Space of modular forms of level 9360, weight 2, and trivial character

• Label: 9360.2.a
• Level: $9360$
• Weight: $2$
• Character orbit: 9360.a
• Rep. character: $\chi_{9360}(1,\cdot)$
• Character field: $\Q$
• Dimension: $120$
• Newform subspaces: $83$
• Sturm bound: $4032$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 9360 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9360.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 83 \)
Sturm bound:			\(4032\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(7\), \(11\), \(17\), \(19\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9360))\).

	Total	New	Old
Modular forms	2064	120	1944
Cusp forms	1969	120	1849
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.

\(2\)	\(3\)	\(5\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	$+$	\(7\)
\(+\)	\(+\)	\(+\)	\(-\)	$-$	\(5\)
\(+\)	\(+\)	\(-\)	\(+\)	$-$	\(7\)
\(+\)	\(+\)	\(-\)	\(-\)	$+$	\(5\)
\(+\)	\(-\)	\(+\)	\(+\)	$-$	\(9\)
\(+\)	\(-\)	\(+\)	\(-\)	$+$	\(8\)
\(+\)	\(-\)	\(-\)	\(+\)	$+$	\(8\)
\(+\)	\(-\)	\(-\)	\(-\)	$-$	\(11\)
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(5\)
\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(7\)
\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(5\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(7\)
\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(9\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(10\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(10\)
\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(7\)
Plus space				\(+\)	\(56\)
Minus space				\(-\)	\(64\)

Trace form

\( 120 q + 4 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9360))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	13
9360.2.a.a	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-4\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-4q^{7}+q^{13}-2q^{17}+q^{25}+\cdots\)
9360.2.a.b	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-4\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-4q^{7}+4q^{11}+q^{13}-6q^{17}+\cdots\)
9360.2.a.c	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-3\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{7}-5q^{11}-q^{13}-3q^{17}+\cdots\)
9360.2.a.d	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-3\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{7}-q^{11}-q^{13}+q^{17}+\cdots\)
9360.2.a.e	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-3\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{7}+q^{11}+q^{13}+3q^{17}+\cdots\)
9360.2.a.f	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}-4q^{11}-q^{13}-4q^{17}+\cdots\)
9360.2.a.g	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}+q^{13}-2q^{19}-6q^{23}+\cdots\)
9360.2.a.h	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}+4q^{11}-q^{13}-8q^{17}+\cdots\)
9360.2.a.i	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}+4q^{11}-q^{13}-4q^{17}+\cdots\)
9360.2.a.j	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}+4q^{11}-q^{13}-2q^{19}+\cdots\)
9360.2.a.k	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-4q^{11}+q^{13}-2q^{17}+4q^{19}+\cdots\)
9360.2.a.l	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{13}-2q^{17}+8q^{19}-4q^{23}+\cdots\)
9360.2.a.m	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{13}+6q^{17}+8q^{19}+6q^{23}+\cdots\)
9360.2.a.n	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{11}+q^{13}-2q^{17}-2q^{19}+\cdots\)
9360.2.a.o	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{11}+q^{13}-2q^{17}+4q^{19}+\cdots\)
9360.2.a.p	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{11}+q^{13}+6q^{17}-4q^{19}+\cdots\)
9360.2.a.q	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+6q^{11}+q^{13}+4q^{17}-4q^{19}+\cdots\)
9360.2.a.r	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}-3q^{11}+q^{13}+3q^{17}+\cdots\)
9360.2.a.s	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}-q^{11}-q^{13}+5q^{17}+\cdots\)
9360.2.a.t	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-2q^{11}-q^{13}+2q^{17}+\cdots\)
9360.2.a.u	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}+q^{13}+4q^{17}-6q^{19}+\cdots\)
9360.2.a.v	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}+4q^{11}-q^{13}-4q^{17}+\cdots\)
9360.2.a.w	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(3\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+3q^{7}-5q^{11}+q^{13}-5q^{17}+\cdots\)
9360.2.a.x	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(3\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+3q^{7}-3q^{11}-q^{13}+q^{17}+\cdots\)
9360.2.a.y	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(3\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+3q^{7}+3q^{11}+q^{13}+3q^{17}+\cdots\)
9360.2.a.z	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(4\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{7}-6q^{11}+q^{13}+6q^{17}+\cdots\)
9360.2.a.ba	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(4\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{7}+q^{13}-6q^{17}+4q^{19}+\cdots\)
9360.2.a.bb	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(5\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+5q^{7}+q^{11}+q^{13}+3q^{17}+\cdots\)
9360.2.a.bc	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-4\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{7}-q^{13}+2q^{17}-4q^{19}+\cdots\)
9360.2.a.bd	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-3\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-3q^{7}+5q^{11}-q^{13}+3q^{17}+\cdots\)
9360.2.a.be	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-4q^{11}-q^{13}+4q^{17}+\cdots\)
9360.2.a.bf	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-4q^{11}-q^{13}+8q^{17}+\cdots\)
9360.2.a.bg	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}+q^{13}-2q^{19}-6q^{23}+\cdots\)
9360.2.a.bh	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}+4q^{11}-q^{13}-8q^{17}+\cdots\)
9360.2.a.bi	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}+4q^{11}-q^{13}-2q^{17}+\cdots\)
9360.2.a.bj	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}+4q^{11}-q^{13}+4q^{17}+\cdots\)
9360.2.a.bk	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-6q^{11}+q^{13}-4q^{17}-4q^{19}+\cdots\)
9360.2.a.bl	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{11}-q^{13}+6q^{17}-4q^{19}+\cdots\)
9360.2.a.bm	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{13}-2q^{17}+4q^{23}+q^{25}+\cdots\)
9360.2.a.bn	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{13}+6q^{17}-4q^{23}+q^{25}+\cdots\)
9360.2.a.bo	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{13}-6q^{17}+8q^{19}-6q^{23}+\cdots\)
9360.2.a.bp	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{13}+6q^{17}-4q^{19}+q^{25}+\cdots\)
9360.2.a.bq	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{11}+q^{13}+2q^{17}+4q^{19}+\cdots\)
9360.2.a.br	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-5q^{11}+q^{13}-3q^{17}+\cdots\)
9360.2.a.bs	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}+q^{11}-q^{13}-5q^{17}+\cdots\)
9360.2.a.bt	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}+3q^{11}+q^{13}-3q^{17}+\cdots\)
9360.2.a.bu	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}+3q^{11}+q^{13}-3q^{17}+\cdots\)
9360.2.a.bv	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}+5q^{11}-q^{13}+7q^{17}+\cdots\)
9360.2.a.bw	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-6q^{11}-q^{13}+2q^{17}+\cdots\)
9360.2.a.bx	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(3\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+3q^{7}-3q^{11}+q^{13}-3q^{17}+\cdots\)
9360.2.a.by	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(4\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{7}-2q^{11}-q^{13}-2q^{17}+\cdots\)
9360.2.a.bz	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(4\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{7}+q^{13}+6q^{17}+4q^{19}+\cdots\)
9360.2.a.ca	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(4\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{7}+2q^{11}-q^{13}-2q^{17}+\cdots\)
9360.2.a.cb	$9360$	$2$	9360.a	1.a	$1$	$1$	$1$	$74.740$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(4\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{7}+4q^{11}+q^{13}+6q^{17}+\cdots\)
9360.2.a.cc	$9360$	$2$	9360.a	1.a	$1$	$2$	$2$	$74.740$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-4\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}+(-2+\beta )q^{11}-q^{13}+\cdots\)
9360.2.a.cd	$9360$	$2$	9360.a	1.a	$1$	$2$	$2$	$74.740$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(-2+2\beta )q^{7}+(2-\beta )q^{11}+\cdots\)
9360.2.a.ce	$9360$	$2$	9360.a	1.a	$1$	$2$	$2$	$74.740$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-3\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(-1-\beta )q^{7}+(1+\beta )q^{11}-q^{13}+\cdots\)
9360.2.a.cf	$9360$	$2$	9360.a	1.a	$1$	$2$	$2$	$74.740$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}+(-1-\beta )q^{7}+q^{13}+(-1+\beta )q^{17}+\cdots\)
9360.2.a.cg	$9360$	$2$	9360.a	1.a	$1$	$2$	$2$	$74.740$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-\beta q^{7}+(-2+\beta )q^{11}+q^{13}+\cdots\)
9360.2.a.ch	$9360$	$2$	9360.a	1.a	$1$	$2$	$2$	$74.740$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}+\beta q^{7}+2\beta q^{11}-q^{13}+(2-\beta )q^{17}+\cdots\)
9360.2.a.ci	$9360$	$2$	9360.a	1.a	$1$	$2$	$2$	$74.740$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+\beta q^{7}+(-4+\beta )q^{11}+q^{13}+\cdots\)
9360.2.a.cj	$9360$	$2$	9360.a	1.a	$1$	$2$	$2$	$74.740$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(4\)		$+$	$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-q^{13}+(2+\beta )q^{17}-2q^{19}+\cdots\)
9360.2.a.ck	$9360$	$2$	9360.a	1.a	$1$	$2$	$2$	$74.740$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-3\beta q^{11}-q^{13}+(2-2\beta )q^{17}+\cdots\)
9360.2.a.cl	$9360$	$2$	9360.a	1.a	$1$	$2$	$2$	$74.740$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(5\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(3-\beta )q^{7}+(1-\beta )q^{11}-q^{13}+\cdots\)
9360.2.a.cm	$9360$	$2$	9360.a	1.a	$1$	$2$	$2$	$74.740$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-4\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}+(-3+\beta )q^{11}+q^{13}+\cdots\)
9360.2.a.cn	$9360$	$2$	9360.a	1.a	$1$	$2$	$2$	$74.740$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{5}+(-1-\beta )q^{7}+q^{13}+(1-\beta )q^{17}+\cdots\)
9360.2.a.co	$9360$	$2$	9360.a	1.a	$1$	$2$	$2$	$74.740$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-\beta q^{7}-\beta q^{11}-q^{13}+(-2+\cdots)q^{17}+\cdots\)
9360.2.a.cp	$9360$	$2$	9360.a	1.a	$1$	$2$	$2$	$74.740$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-\beta q^{7}+(2-\beta )q^{11}+q^{13}+(4+\cdots)q^{17}+\cdots\)
9360.2.a.cq	$9360$	$2$	9360.a	1.a	$1$	$2$	$2$	$74.740$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2\beta q^{7}+(-3+\beta )q^{11}+q^{13}+\cdots\)
9360.2.a.cr	$9360$	$2$	9360.a	1.a	$1$	$2$	$2$	$74.740$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2\beta q^{7}+(1-\beta )q^{11}+q^{13}+\cdots\)
9360.2.a.cs	$9360$	$2$	9360.a	1.a	$1$	$2$	$2$	$74.740$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{5}+(3+\beta )q^{11}-q^{13}-2q^{17}+\cdots\)
9360.2.a.ct	$9360$	$2$	9360.a	1.a	$1$	$2$	$2$	$74.740$	\(\Q(\sqrt{41}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+\beta q^{7}+(-2-\beta )q^{11}-q^{13}+\cdots\)
9360.2.a.cu	$9360$	$2$	9360.a	1.a	$1$	$2$	$2$	$74.740$	\(\Q(\sqrt{73}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+\beta q^{7}+\beta q^{11}-q^{13}+\beta q^{17}+\cdots\)
9360.2.a.cv	$9360$	$2$	9360.a	1.a	$1$	$2$	$2$	$74.740$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(4\)		$+$	$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-q^{13}+(-2-\beta )q^{17}+\cdots\)
9360.2.a.cw	$9360$	$2$	9360.a	1.a	$1$	$2$	$2$	$74.740$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(5\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(3-\beta )q^{7}+(-1+\beta )q^{11}-q^{13}+\cdots\)
9360.2.a.cx	$9360$	$2$	9360.a	1.a	$1$	$3$	$3$	$74.740$	3.3.621.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(-3\)		$+$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}+(-1-\beta _{2})q^{7}+(1-\beta _{1}-\beta _{2})q^{11}+\cdots\)
9360.2.a.cy	$9360$	$2$	9360.a	1.a	$1$	$3$	$3$	$74.740$	3.3.940.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}-\beta _{2}q^{7}+(2+\beta _{1})q^{11}-q^{13}+\cdots\)
9360.2.a.cz	$9360$	$2$	9360.a	1.a	$1$	$3$	$3$	$74.740$	3.3.1016.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(1\)		$+$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}+\beta _{2}q^{7}+(-2+\beta _{1})q^{11}-q^{13}+\cdots\)
9360.2.a.da	$9360$	$2$	9360.a	1.a	$1$	$3$	$3$	$74.740$	3.3.564.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(2\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}+(1+\beta _{1})q^{7}+(\beta _{1}-\beta _{2})q^{11}+\cdots\)
9360.2.a.db	$9360$	$2$	9360.a	1.a	$1$	$3$	$3$	$74.740$	3.3.1849.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-5\)		$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{5}+(-2+\beta _{1})q^{7}+(1+\beta _{2})q^{11}+\cdots\)
9360.2.a.dc	$9360$	$2$	9360.a	1.a	$1$	$3$	$3$	$74.740$	3.3.621.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-3\)		$+$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{5}+(-1-\beta _{2})q^{7}+(-1+\beta _{1}+\beta _{2})q^{11}+\cdots\)
9360.2.a.dd	$9360$	$2$	9360.a	1.a	$1$	$3$	$3$	$74.740$	3.3.316.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-1\)		$-$	$-$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{5}+\beta _{1}q^{7}-\beta _{1}q^{11}+q^{13}+(-\beta _{1}+\cdots)q^{17}+\cdots\)
9360.2.a.de	$9360$	$2$	9360.a	1.a	$1$	$3$	$3$	$74.740$	3.3.1016.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{5}+\beta _{2}q^{7}+(2-\beta _{1})q^{11}-q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9360))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9360)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(60))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(130))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(195))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(234))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(260))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(390))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(468))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(520))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(585))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(624))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(720))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(780))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(936))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1040))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1170))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1560))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1872))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2340))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4680))\)\(^{\oplus 2}\)