Space of modular forms of level 3920, weight 2, and trivial character

• Label: 3920.2.a
• Level: $3920$
• Weight: $2$
• Character orbit: 3920.a
• Rep. character: $\chi_{3920}(1,\cdot)$
• Character field: $\Q$
• Dimension: $82$
• Newform subspaces: $57$
• Sturm bound: $1344$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 3920 = 2^{4} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3920.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 57 \)
Sturm bound:			\(1344\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(3\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3920))\).

	Total	New	Old
Modular forms	720	82	638
Cusp forms	625	82	543
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.

\(2\)	\(5\)	\(7\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(9\)
\(+\)	\(+\)	\(-\)	\(-\)	\(12\)
\(+\)	\(-\)	\(+\)	\(-\)	\(11\)
\(+\)	\(-\)	\(-\)	\(+\)	\(9\)
\(-\)	\(+\)	\(+\)	\(-\)	\(11\)
\(-\)	\(+\)	\(-\)	\(+\)	\(9\)
\(-\)	\(-\)	\(+\)	\(+\)	\(9\)
\(-\)	\(-\)	\(-\)	\(-\)	\(12\)
Plus space			\(+\)	\(36\)
Minus space			\(-\)	\(46\)

Trace form

82 * q - 2 * q^3 + 78 * q^9 + 4 * q^11 - 2 * q^15 - 4 * q^17 - 8 * q^19 - 2 * q^23 + 82 * q^25 - 20 * q^27 - 4 * q^29 - 20 * q^31 - 8 * q^37 - 28 * q^39 + 8 * q^41 - 6 * q^43 + 4 * q^45 + 22 * q^47 + 4 * q^51 + 4 * q^55 - 8 * q^57 + 8 * q^59 + 16 * q^61 + 4 * q^65 + 22 * q^67 + 28 * q^69 + 12 * q^71 - 20 * q^73 - 2 * q^75 + 24 * q^79 + 70 * q^81 + 14 * q^83 + 8 * q^85 - 36 * q^87 - 12 * q^89 + 40 * q^93 - 8 * q^95 - 28 * q^97 - 44 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3920))\) 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	7
3920.2.a.a	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				245.2.a.a	$1$	$1$	\(0\)	\(-3\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-q^{5}+6q^{9}-q^{11}+3q^{13}+\cdots\)
3920.2.a.b	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				70.2.e.a	$1$	$0$	\(0\)	\(-3\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-q^{5}+6q^{9}+2q^{11}+3q^{15}+\cdots\)
3920.2.a.c	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				280.2.a.a	$1$	$0$	\(0\)	\(-3\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-q^{5}+6q^{9}+5q^{11}+5q^{13}+\cdots\)
3920.2.a.d	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				140.2.i.b	$1$	$0$	\(0\)	\(-3\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+q^{5}+6q^{9}+2q^{11}+6q^{13}+\cdots\)
3920.2.a.e	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				70.2.e.d	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+q^{9}-3q^{11}+q^{13}+\cdots\)
3920.2.a.f	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				1960.2.a.b	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
3920.2.a.g	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				70.2.e.b	$1$	$0$	\(0\)	\(-2\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}+q^{9}-3q^{11}-5q^{13}+\cdots\)
3920.2.a.h	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				20.2.a.a	$1$	$0$	\(0\)	\(-2\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}+q^{9}-2q^{13}-2q^{15}+\cdots\)
3920.2.a.i	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				280.2.q.c	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}+q^{9}+q^{11}+3q^{13}+\cdots\)
3920.2.a.j	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				490.2.a.f	$1$	$0$	\(0\)	\(-2\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
3920.2.a.k	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				140.2.i.a	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{9}-6q^{11}+2q^{13}+\cdots\)
3920.2.a.l	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				1960.2.a.f	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{9}-3q^{11}-q^{13}+\cdots\)
3920.2.a.m	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				280.2.q.a	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{9}-2q^{11}+q^{15}+\cdots\)
3920.2.a.n	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				980.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{9}+q^{11}-5q^{13}+\cdots\)
3920.2.a.o	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				1960.2.a.d	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{9}+5q^{11}+7q^{13}+\cdots\)
3920.2.a.p	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				70.2.e.c	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{9}+6q^{11}-4q^{13}+\cdots\)
3920.2.a.q	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				280.2.q.b	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{9}+2q^{11}-4q^{13}+\cdots\)
3920.2.a.r	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				280.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{9}+5q^{11}-q^{13}+\cdots\)
3920.2.a.s	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				40.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{9}-4q^{11}+2q^{13}-2q^{17}+\cdots\)
3920.2.a.t	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				70.2.a.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-3q^{9}-4q^{11}+6q^{13}-2q^{17}+\cdots\)
3920.2.a.u	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				140.2.a.a	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{9}-3q^{11}+q^{13}+\cdots\)
3920.2.a.v	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				280.2.q.b	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{9}+2q^{11}+4q^{13}+\cdots\)
3920.2.a.w	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				140.2.i.a	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{9}-6q^{11}-2q^{13}+\cdots\)
3920.2.a.x	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				1960.2.a.f	$1$	$1$	\(0\)	\(1\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{9}-3q^{11}+q^{13}+\cdots\)
3920.2.a.y	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				280.2.q.a	$1$	$1$	\(0\)	\(1\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{9}-2q^{11}+q^{15}+\cdots\)
3920.2.a.z	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				980.2.a.d	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{9}+q^{11}+5q^{13}+\cdots\)
3920.2.a.ba	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				35.2.a.a	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{9}+3q^{11}-5q^{13}+\cdots\)
3920.2.a.bb	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				1960.2.a.d	$1$	$1$	\(0\)	\(1\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{9}+5q^{11}-7q^{13}+\cdots\)
3920.2.a.bc	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				70.2.e.c	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{9}+6q^{11}+4q^{13}+\cdots\)
3920.2.a.bd	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				1960.2.a.b	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
3920.2.a.be	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				70.2.e.b	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+q^{9}-3q^{11}+5q^{13}+\cdots\)
3920.2.a.bf	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				280.2.q.c	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+q^{9}+q^{11}-3q^{13}+\cdots\)
3920.2.a.bg	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				490.2.a.f	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
3920.2.a.bh	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				70.2.e.d	$1$	$1$	\(0\)	\(2\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}+q^{9}-3q^{11}-q^{13}+\cdots\)
3920.2.a.bi	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				140.2.i.b	$1$	$0$	\(0\)	\(3\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-q^{5}+6q^{9}+2q^{11}-6q^{13}+\cdots\)
3920.2.a.bj	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				245.2.a.a	$1$	$0$	\(0\)	\(3\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+q^{5}+6q^{9}-q^{11}-3q^{13}+\cdots\)
3920.2.a.bk	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				70.2.e.a	$1$	$0$	\(0\)	\(3\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+q^{5}+6q^{9}+2q^{11}+3q^{15}+\cdots\)
3920.2.a.bl	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	\(\Q\)	None	✓				140.2.a.b	$1$	$0$	\(0\)	\(3\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+q^{5}+6q^{9}+5q^{11}+3q^{13}+\cdots\)
3920.2.a.bm	$3920$	$2$	3920.a	1.a	$1$	$2$	$2$	$31.301$	\(\Q(\sqrt{2}) \)	None	✓				490.2.a.l	$1$	$1$	\(0\)	\(-4\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-2+\beta )q^{3}+q^{5}+(3-4\beta )q^{9}+(-2+\cdots)q^{11}+\cdots\)
3920.2.a.bn	$3920$	$2$	3920.a	1.a	$1$	$2$	$2$	$31.301$	\(\Q(\sqrt{2}) \)	None	✓				1960.2.a.q	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}-q^{5}-2\beta q^{9}+q^{11}+\cdots\)
3920.2.a.bo	$3920$	$2$	3920.a	1.a	$1$	$2$	$2$	$31.301$	\(\Q(\sqrt{2}) \)	None	✓				980.2.a.j	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}-q^{5}-2\beta q^{9}+(1+2\beta )q^{11}+\cdots\)
3920.2.a.bp	$3920$	$2$	3920.a	1.a	$1$	$2$	$2$	$31.301$	\(\Q(\sqrt{2}) \)	None	✓				280.2.q.d	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}-q^{5}-2\beta q^{9}+(2-2\beta )q^{11}+\cdots\)
3920.2.a.bq	$3920$	$2$	3920.a	1.a	$1$	$2$	$2$	$31.301$	\(\Q(\sqrt{2}) \)	None	✓				35.2.e.a	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+q^{5}-2\beta q^{9}+(-2+\cdots)q^{11}+\cdots\)
3920.2.a.br	$3920$	$2$	3920.a	1.a	$1$	$2$	$2$	$31.301$	\(\Q(\sqrt{2}) \)	None	✓				245.2.a.e	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+q^{5}-2\beta q^{9}+(3-2\beta )q^{11}+\cdots\)
3920.2.a.bs	$3920$	$2$	3920.a	1.a	$1$	$2$	$2$	$31.301$	\(\Q(\sqrt{17}) \)	None	✓				35.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-q^{5}+(1+\beta )q^{9}-\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
3920.2.a.bt	$3920$	$2$	3920.a	1.a	$1$	$2$	$2$	$31.301$	\(\Q(\sqrt{33}) \)	None	✓		✓		280.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+q^{5}+(5+\beta )q^{9}+(-4+\beta )q^{11}+\cdots\)
3920.2.a.bu	$3920$	$2$	3920.a	1.a	$1$	$2$	$2$	$31.301$	\(\Q(\sqrt{17}) \)	None	✓				280.2.a.d	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}+(1+\beta )q^{9}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
3920.2.a.bv	$3920$	$2$	3920.a	1.a	$1$	$2$	$2$	$31.301$	\(\Q(\sqrt{2}) \)	None	✓				35.2.e.a	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-q^{5}+2\beta q^{9}+(-2-2\beta )q^{11}+\cdots\)
3920.2.a.bw	$3920$	$2$	3920.a	1.a	$1$	$2$	$2$	$31.301$	\(\Q(\sqrt{2}) \)	None	✓				245.2.a.e	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-q^{5}+2\beta q^{9}+(3+2\beta )q^{11}+\cdots\)
3920.2.a.bx	$3920$	$2$	3920.a	1.a	$1$	$2$	$2$	$31.301$	\(\Q(\sqrt{2}) \)	None	✓				980.2.a.j	$1$	$1$	\(0\)	\(2\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+q^{5}+2\beta q^{9}+(1-2\beta )q^{11}+\cdots\)
3920.2.a.by	$3920$	$2$	3920.a	1.a	$1$	$2$	$2$	$31.301$	\(\Q(\sqrt{2}) \)	None	✓				1960.2.a.q	$1$	$0$	\(0\)	\(2\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+q^{5}+2\beta q^{9}+q^{11}+(-1+\cdots)q^{13}+\cdots\)
3920.2.a.bz	$3920$	$2$	3920.a	1.a	$1$	$2$	$2$	$31.301$	\(\Q(\sqrt{2}) \)	None	✓				280.2.q.d	$1$	$0$	\(0\)	\(2\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+q^{5}+2\beta q^{9}+(2+2\beta )q^{11}+\cdots\)
3920.2.a.ca	$3920$	$2$	3920.a	1.a	$1$	$2$	$2$	$31.301$	\(\Q(\sqrt{2}) \)	None	✓				490.2.a.l	$1$	$0$	\(0\)	\(4\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(2+\beta )q^{3}-q^{5}+(3+4\beta )q^{9}+(-2+\cdots)q^{11}+\cdots\)
3920.2.a.cb	$3920$	$2$	3920.a	1.a	$1$	$3$	$3$	$31.301$	3.3.1944.1	None	✓		✓		280.2.q.e	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+(3+\beta _{1}+\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots\)
3920.2.a.cc	$3920$	$2$	3920.a	1.a	$1$	$3$	$3$	$31.301$	3.3.1944.1	None	✓				280.2.q.e	$1$	$0$	\(0\)	\(0\)	\(3\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+(3+\beta _{1}+\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots\)
3920.2.a.cd	$3920$	$2$	3920.a	1.a	$1$	$4$	$4$	$31.301$	4.4.16448.2	None	✓		✓		1960.2.a.x	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
3920.2.a.ce	$3920$	$2$	3920.a	1.a	$1$	$4$	$4$	$31.301$	4.4.16448.2	None	✓		✓		1960.2.a.x	$1$	$1$	\(0\)	\(2\)	\(-4\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3920))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3920)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(490))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(560))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(784))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(980))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1960))\)\(^{\oplus 2}\)