a.f	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-q^{5}+2\beta q^{7}+(1+\beta )q^{9}+4q^{11}+\cdots\)
7360.2.a.bk	$7360$	$2$	7360.a	1.a	$1$	$2$	$2$	$58.770$	\(\Q(\sqrt{21}) \)	None	✓				230.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+q^{5}+(-1+\beta )q^{7}+(2+\beta )q^{9}+\cdots\)
7360.2.a.bl	$7360$	$2$	7360.a	1.a	$1$	$2$	$2$	$58.770$	\(\Q(\sqrt{17}) \)	None	✓				920.2.a.e	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+q^{5}+(1-\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
7360.2.a.bm	$7360$	$2$	7360.a	1.a	$1$	$2$	$2$	$58.770$	\(\Q(\sqrt{17}) \)	None	✓				920.2.a.f	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}-2\beta q^{7}+(1+\beta )q^{9}-4q^{11}+\cdots\)
7360.2.a.bn	$7360$	$2$	7360.a	1.a	$1$	$2$	$2$	$58.770$	\(\Q(\sqrt{5}) \)	None	✓				230.2.a.c	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}+(-1+\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
7360.2.a.bo	$7360$	$2$	7360.a	1.a	$1$	$2$	$2$	$58.770$	\(\Q(\sqrt{17}) \)	None	✓				460.2.a.e	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}+(-1+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
7360.2.a.bp	$7360$	$2$	7360.a	1.a	$1$	$2$	$2$	$58.770$	\(\Q(\sqrt{17}) \)	None	✓				920.2.a.e	$1$	$0$	\(0\)	\(1\)	\(2\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}+(-1+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
7360.2.a.bq	$7360$	$2$	7360.a	1.a	$1$	$2$	$2$	$58.770$	\(\Q(\sqrt{21}) \)	None	✓				230.2.a.a	$1$	$1$	\(0\)	\(1\)	\(2\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}+(1-\beta )q^{7}+(2+\beta )q^{9}+\cdots\)
7360.2.a.br	$7360$	$2$	7360.a	1.a	$1$	$2$	$2$	$58.770$	\(\Q(\sqrt{7}) \)	None	✓				3680.2.a.m	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+(1+\beta )q^{7}-2q^{9}+(1+\beta )q^{11}+\cdots\)
7360.2.a.bs	$7360$	$2$	7360.a	1.a	$1$	$2$	$2$	$58.770$	\(\Q(\sqrt{3}) \)	None	✓				3680.2.a.l	$1$	$1$	\(0\)	\(2\)	\(2\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+(-1+\beta )q^{7}-2q^{9}+(-1+\cdots)q^{11}+\cdots\)
7360.2.a.bt	$7360$	$2$	7360.a	1.a	$1$	$2$	$2$	$58.770$	\(\Q(\sqrt{5}) \)	None	✓				115.2.a.b	$1$	$0$	\(0\)	\(2\)	\(2\)	\(-2\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+(-1-\beta )q^{7}-2q^{9}+(1+\cdots)q^{11}+\cdots\)
7360.2.a.bu	$7360$	$2$	7360.a	1.a	$1$	$2$	$2$	$58.770$	\(\Q(\sqrt{13}) \)	None	✓				230.2.a.b	$1$	$1$	\(0\)	\(3\)	\(-2\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-q^{5}+(-2+\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
7360.2.a.bv	$7360$	$2$	7360.a	1.a	$1$	$2$	$2$	$58.770$	\(\Q(\sqrt{13}) \)	None	✓				3680.2.a.k	$1$	$0$	\(0\)	\(3\)	\(2\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+q^{5}+(2-\beta )q^{7}+(1+3\beta )q^{9}+\cdots\)
7360.2.a.bw	$7360$	$2$	7360.a	1.a	$1$	$3$	$3$	$58.770$	3.3.229.1	None	✓				920.2.a.i	$1$	$1$	\(0\)	\(-2\)	\(-3\)	\(7\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}-q^{5}+(2-\beta _{2})q^{7}+\cdots\)
7360.2.a.bx	$7360$	$2$	7360.a	1.a	$1$	$3$	$3$	$58.770$	3.3.1573.1	None	✓				3680.2.a.q	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+(-1-\beta _{1})q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots\)
7360.2.a.by	$7360$	$2$	7360.a	1.a	$1$	$3$	$3$	$58.770$	3.3.2597.1	None	✓				920.2.a.h	$1$	$0$	\(0\)	\(-1\)	\(-3\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+(1-\beta _{1})q^{7}+(3+\beta _{2})q^{9}+\cdots\)
7360.2.a.bz	$7360$	$2$	7360.a	1.a	$1$	$3$	$3$	$58.770$	3.3.1101.1	None	✓				230.2.a.d	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+(4+\cdots)q^{9}+\cdots\)
7360.2.a.ca	$7360$	$2$	7360.a	1.a	$1$	$3$	$3$	$58.770$	3.3.621.1	None	✓				920.2.a.g	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+(-1-\beta _{1})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
7360.2.a.cb	$7360$	$2$	7360.a	1.a	$1$	$3$	$3$	$58.770$	3.3.621.1	None	✓				920.2.a.g	$1$	$1$	\(0\)	\(0\)	\(3\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+(1+\beta _{1})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
7360.2.a.cc	$7360$	$2$	7360.a	1.a	$1$	$3$	$3$	$58.770$	3.3.2597.1	None	✓				920.2.a.h	$1$	$0$	\(0\)	\(1\)	\(-3\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+(-1+\beta _{1})q^{7}+(3+\beta _{2})q^{9}+\cdots\)
7360.2.a.cd	$7360$	$2$	7360.a	1.a	$1$	$3$	$3$	$58.770$	3.3.1573.1	None	✓				3680.2.a.q	$1$	$0$	\(0\)	\(1\)	\(-3\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+(1+\beta _{1})q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots\)
7360.2.a.ce	$7360$	$2$	7360.a	1.a	$1$	$3$	$3$	$58.770$	3.3.1101.1	None	✓				230.2.a.d	$1$	$0$	\(0\)	\(1\)	\(3\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+(-1+\beta _{1}+\beta _{2})q^{7}+\cdots\)
7360.2.a.cf	$7360$	$2$	7360.a	1.a	$1$	$3$	$3$	$58.770$	3.3.229.1	None	✓				920.2.a.i	$1$	$1$	\(0\)	\(2\)	\(-3\)	\(-7\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}-q^{5}+(-2+\beta _{2})q^{7}+\cdots\)
7360.2.a.cg	$7360$	$2$	7360.a	1.a	$1$	$4$	$4$	$58.770$	4.4.15317.1	None	✓				115.2.a.c	$1$	$1$	\(0\)	\(-2\)	\(-4\)	\(3\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}-q^{5}+(1+\beta _{3})q^{7}+\cdots\)
7360.2.a.ch	$7360$	$2$	7360.a	1.a	$1$	$4$	$4$	$58.770$	4.4.21208.1	None	✓				3680.2.a.s	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}+q^{5}+(1+\beta _{1})q^{7}+(3-\beta _{1}+\cdots)q^{9}+\cdots\)
7360.2.a.ci	$7360$	$2$	7360.a	1.a	$1$	$4$	$4$	$58.770$	4.4.21208.1	None	✓				3680.2.a.s	$1$	$1$	\(0\)	\(1\)	\(4\)	\(-5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}+q^{5}+(-1-\beta _{1})q^{7}+(3-\beta _{1}+\cdots)q^{9}+\cdots\)
7360.2.a.cj	$7360$	$2$	7360.a	1.a	$1$	$4$	$4$	$58.770$	4.4.15317.1	None	✓				115.2.a.c	$1$	$1$	\(0\)	\(2\)	\(-4\)	\(-3\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}-q^{5}+(-1-\beta _{3})q^{7}+\cdots\)
7360.2.a.ck	$7360$	$2$	7360.a	1.a	$1$	$5$	$5$	$58.770$	5.5.406264.1	None	✓				3680.2.a.u	$1$	$0$	\(0\)	\(-3\)	\(-5\)	\(8\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}-q^{5}+(2-\beta _{1}+\beta _{4})q^{7}+\cdots\)
7360.2.a.cl	$7360$	$2$	7360.a	1.a	$1$	$5$	$5$	$58.770$	5.5.876604.1	None	✓		✓		3680.2.a.x	$1$	$1$	\(0\)	\(-1\)	\(-5\)	\(1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}-q^{5}+(\beta _{2}+\beta _{3}+\beta _{4})q^{7}+\cdots\)
7360.2.a.cm	$7360$	$2$	7360.a	1.a	$1$	$5$	$5$	$58.770$	5.5.2255384.1	None	✓		✓		3680.2.a.w	$1$	$1$	\(0\)	\(-1\)	\(5\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+(-\beta _{2}+\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots\)
7360.2.a.cn	$7360$	$2$	7360.a	1.a	$1$	$5$	$5$	$58.770$	5.5.1143052.1	None	✓		✓		3680.2.a.v	$1$	$1$	\(0\)	\(-1\)	\(5\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+q^{5}+(-1+2\beta _{1}-\beta _{2}+\beta _{4})q^{7}+\cdots\)
7360.2.a.co	$7360$	$2$	7360.a	1.a	$1$	$5$	$5$	$58.770$	5.5.13955077.1	None	✓				920.2.a.j	$1$	$0$	\(0\)	\(0\)	\(5\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+(-\beta _{3}-\beta _{4})q^{7}+(2+\cdots)q^{9}+\cdots\)
7360.2.a.cp	$7360$	$2$	7360.a	1.a	$1$	$5$	$5$	$58.770$	5.5.13955077.1	None	✓				920.2.a.j	$1$	$0$	\(0\)	\(0\)	\(5\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+(\beta _{3}+\beta _{4})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
7360.2.a.cq	$7360$	$2$	7360.a	1.a	$1$	$5$	$5$	$58.770$	5.5.876604.1	None	✓		✓		3680.2.a.x	$1$	$0$	\(0\)	\(1\)	\(-5\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}-q^{5}+(-\beta _{2}-\beta _{3}-\beta _{4})q^{7}+\cdots\)
7360.2.a.cr	$7360$	$2$	7360.a	1.a	$1$	$5$	$5$	$58.770$	5.5.1143052.1	None	✓				3680.2.a.v	$1$	$0$	\(0\)	\(1\)	\(5\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+q^{5}+(1-2\beta _{1}+\beta _{2}-\beta _{4})q^{7}+\cdots\)
7360.2.a.cs	$7360$	$2$	7360.a	1.a	$1$	$5$	$5$	$58.770$	5.5.2255384.1	None	✓				3680.2.a.w	$1$	$0$	\(0\)	\(1\)	\(5\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+(\beta _{2}-\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots\)
7360.2.a.ct	$7360$	$2$	7360.a	1.a	$1$	$5$	$5$	$58.770$	5.5.406264.1	None	✓				3680.2.a.u	$1$	$1$	\(0\)	\(3\)	\(-5\)	\(-8\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}-q^{5}+(-2+\beta _{1}-\beta _{4})q^{7}+\cdots\)
7360.2.a.cu	$7360$	$2$	7360.a	1.a	$1$	$6$	$6$	$58.770$	6.6.255601784.1	None	✓		✓		3680.2.a.bc	$1$	$1$	\(0\)	\(-5\)	\(-6\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}-q^{5}+(1+\beta _{3})q^{7}+\cdots\)
7360.2.a.cv	$7360$	$2$	7360.a	1.a	$1$	$6$	$6$	$58.770$	6.6.255601784.1	None	✓		✓		3680.2.a.bc	$1$	$0$	\(0\)	\(5\)	\(-6\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}-q^{5}+(-1-\beta _{3})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7360))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7360)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(368))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(460))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(736))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(920))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1472))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1840))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3680))\)\(^{\oplus 2}\)