Space of modular forms of level 9280, weight 2, and trivial character

• Label: 9280.2.a
• Level: $9280$
• Weight: $2$
• Character orbit: 9280.a
• Rep. character: $\chi_{9280}(1,\cdot)$
• Character field: $\Q$
• Dimension: $224$
• Newform subspaces: $73$
• Sturm bound: $2880$
• Trace bound: $21$

Defining parameters

Level:	\( N \)	\(=\)	\( 9280 = 2^{6} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9280.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 73 \)
Sturm bound:			\(2880\)
Trace bound:			\(21\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\), \(13\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9280))\).

	Total	New	Old
Modular forms	1464	224	1240
Cusp forms	1417	224	1193
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.

\(2\)	\(5\)	\(29\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(170\)	\(26\)	\(144\)		\(165\)	\(26\)	\(139\)		\(5\)	\(0\)	\(5\)
\(+\)	\(+\)	\(-\)	\(-\)		\(190\)	\(30\)	\(160\)		\(184\)	\(30\)	\(154\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)		\(182\)	\(30\)	\(152\)		\(176\)	\(30\)	\(146\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)		\(186\)	\(26\)	\(160\)		\(180\)	\(26\)	\(154\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)		\(196\)	\(30\)	\(166\)		\(190\)	\(30\)	\(160\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)		\(176\)	\(26\)	\(150\)		\(170\)	\(26\)	\(144\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)		\(184\)	\(26\)	\(158\)		\(178\)	\(26\)	\(152\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)		\(180\)	\(30\)	\(150\)		\(174\)	\(30\)	\(144\)		\(6\)	\(0\)	\(6\)
Plus space			\(+\)		\(716\)	\(104\)	\(612\)		\(693\)	\(104\)	\(589\)		\(23\)	\(0\)	\(23\)
Minus space			\(-\)		\(748\)	\(120\)	\(628\)		\(724\)	\(120\)	\(604\)		\(24\)	\(0\)	\(24\)

Trace form

\( 224 q + 224 q^{9} - 32 q^{13} - 32 q^{21} + 224 q^{25} + 32 q^{33} - 32 q^{37} + 32 q^{41} + 224 q^{49} + 32 q^{57} + 32 q^{69} + 256 q^{81} + 32 q^{85} - 32 q^{93}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9280))\) 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	29
9280.2.a.a	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	\(\Q\)	None	✓				4640.2.a.b	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+4q^{7}+q^{9}+2q^{11}+\cdots\)
9280.2.a.b	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	\(\Q\)	None	✓				1160.2.a.c	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}-4q^{7}+q^{9}+2q^{13}+\cdots\)
9280.2.a.c	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	\(\Q\)	None	✓				4640.2.a.a	$1$	$0$	\(0\)	\(-2\)	\(1\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}-2q^{7}+q^{9}+4q^{11}+\cdots\)
9280.2.a.d	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	\(\Q\)	None	✓				1160.2.a.a	$1$	$0$	\(0\)	\(-2\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
9280.2.a.e	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	\(\Q\)	None	✓				1160.2.a.d	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}+4q^{7}+q^{9}-6q^{13}+\cdots\)
9280.2.a.f	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	\(\Q\)	None	✓				580.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}-3q^{9}+4q^{11}+6q^{13}+\cdots\)
9280.2.a.g	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	\(\Q\)	None	✓				1160.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{9}+2q^{13}-6q^{17}-8q^{19}+\cdots\)
9280.2.a.h	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	\(\Q\)	None	✓				1160.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{9}+2q^{13}-6q^{17}+8q^{19}+\cdots\)
9280.2.a.i	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	\(\Q\)	None	✓				580.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-3q^{9}-4q^{11}+6q^{13}+\cdots\)
9280.2.a.j	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	\(\Q\)	None	✓				4640.2.a.c	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-3q^{9}-2q^{11}-2q^{13}+\cdots\)
9280.2.a.k	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	\(\Q\)	None	✓				290.2.a.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-3q^{9}-2q^{11}+6q^{13}+\cdots\)
9280.2.a.l	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	\(\Q\)	None	✓				145.2.a.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-3q^{9}+6q^{11}-2q^{13}+\cdots\)
9280.2.a.m	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	\(\Q\)	None	✓				580.2.a.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-3q^{9}-2q^{11}+2q^{13}-2q^{19}+\cdots\)
9280.2.a.n	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	\(\Q\)	None	✓				580.2.a.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-3q^{9}+2q^{11}+2q^{13}+2q^{19}+\cdots\)
9280.2.a.o	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	\(\Q\)	None	✓				145.2.a.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-3q^{9}-6q^{11}-2q^{13}+\cdots\)
9280.2.a.p	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	\(\Q\)	None	✓				4640.2.a.c	$1$	$0$	\(0\)	\(0\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-3q^{9}+2q^{11}-2q^{13}+\cdots\)
9280.2.a.q	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	\(\Q\)	None	✓				290.2.a.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-3q^{9}+2q^{11}+6q^{13}+\cdots\)
9280.2.a.r	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	\(\Q\)	None	✓				4640.2.a.b	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}-4q^{7}+q^{9}-2q^{11}+\cdots\)
9280.2.a.s	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	\(\Q\)	None	✓				1160.2.a.d	$1$	$0$	\(0\)	\(2\)	\(1\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}-4q^{7}+q^{9}-6q^{13}+\cdots\)
9280.2.a.t	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	\(\Q\)	None	✓				1160.2.a.a	$1$	$1$	\(0\)	\(2\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
9280.2.a.u	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	\(\Q\)	None	✓				4640.2.a.a	$1$	$0$	\(0\)	\(2\)	\(1\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}+2q^{7}+q^{9}-4q^{11}+\cdots\)
9280.2.a.v	$9280$	$2$	9280.a	1.a	$1$	$1$	$1$	$74.101$	\(\Q\)	None	✓				1160.2.a.c	$1$	$0$	\(0\)	\(2\)	\(1\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}+4q^{7}+q^{9}+2q^{13}+\cdots\)
9280.2.a.w	$9280$	$2$	9280.a	1.a	$1$	$2$	$2$	$74.101$	\(\Q(\sqrt{2}) \)	None	✓				145.2.a.b	$1$	$0$	\(0\)	\(-4\)	\(-2\)	\(4\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+(2+\beta )q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
9280.2.a.x	$9280$	$2$	9280.a	1.a	$1$	$2$	$2$	$74.101$	\(\Q(\sqrt{13}) \)	None	✓				290.2.a.c	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-q^{5}+(1+\beta )q^{7}+\beta q^{9}+(-2+\cdots)q^{11}+\cdots\)
9280.2.a.y	$9280$	$2$	9280.a	1.a	$1$	$2$	$2$	$74.101$	\(\Q(\sqrt{5}) \)	None	✓				4640.2.a.g	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+q^{5}+(1-3\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
9280.2.a.z	$9280$	$2$	9280.a	1.a	$1$	$2$	$2$	$74.101$	\(\Q(\sqrt{13}) \)	None	✓				290.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(5\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+q^{5}+(3-\beta )q^{7}+\beta q^{9}+(2+\cdots)q^{11}+\cdots\)
9280.2.a.ba	$9280$	$2$	9280.a	1.a	$1$	$2$	$2$	$74.101$	\(\Q(\sqrt{2}) \)	None	✓				4640.2.a.h	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}-\beta q^{7}-3q^{9}+\beta q^{11}+2q^{13}+\cdots\)
9280.2.a.bb	$9280$	$2$	9280.a	1.a	$1$	$2$	$2$	$74.101$	\(\Q(\sqrt{13}) \)	None	✓				290.2.a.c	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}+(-1-\beta )q^{7}+\beta q^{9}+\cdots\)
9280.2.a.bc	$9280$	$2$	9280.a	1.a	$1$	$2$	$2$	$74.101$	\(\Q(\sqrt{13}) \)	None	✓				290.2.a.b	$1$	$1$	\(0\)	\(1\)	\(2\)	\(-5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}+(-3+\beta )q^{7}+\beta q^{9}+\cdots\)
9280.2.a.bd	$9280$	$2$	9280.a	1.a	$1$	$2$	$2$	$74.101$	\(\Q(\sqrt{5}) \)	None	✓				4640.2.a.g	$1$	$1$	\(0\)	\(1\)	\(2\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}+(-1+3\beta )q^{7}+(-2+\cdots)q^{9}+\cdots\)
9280.2.a.be	$9280$	$2$	9280.a	1.a	$1$	$2$	$2$	$74.101$	\(\Q(\sqrt{2}) \)	None	✓				145.2.a.b	$1$	$1$	\(0\)	\(4\)	\(-2\)	\(-4\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+(-2-\beta )q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)
9280.2.a.bf	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.621.1	None	✓				290.2.a.e	$1$	$1$	\(0\)	\(-3\)	\(3\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+q^{5}+(1+\beta _{1}-\beta _{2})q^{7}+\cdots\)
9280.2.a.bg	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.229.1	None	✓				4640.2.a.j	$1$	$0$	\(0\)	\(-3\)	\(3\)	\(7\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}+q^{5}+(2+2\beta _{1}-\beta _{2})q^{7}+\cdots\)
9280.2.a.bh	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.148.1	None	✓				580.2.a.d	$1$	$1$	\(0\)	\(-2\)	\(-3\)	\(2\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}-q^{5}+(1-\beta _{2})q^{7}+\cdots\)
9280.2.a.bi	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.148.1	None	✓				1160.2.a.f	$1$	$1$	\(0\)	\(-2\)	\(-3\)	\(4\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}-q^{5}+(1+\beta _{1})q^{7}+\cdots\)
9280.2.a.bj	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.148.1	None	✓				145.2.a.c	$1$	$0$	\(0\)	\(-2\)	\(-3\)	\(4\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}-q^{5}+(1+\beta _{1})q^{7}+\cdots\)
9280.2.a.bk	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.564.1	None	✓				580.2.a.c	$1$	$1$	\(0\)	\(-2\)	\(3\)	\(-4\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
9280.2.a.bl	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.148.1	None	✓				1160.2.a.e	$1$	$1$	\(0\)	\(-2\)	\(3\)	\(-2\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
9280.2.a.bm	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.148.1	None	✓				145.2.a.d	$1$	$1$	\(0\)	\(-2\)	\(3\)	\(2\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+q^{5}+(1-\beta _{2})q^{7}+\cdots\)
9280.2.a.bn	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.469.1	None	✓				290.2.a.d	$1$	$0$	\(0\)	\(-1\)	\(-3\)	\(1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}-q^{5}+\beta _{1}q^{7}+(1+\beta _{1}-2\beta _{2})q^{9}+\cdots\)
9280.2.a.bo	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.229.1	None	✓				1160.2.a.g	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+q^{5}+(-1+\beta _{1})q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)
9280.2.a.bp	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.469.1	None	✓				290.2.a.d	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}-q^{5}-\beta _{1}q^{7}+(1+\beta _{1}-2\beta _{2})q^{9}+\cdots\)
9280.2.a.bq	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.229.1	None	✓				1160.2.a.g	$1$	$0$	\(0\)	\(1\)	\(3\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+q^{5}+(1-\beta _{1})q^{7}+(\beta _{1}-2\beta _{2})q^{9}+\cdots\)
9280.2.a.br	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.148.1	None	✓				145.2.a.c	$1$	$1$	\(0\)	\(2\)	\(-3\)	\(-4\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}-q^{5}+(-1-\beta _{1})q^{7}+\cdots\)
9280.2.a.bs	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.148.1	None	✓				1160.2.a.f	$1$	$0$	\(0\)	\(2\)	\(-3\)	\(-4\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}-q^{5}+(-1-\beta _{1})q^{7}+\cdots\)
9280.2.a.bt	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.148.1	None	✓				580.2.a.d	$1$	$0$	\(0\)	\(2\)	\(-3\)	\(-2\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}-q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
9280.2.a.bu	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.148.1	None	✓				145.2.a.d	$1$	$0$	\(0\)	\(2\)	\(3\)	\(-2\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
9280.2.a.bv	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.148.1	None	✓				1160.2.a.e	$1$	$0$	\(0\)	\(2\)	\(3\)	\(2\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+q^{5}+(1-\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots\)
9280.2.a.bw	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.564.1	None	✓				580.2.a.c	$1$	$0$	\(0\)	\(2\)	\(3\)	\(4\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}+q^{5}+(1-\beta _{2})q^{7}+(4+\cdots)q^{9}+\cdots\)
9280.2.a.bx	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.229.1	None	✓				4640.2.a.j	$1$	$0$	\(0\)	\(3\)	\(3\)	\(-7\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+q^{5}+(-2-2\beta _{1}+\beta _{2})q^{7}+\cdots\)
9280.2.a.by	$9280$	$2$	9280.a	1.a	$1$	$3$	$3$	$74.101$	3.3.621.1	None	✓				290.2.a.e	$1$	$0$	\(0\)	\(3\)	\(3\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+q^{5}+(-1-\beta _{1}+\beta _{2})q^{7}+\cdots\)
9280.2.a.bz	$9280$	$2$	9280.a	1.a	$1$	$4$	$4$	$74.101$	4.4.11344.1	None	✓				4640.2.a.l	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(-2\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}+q^{5}+\beta _{3}q^{7}+(2-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
9280.2.a.ca	$9280$	$2$	9280.a	1.a	$1$	$4$	$4$	$74.101$	\(\Q(\zeta_{24})^+\)	None	✓				4640.2.a.q	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}-q^{5}-\beta _{3}q^{7}-q^{9}-\beta _{2}q^{11}+\cdots\)
9280.2.a.cb	$9280$	$2$	9280.a	1.a	$1$	$4$	$4$	$74.101$	\(\Q(\zeta_{24})^+\)	None	✓				4640.2.a.p	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}-q^{5}+\beta _{2}q^{7}-q^{9}+\beta _{2}q^{11}+\cdots\)
9280.2.a.cc	$9280$	$2$	9280.a	1.a	$1$	$4$	$4$	$74.101$	\(\Q(\zeta_{24})^+\)	None	✓				4640.2.a.m	$2$	$1$	\(0\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+q^{5}-\beta _{2}q^{7}-q^{9}+\beta _{3}q^{11}+\cdots\)
9280.2.a.cd	$9280$	$2$	9280.a	1.a	$1$	$4$	$4$	$74.101$	\(\Q(\sqrt{6}, \sqrt{26})\)	None	✓				4640.2.a.o	$2$	$1$	\(0\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+\beta _{1}q^{7}+3q^{9}-\beta _{2}q^{11}+\cdots\)
9280.2.a.ce	$9280$	$2$	9280.a	1.a	$1$	$4$	$4$	$74.101$	\(\Q(\sqrt{6}, \sqrt{10})\)	None	✓				4640.2.a.n	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+q^{5}+\beta _{3}q^{7}+3q^{9}+\beta _{3}q^{11}+\cdots\)
9280.2.a.cf	$9280$	$2$	9280.a	1.a	$1$	$4$	$4$	$74.101$	4.4.11344.1	None	✓				4640.2.a.l	$1$	$0$	\(0\)	\(2\)	\(4\)	\(2\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}+q^{5}-\beta _{3}q^{7}+(2-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
9280.2.a.cg	$9280$	$2$	9280.a	1.a	$1$	$5$	$5$	$74.101$	5.5.580484.1	None	✓				1160.2.a.j	$1$	$1$	\(0\)	\(-3\)	\(-5\)	\(7\)		$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{3})q^{3}-q^{5}+(1-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
9280.2.a.ch	$9280$	$2$	9280.a	1.a	$1$	$5$	$5$	$74.101$	5.5.6083172.1	None	✓				1160.2.a.i	$1$	$1$	\(0\)	\(-1\)	\(-5\)	\(1\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+(\beta _{2}-\beta _{3})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
9280.2.a.ci	$9280$	$2$	9280.a	1.a	$1$	$5$	$5$	$74.101$	5.5.3145252.1	None	✓		✓		1160.2.a.h	$1$	$1$	\(0\)	\(-1\)	\(5\)	\(-7\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}+q^{5}+(-1+\beta _{2})q^{7}+(2-\beta _{2}+\cdots)q^{9}+\cdots\)
9280.2.a.cj	$9280$	$2$	9280.a	1.a	$1$	$5$	$5$	$74.101$	5.5.6083172.1	None	✓				1160.2.a.i	$1$	$0$	\(0\)	\(1\)	\(-5\)	\(-1\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+(-\beta _{2}+\beta _{3})q^{7}+(2+\cdots)q^{9}+\cdots\)
9280.2.a.ck	$9280$	$2$	9280.a	1.a	$1$	$5$	$5$	$74.101$	5.5.3145252.1	None	✓		✓		1160.2.a.h	$1$	$0$	\(0\)	\(1\)	\(5\)	\(7\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}+q^{5}+(1-\beta _{2})q^{7}+(2-\beta _{2}+\cdots)q^{9}+\cdots\)
9280.2.a.cl	$9280$	$2$	9280.a	1.a	$1$	$5$	$5$	$74.101$	5.5.580484.1	None	✓				1160.2.a.j	$1$	$0$	\(0\)	\(3\)	\(-5\)	\(-7\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{3})q^{3}-q^{5}+(-1+\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
9280.2.a.cm	$9280$	$2$	9280.a	1.a	$1$	$6$	$6$	$74.101$	6.6.39643024.1	None	✓				4640.2.a.t	$1$	$1$	\(0\)	\(-1\)	\(-6\)	\(5\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+(1+\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots\)
9280.2.a.cn	$9280$	$2$	9280.a	1.a	$1$	$6$	$6$	$74.101$	6.6.26118032.1	None	✓				4640.2.a.s	$1$	$1$	\(0\)	\(-1\)	\(6\)	\(3\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+(-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
9280.2.a.co	$9280$	$2$	9280.a	1.a	$1$	$6$	$6$	$74.101$	6.6.39643024.1	None	✓				4640.2.a.t	$1$	$1$	\(0\)	\(1\)	\(-6\)	\(-5\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+(-1-\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots\)
9280.2.a.cp	$9280$	$2$	9280.a	1.a	$1$	$6$	$6$	$74.101$	6.6.26118032.1	None	✓				4640.2.a.s	$1$	$1$	\(0\)	\(1\)	\(6\)	\(-3\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+(\beta _{1}+\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
9280.2.a.cq	$9280$	$2$	9280.a	1.a	$1$	$7$	$7$	$74.101$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				4640.2.a.w	$1$	$0$	\(0\)	\(-1\)	\(-7\)	\(1\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+(-\beta _{1}+\beta _{5})q^{7}+(1+\cdots)q^{9}+\cdots\)
9280.2.a.cr	$9280$	$2$	9280.a	1.a	$1$	$7$	$7$	$74.101$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓				4640.2.a.w	$1$	$0$	\(0\)	\(1\)	\(-7\)	\(-1\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+(\beta _{1}-\beta _{5})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
9280.2.a.cs	$9280$	$2$	9280.a	1.a	$1$	$8$	$8$	$74.101$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		4640.2.a.y	$2$	$1$	\(0\)	\(0\)	\(-8\)	\(0\)		$-$	$+$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+(-\beta _{1}-\beta _{5})q^{7}+(1+\cdots)q^{9}+\cdots\)
9280.2.a.ct	$9280$	$2$	9280.a	1.a	$1$	$10$	$10$	$74.101$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		4640.2.a.ba	$2$	$0$	\(0\)	\(0\)	\(-10\)	\(0\)		$-$	$+$	$+$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+\beta _{7}q^{7}+(3+\beta _{2})q^{9}+\cdots\)
9280.2.a.cu	$9280$	$2$	9280.a	1.a	$1$	$10$	$10$	$74.101$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		4640.2.a.z	$2$	$0$	\(0\)	\(0\)	\(10\)	\(0\)		$-$	$-$	$-$	$-$	$2^{6}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}-\beta _{9}q^{7}+(2+\beta _{2})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9280))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9280)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(116))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(145))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(232))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(290))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(464))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(580))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(928))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1856))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2320))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4640))\)\(^{\oplus 2}\)