Space of modular forms of level 8640, weight 2, and trivial character

• Label: 8640.2.a
• Level: $8640$
• Weight: $2$
• Character orbit: 8640.a
• Rep. character: $\chi_{8640}(1,\cdot)$
• Character field: $\Q$
• Dimension: $128$
• Newform subspaces: $92$
• Sturm bound: $3456$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 8640 = 2^{6} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8640.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 92 \)
Sturm bound:			\(3456\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8640))\).

	Total	New	Old
Modular forms	1800	128	1672
Cusp forms	1657	128	1529
Eisenstein series	143	0	143

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	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(16\)
\(+\)	\(+\)	\(-\)	\(-\)	\(18\)
\(+\)	\(-\)	\(+\)	\(-\)	\(16\)
\(+\)	\(-\)	\(-\)	\(+\)	\(14\)
\(-\)	\(+\)	\(+\)	\(-\)	\(16\)
\(-\)	\(+\)	\(-\)	\(+\)	\(14\)
\(-\)	\(-\)	\(+\)	\(+\)	\(16\)
\(-\)	\(-\)	\(-\)	\(-\)	\(18\)
Plus space			\(+\)	\(60\)
Minus space			\(-\)	\(68\)

Trace form

\( 128 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8640))\) 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
8640.2.a.a	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-4q^{7}+2q^{11}-4q^{13}-q^{17}+\cdots\)
8640.2.a.b	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-4q^{7}+6q^{11}+4q^{13}+3q^{17}+\cdots\)
8640.2.a.c	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{7}-2q^{11}+5q^{13}+8q^{17}+\cdots\)
8640.2.a.d	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{7}+2q^{11}-5q^{13}+2q^{17}+\cdots\)
8640.2.a.e	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}-3q^{11}-5q^{13}+3q^{17}+\cdots\)
8640.2.a.f	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}-3q^{11}+q^{13}-3q^{17}+\cdots\)
8640.2.a.g	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}-2q^{13}-3q^{17}+5q^{19}+\cdots\)
8640.2.a.h	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}+6q^{13}-7q^{17}-7q^{19}+\cdots\)
8640.2.a.i	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}+q^{11}-q^{13}-q^{17}+\cdots\)
8640.2.a.j	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}+3q^{11}+5q^{13}-3q^{17}+\cdots\)
8640.2.a.k	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}+4q^{11}+2q^{13}+5q^{17}+\cdots\)
8640.2.a.l	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}-6q^{11}+q^{13}+q^{19}+\cdots\)
8640.2.a.m	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}-2q^{11}+3q^{13}-2q^{17}+\cdots\)
8640.2.a.n	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}+2q^{11}+5q^{13}-4q^{17}+\cdots\)
8640.2.a.o	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{11}+3q^{17}+q^{19}+3q^{23}+\cdots\)
8640.2.a.p	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{11}+3q^{17}-q^{19}-3q^{23}+\cdots\)
8640.2.a.q	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}-2q^{11}+5q^{13}-4q^{17}+\cdots\)
8640.2.a.r	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}+2q^{11}+3q^{13}-2q^{17}+\cdots\)
8640.2.a.s	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}+6q^{11}+q^{13}-q^{19}+\cdots\)
8640.2.a.t	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-4q^{11}+2q^{13}+5q^{17}+\cdots\)
8640.2.a.u	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-3q^{11}+5q^{13}-3q^{17}+\cdots\)
8640.2.a.v	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-q^{11}-q^{13}-q^{17}+\cdots\)
8640.2.a.w	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-2q^{13}-3q^{17}-5q^{19}+\cdots\)
8640.2.a.x	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}+6q^{13}-7q^{17}+7q^{19}+\cdots\)
8640.2.a.y	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}+3q^{11}-5q^{13}+3q^{17}+\cdots\)
8640.2.a.z	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}+3q^{11}+q^{13}-3q^{17}+\cdots\)
8640.2.a.ba	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+3q^{7}-2q^{11}-5q^{13}+2q^{17}+\cdots\)
8640.2.a.bb	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+3q^{7}+2q^{11}+5q^{13}+8q^{17}+\cdots\)
8640.2.a.bc	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{7}-6q^{11}+4q^{13}+3q^{17}+\cdots\)
8640.2.a.bd	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{7}-2q^{11}-4q^{13}-q^{17}+\cdots\)
8640.2.a.be	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{7}-6q^{11}+4q^{13}-3q^{17}+\cdots\)
8640.2.a.bf	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{7}-2q^{11}-4q^{13}+q^{17}+\cdots\)
8640.2.a.bg	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-3q^{7}-2q^{11}-5q^{13}-2q^{17}+\cdots\)
8640.2.a.bh	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-3q^{7}+2q^{11}+5q^{13}-8q^{17}+\cdots\)
8640.2.a.bi	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-4q^{11}+2q^{13}-5q^{17}+\cdots\)
8640.2.a.bj	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-3q^{11}+5q^{13}+3q^{17}+\cdots\)
8640.2.a.bk	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-q^{11}-q^{13}+q^{17}+\cdots\)
8640.2.a.bl	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-2q^{13}+3q^{17}+5q^{19}+\cdots\)
8640.2.a.bm	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}+6q^{13}+7q^{17}-7q^{19}+\cdots\)
8640.2.a.bn	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}+3q^{11}-5q^{13}-3q^{17}+\cdots\)
8640.2.a.bo	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}+3q^{11}+q^{13}+3q^{17}+\cdots\)
8640.2.a.bp	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}-2q^{11}+5q^{13}+4q^{17}+\cdots\)
8640.2.a.bq	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}+2q^{11}+3q^{13}+2q^{17}+\cdots\)
8640.2.a.br	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}+6q^{11}+q^{13}+q^{19}+\cdots\)
8640.2.a.bs	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{11}-3q^{17}-q^{19}+3q^{23}+\cdots\)
8640.2.a.bt	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{11}-3q^{17}+q^{19}-3q^{23}+\cdots\)
8640.2.a.bu	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-6q^{11}+q^{13}-q^{19}+\cdots\)
8640.2.a.bv	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-2q^{11}+3q^{13}+2q^{17}+\cdots\)
8640.2.a.bw	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}+2q^{11}+5q^{13}+4q^{17}+\cdots\)
8640.2.a.bx	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-3q^{11}-5q^{13}-3q^{17}+\cdots\)
8640.2.a.by	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-3q^{11}+q^{13}+3q^{17}+\cdots\)
8640.2.a.bz	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-2q^{13}+3q^{17}-5q^{19}+\cdots\)
8640.2.a.ca	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}+6q^{13}+7q^{17}+7q^{19}+\cdots\)
8640.2.a.cb	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}+q^{11}-q^{13}+q^{17}+\cdots\)
8640.2.a.cc	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}+3q^{11}+5q^{13}+3q^{17}+\cdots\)
8640.2.a.cd	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}+4q^{11}+2q^{13}-5q^{17}+\cdots\)
8640.2.a.ce	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+3q^{7}-2q^{11}+5q^{13}-8q^{17}+\cdots\)
8640.2.a.cf	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+3q^{7}+2q^{11}-5q^{13}-2q^{17}+\cdots\)
8640.2.a.cg	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{7}+2q^{11}-4q^{13}+q^{17}+\cdots\)
8640.2.a.ch	$8640$	$2$	8640.a	1.a	$1$	$1$	$1$	$68.991$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{7}+6q^{11}+4q^{13}-3q^{17}+\cdots\)
8640.2.a.ci	$8640$	$2$	8640.a	1.a	$1$	$2$	$2$	$68.991$	\(\Q(\sqrt{10}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(-2+\beta )q^{7}+(2+\beta )q^{11}-\beta q^{13}+\cdots\)
8640.2.a.cj	$8640$	$2$	8640.a	1.a	$1$	$2$	$2$	$68.991$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(-1-\beta )q^{7}+(2-\beta )q^{11}-q^{13}+\cdots\)
8640.2.a.ck	$8640$	$2$	8640.a	1.a	$1$	$2$	$2$	$68.991$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-2\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}+(-1-\beta )q^{7}+(1-\beta )q^{11}+(-3+\cdots)q^{13}+\cdots\)
8640.2.a.cl	$8640$	$2$	8640.a	1.a	$1$	$2$	$2$	$68.991$	\(\Q(\sqrt{7}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(-1+\beta )q^{7}+(1-\beta )q^{11}+(-1+\cdots)q^{13}+\cdots\)
8640.2.a.cm	$8640$	$2$	8640.a	1.a	$1$	$2$	$2$	$68.991$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(-1+\beta )q^{7}+(1+3\beta )q^{11}+\cdots\)
8640.2.a.cn	$8640$	$2$	8640.a	1.a	$1$	$2$	$2$	$68.991$	\(\Q(\sqrt{73}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-\beta q^{7}+(-1+\beta )q^{11}-3q^{13}+\cdots\)
8640.2.a.co	$8640$	$2$	8640.a	1.a	$1$	$2$	$2$	$68.991$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+\beta q^{7}+\beta q^{11}+(2+3\beta )q^{13}+\cdots\)
8640.2.a.cp	$8640$	$2$	8640.a	1.a	$1$	$2$	$2$	$68.991$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+\beta q^{7}+\beta q^{11}+(2-3\beta )q^{13}+\cdots\)
8640.2.a.cq	$8640$	$2$	8640.a	1.a	$1$	$2$	$2$	$68.991$	\(\Q(\sqrt{73}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+\beta q^{7}+(1-\beta )q^{11}-3q^{13}+\cdots\)
8640.2.a.cr	$8640$	$2$	8640.a	1.a	$1$	$2$	$2$	$68.991$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}+(1+\beta )q^{7}+(-1+\beta )q^{11}+(-3+\cdots)q^{13}+\cdots\)
8640.2.a.cs	$8640$	$2$	8640.a	1.a	$1$	$2$	$2$	$68.991$	\(\Q(\sqrt{7}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(1+\beta )q^{7}+(-1-\beta )q^{11}+(-1+\cdots)q^{13}+\cdots\)
8640.2.a.ct	$8640$	$2$	8640.a	1.a	$1$	$2$	$2$	$68.991$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(1+\beta )q^{7}+(-1+3\beta )q^{11}+\cdots\)
8640.2.a.cu	$8640$	$2$	8640.a	1.a	$1$	$2$	$2$	$68.991$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(1+\beta )q^{7}+(-2+\beta )q^{11}-q^{13}+\cdots\)
8640.2.a.cv	$8640$	$2$	8640.a	1.a	$1$	$2$	$2$	$68.991$	\(\Q(\sqrt{10}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(2+\beta )q^{7}+(-2+\beta )q^{11}+\beta q^{13}+\cdots\)
8640.2.a.cw	$8640$	$2$	8640.a	1.a	$1$	$2$	$2$	$68.991$	\(\Q(\sqrt{10}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(-2+\beta )q^{7}+(-2-\beta )q^{11}+\cdots\)
8640.2.a.cx	$8640$	$2$	8640.a	1.a	$1$	$2$	$2$	$68.991$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(-1-\beta )q^{7}+(-2+\beta )q^{11}+\cdots\)
8640.2.a.cy	$8640$	$2$	8640.a	1.a	$1$	$2$	$2$	$68.991$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{5}+(-1-\beta )q^{7}+(-1+\beta )q^{11}+\cdots\)
8640.2.a.cz	$8640$	$2$	8640.a	1.a	$1$	$2$	$2$	$68.991$	\(\Q(\sqrt{7}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(-1+\beta )q^{7}+(-1+\beta )q^{11}+\cdots\)
8640.2.a.da	$8640$	$2$	8640.a	1.a	$1$	$2$	$2$	$68.991$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(-1+\beta )q^{7}+(-1-3\beta )q^{11}+\cdots\)
8640.2.a.db	$8640$	$2$	8640.a	1.a	$1$	$2$	$2$	$68.991$	\(\Q(\sqrt{73}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-\beta q^{7}+(1-\beta )q^{11}-3q^{13}+\cdots\)
8640.2.a.dc	$8640$	$2$	8640.a	1.a	$1$	$2$	$2$	$68.991$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+\beta q^{7}-\beta q^{11}+(2+3\beta )q^{13}+\cdots\)
8640.2.a.dd	$8640$	$2$	8640.a	1.a	$1$	$2$	$2$	$68.991$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+\beta q^{7}-\beta q^{11}+(2-3\beta )q^{13}+\cdots\)
8640.2.a.de	$8640$	$2$	8640.a	1.a	$1$	$2$	$2$	$68.991$	\(\Q(\sqrt{73}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+\beta q^{7}+(-1+\beta )q^{11}-3q^{13}+\cdots\)
8640.2.a.df	$8640$	$2$	8640.a	1.a	$1$	$2$	$2$	$68.991$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{5}+(1+\beta )q^{7}+(1-\beta )q^{11}+(-3+\cdots)q^{13}+\cdots\)
8640.2.a.dg	$8640$	$2$	8640.a	1.a	$1$	$2$	$2$	$68.991$	\(\Q(\sqrt{7}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(1+\beta )q^{7}+(1+\beta )q^{11}+(-1+\cdots)q^{13}+\cdots\)
8640.2.a.dh	$8640$	$2$	8640.a	1.a	$1$	$2$	$2$	$68.991$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(1+\beta )q^{7}+(1-3\beta )q^{11}+(3+\cdots)q^{13}+\cdots\)
8640.2.a.di	$8640$	$2$	8640.a	1.a	$1$	$2$	$2$	$68.991$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(1+\beta )q^{7}+(2-\beta )q^{11}-q^{13}+\cdots\)
8640.2.a.dj	$8640$	$2$	8640.a	1.a	$1$	$2$	$2$	$68.991$	\(\Q(\sqrt{10}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(2+\beta )q^{7}+(2-\beta )q^{11}+\beta q^{13}+\cdots\)
8640.2.a.dk	$8640$	$2$	8640.a	1.a	$1$	$3$	$3$	$68.991$	3.3.1509.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-1\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}+\beta _{2}q^{7}+(\beta _{1}+\beta _{2})q^{11}+(-2+\cdots)q^{13}+\cdots\)
8640.2.a.dl	$8640$	$2$	8640.a	1.a	$1$	$3$	$3$	$68.991$	3.3.1509.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(1\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}-\beta _{2}q^{7}+(-\beta _{1}-\beta _{2})q^{11}+(-2+\cdots)q^{13}+\cdots\)
8640.2.a.dm	$8640$	$2$	8640.a	1.a	$1$	$3$	$3$	$68.991$	3.3.1509.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-1\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{5}+\beta _{2}q^{7}+(-\beta _{1}-\beta _{2})q^{11}+(-2+\cdots)q^{13}+\cdots\)
8640.2.a.dn	$8640$	$2$	8640.a	1.a	$1$	$3$	$3$	$68.991$	3.3.1509.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(1\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{5}-\beta _{2}q^{7}+(\beta _{1}+\beta _{2})q^{11}+(-2+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8640))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8640)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 21}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(135))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(216))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(270))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(432))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(480))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(540))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(576))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(720))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(864))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(960))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1080))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1440))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1728))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2160))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2880))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4320))\)\(^{\oplus 2}\)