Space of modular forms of level 7920, weight 2, and trivial character

• Label: 7920.2.a
• Level: $7920$
• Weight: $2$
• Character orbit: 7920.a
• Rep. character: $\chi_{7920}(1,\cdot)$
• Character field: $\Q$
• Dimension: $100$
• Newform subspaces: $66$
• Sturm bound: $3456$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 7920 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7920.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 66 \)
Sturm bound:			\(3456\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(7\), \(13\), \(17\), \(19\), \(23\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7920))\).

	Total	New	Old
Modular forms	1776	100	1676
Cusp forms	1681	100	1581
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.

\(2\)	\(3\)	\(5\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(5\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(5\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(5\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(5\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(7\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(7\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(8\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(8\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(7\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(7\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(7\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(9\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(8\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(6\)
Plus space				\(+\)	\(44\)
Minus space				\(-\)	\(56\)

Trace form

\( 100 q + 8 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7920))\) 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	11
7920.2.a.a	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				3960.2.a.h	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-4\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-4q^{7}-q^{11}-4q^{13}+2q^{17}+\cdots\)
7920.2.a.b	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				440.2.a.c	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-4\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-4q^{7}-q^{11}+6q^{13}+6q^{17}+\cdots\)
7920.2.a.c	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				1320.2.a.h	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-4\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-4q^{7}+q^{11}+2q^{13}+2q^{17}+\cdots\)
7920.2.a.d	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				110.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-3\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{7}+q^{11}-6q^{13}+7q^{17}+\cdots\)
7920.2.a.e	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				440.2.a.d	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}-q^{11}-6q^{13}-3q^{17}+\cdots\)
7920.2.a.f	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				1320.2.a.n	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{11}-2q^{13}-2q^{17}-4q^{19}+\cdots\)
7920.2.a.g	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				330.2.a.e	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{11}-2q^{13}-2q^{17}+4q^{19}+\cdots\)
7920.2.a.h	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				1320.2.a.f	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{11}-2q^{13}+6q^{17}+4q^{19}+\cdots\)
7920.2.a.i	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				55.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{11}+2q^{13}-6q^{17}+4q^{19}+\cdots\)
7920.2.a.j	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				1320.2.a.g	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{11}-6q^{13}+6q^{17}+q^{25}+\cdots\)
7920.2.a.k	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				990.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{11}-2q^{17}-2q^{19}+6q^{23}+\cdots\)
7920.2.a.l	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				220.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{11}+4q^{17}+4q^{19}+6q^{23}+\cdots\)
7920.2.a.m	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				330.2.a.d	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{11}+6q^{13}-2q^{17}+4q^{19}+\cdots\)
7920.2.a.n	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				990.2.a.e	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(4\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{7}-q^{11}-4q^{13}-6q^{17}+\cdots\)
7920.2.a.o	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				220.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(4\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{7}-q^{11}-4q^{13}+4q^{19}+\cdots\)
7920.2.a.p	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				1320.2.a.e	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(4\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{7}-q^{11}+2q^{13}-6q^{17}+\cdots\)
7920.2.a.q	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				1320.2.a.m	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(4\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{7}+q^{11}-6q^{13}+2q^{17}+\cdots\)
7920.2.a.r	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				330.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(4\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{7}+q^{11}-2q^{13}+2q^{17}+\cdots\)
7920.2.a.s	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				110.2.a.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-5\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-5q^{7}+q^{11}+2q^{13}-3q^{17}+\cdots\)
7920.2.a.t	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				330.2.a.c	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-4\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{7}-q^{11}+2q^{13}-2q^{17}+\cdots\)
7920.2.a.u	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				1320.2.a.d	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-4\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{7}-q^{11}+2q^{13}-2q^{17}+\cdots\)
7920.2.a.v	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				3960.2.a.h	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-4\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{7}+q^{11}-4q^{13}-2q^{17}+\cdots\)
7920.2.a.w	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				1320.2.a.c	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-q^{11}-4q^{13}+4q^{19}+\cdots\)
7920.2.a.x	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				1320.2.a.l	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}+q^{11}-4q^{17}+4q^{19}+\cdots\)
7920.2.a.y	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				660.2.a.d	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}+q^{11}+2q^{13}-2q^{19}+\cdots\)
7920.2.a.z	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				990.2.a.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{11}+2q^{17}-2q^{19}-6q^{23}+\cdots\)
7920.2.a.ba	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				660.2.a.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{11}-4q^{13}+2q^{17}-2q^{19}+\cdots\)
7920.2.a.bb	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				330.2.a.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{11}+2q^{13}+2q^{17}-8q^{19}+\cdots\)
7920.2.a.bc	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				110.2.a.c	$1$	$0$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-q^{11}+2q^{13}+3q^{17}+\cdots\)
7920.2.a.bd	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				1320.2.a.i	$1$	$1$	\(0\)	\(0\)	\(1\)	\(2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-q^{11}-4q^{13}-4q^{17}+\cdots\)
7920.2.a.be	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				1320.2.a.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-q^{11}-4q^{13}+4q^{17}+\cdots\)
7920.2.a.bf	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				1320.2.a.j	$1$	$1$	\(0\)	\(0\)	\(1\)	\(2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-q^{11}-4q^{17}-4q^{19}+\cdots\)
7920.2.a.bg	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				440.2.a.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-q^{11}+8q^{19}-8q^{23}+\cdots\)
7920.2.a.bh	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				660.2.a.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-q^{11}+2q^{13}-8q^{17}+\cdots\)
7920.2.a.bi	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				440.2.a.b	$1$	$0$	\(0\)	\(0\)	\(1\)	\(2\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}+q^{11}-4q^{13}+4q^{17}+\cdots\)
7920.2.a.bj	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				1320.2.a.k	$1$	$0$	\(0\)	\(0\)	\(1\)	\(2\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}+q^{11}+8q^{17}+8q^{19}+\cdots\)
7920.2.a.bk	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				1320.2.a.b	$1$	$0$	\(0\)	\(0\)	\(1\)	\(2\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}+q^{11}+4q^{13}+4q^{19}+\cdots\)
7920.2.a.bl	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				660.2.a.c	$1$	$0$	\(0\)	\(0\)	\(1\)	\(4\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{7}-q^{11}-4q^{13}+6q^{17}+\cdots\)
7920.2.a.bm	$7920$	$2$	7920.a	1.a	$1$	$1$	$1$	$63.242$	\(\Q\)	None	✓				990.2.a.e	$1$	$0$	\(0\)	\(0\)	\(1\)	\(4\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{7}+q^{11}-4q^{13}+6q^{17}+\cdots\)
7920.2.a.bn	$7920$	$2$	7920.a	1.a	$1$	$2$	$2$	$63.242$	\(\Q(\sqrt{13}) \)	None	✓				660.2.a.f	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}+(-1-\beta )q^{7}-q^{11}+(3-\beta )q^{13}+\cdots\)
7920.2.a.bo	$7920$	$2$	7920.a	1.a	$1$	$2$	$2$	$63.242$	\(\Q(\sqrt{13}) \)	None	✓				660.2.a.e	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}+(-1-\beta )q^{7}+q^{11}+(-1-\beta )q^{13}+\cdots\)
7920.2.a.bp	$7920$	$2$	7920.a	1.a	$1$	$2$	$2$	$63.242$	\(\Q(\sqrt{7}) \)	None	✓		✓		1980.2.a.i	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(-1+\beta )q^{7}+q^{11}+(1-\beta )q^{13}+\cdots\)
7920.2.a.bq	$7920$	$2$	7920.a	1.a	$1$	$2$	$2$	$63.242$	\(\Q(\sqrt{33}) \)	None	✓				110.2.a.d	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-\beta q^{7}-q^{11}+2q^{13}+(2-\beta )q^{17}+\cdots\)
7920.2.a.br	$7920$	$2$	7920.a	1.a	$1$	$2$	$2$	$63.242$	\(\Q(\sqrt{2}) \)	None	✓				3960.2.a.y	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+\beta q^{7}-q^{11}+(-2-\beta )q^{13}+\cdots\)
7920.2.a.bs	$7920$	$2$	7920.a	1.a	$1$	$2$	$2$	$63.242$	\(\Q(\sqrt{2}) \)	None	✓		✓		1320.2.a.p	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}+\beta q^{7}-q^{11}+(2+\beta )q^{13}+(-2+\cdots)q^{17}+\cdots\)
7920.2.a.bt	$7920$	$2$	7920.a	1.a	$1$	$2$	$2$	$63.242$	\(\Q(\sqrt{2}) \)	None	✓				1320.2.a.q	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}+\beta q^{7}+q^{11}+(2+\beta )q^{13}+(-2+\cdots)q^{17}+\cdots\)
7920.2.a.bu	$7920$	$2$	7920.a	1.a	$1$	$2$	$2$	$63.242$	\(\Q(\sqrt{17}) \)	None	✓				440.2.a.e	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+\beta q^{7}+q^{11}+2q^{13}+(-2+\cdots)q^{17}+\cdots\)
7920.2.a.bv	$7920$	$2$	7920.a	1.a	$1$	$2$	$2$	$63.242$	\(\Q(\sqrt{3}) \)	None	✓				1980.2.a.g	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(1+\beta )q^{7}-q^{11}+(-1+3\beta )q^{13}+\cdots\)
7920.2.a.bw	$7920$	$2$	7920.a	1.a	$1$	$2$	$2$	$63.242$	\(\Q(\sqrt{6}) \)	None	✓				3960.2.a.v	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(4\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(2+\beta )q^{7}-q^{11}-\beta q^{13}+3\beta q^{17}+\cdots\)
7920.2.a.bx	$7920$	$2$	7920.a	1.a	$1$	$2$	$2$	$63.242$	\(\Q(\sqrt{2}) \)	None	✓				3960.2.a.u	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(2+\beta )q^{7}+q^{11}-\beta q^{13}-3\beta q^{17}+\cdots\)
7920.2.a.by	$7920$	$2$	7920.a	1.a	$1$	$2$	$2$	$63.242$	\(\Q(\sqrt{17}) \)	None	✓		✓		440.2.a.g	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-5\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(-2-\beta )q^{7}-q^{11}+(4-2\beta )q^{13}+\cdots\)
7920.2.a.bz	$7920$	$2$	7920.a	1.a	$1$	$2$	$2$	$63.242$	\(\Q(\sqrt{3}) \)	None	✓				165.2.a.b	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-4\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-q^{11}+(2+\beta )q^{13}+(-2+\cdots)q^{19}+\cdots\)
7920.2.a.ca	$7920$	$2$	7920.a	1.a	$1$	$2$	$2$	$63.242$	\(\Q(\sqrt{17}) \)	None	✓				440.2.a.f	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-3\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(-1-\beta )q^{7}+q^{11}+(2-2\beta )q^{13}+\cdots\)
7920.2.a.cb	$7920$	$2$	7920.a	1.a	$1$	$2$	$2$	$63.242$	\(\Q(\sqrt{7}) \)	None	✓		✓		1980.2.a.i	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(-1+\beta )q^{7}-q^{11}+(1-\beta )q^{13}+\cdots\)
7920.2.a.cc	$7920$	$2$	7920.a	1.a	$1$	$2$	$2$	$63.242$	\(\Q(\sqrt{2}) \)	None	✓				3960.2.a.y	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+\beta q^{7}+q^{11}+(-2-\beta )q^{13}+\cdots\)
7920.2.a.cd	$7920$	$2$	7920.a	1.a	$1$	$2$	$2$	$63.242$	\(\Q(\sqrt{3}) \)	None	✓				1980.2.a.g	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(1+\beta )q^{7}+q^{11}+(-1+3\beta )q^{13}+\cdots\)
7920.2.a.ce	$7920$	$2$	7920.a	1.a	$1$	$2$	$2$	$63.242$	\(\Q(\sqrt{17}) \)	None	✓				1320.2.a.o	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{5}+(1+\beta )q^{7}+q^{11}+(1-\beta )q^{13}+\cdots\)
7920.2.a.cf	$7920$	$2$	7920.a	1.a	$1$	$2$	$2$	$63.242$	\(\Q(\sqrt{2}) \)	None	✓				3960.2.a.u	$1$	$0$	\(0\)	\(0\)	\(2\)	\(4\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(2+\beta )q^{7}-q^{11}-\beta q^{13}+3\beta q^{17}+\cdots\)
7920.2.a.cg	$7920$	$2$	7920.a	1.a	$1$	$2$	$2$	$63.242$	\(\Q(\sqrt{2}) \)	None	✓				165.2.a.a	$1$	$0$	\(0\)	\(0\)	\(2\)	\(4\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{5}+(2+\beta )q^{7}-q^{11}+2\beta q^{13}+\cdots\)
7920.2.a.ch	$7920$	$2$	7920.a	1.a	$1$	$2$	$2$	$63.242$	\(\Q(\sqrt{2}) \)	None	✓		✓		55.2.a.b	$1$	$1$	\(0\)	\(0\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}+q^{11}+(-4+\beta )q^{13}+\cdots\)
7920.2.a.ci	$7920$	$2$	7920.a	1.a	$1$	$2$	$2$	$63.242$	\(\Q(\sqrt{6}) \)	None	✓				3960.2.a.v	$1$	$1$	\(0\)	\(0\)	\(2\)	\(4\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(2+\beta )q^{7}+q^{11}-\beta q^{13}-3\beta q^{17}+\cdots\)
7920.2.a.cj	$7920$	$2$	7920.a	1.a	$1$	$3$	$3$	$63.242$	3.3.148.1	None	✓		✓		165.2.a.c	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{5}-\beta _{2}q^{7}+q^{11}+(-1-\beta _{1})q^{13}+\cdots\)
7920.2.a.ck	$7920$	$2$	7920.a	1.a	$1$	$3$	$3$	$63.242$	3.3.1016.1	None	✓		✓		3960.2.a.bg	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)		$+$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}-\beta _{2}q^{7}+q^{11}+(1-\beta _{1}-\beta _{2})q^{13}+\cdots\)
7920.2.a.cl	$7920$	$2$	7920.a	1.a	$1$	$3$	$3$	$63.242$	3.3.1016.1	None	✓		✓		3960.2.a.bg	$1$	$0$	\(0\)	\(0\)	\(3\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{5}-\beta _{2}q^{7}-q^{11}+(1-\beta _{1}-\beta _{2})q^{13}+\cdots\)
7920.2.a.cm	$7920$	$2$	7920.a	1.a	$1$	$4$	$4$	$63.242$	4.4.48704.2	None	✓		✓		495.2.a.f	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(-4\)		$-$	$+$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{5}+(-1-\beta _{3})q^{7}-q^{11}+(2+\beta _{1}+\cdots)q^{13}+\cdots\)
7920.2.a.cn	$7920$	$2$	7920.a	1.a	$1$	$4$	$4$	$63.242$	4.4.48704.2	None	✓		✓		495.2.a.f	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)		$-$	$+$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{5}+(-1-\beta _{3})q^{7}+q^{11}+(2+\beta _{1}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7920))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7920)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(220))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(330))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(396))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(440))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(495))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(528))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(660))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(720))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(792))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(880))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(990))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1320))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1584))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1980))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2640))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3960))\)\(^{\oplus 2}\)