Space of modular forms of level 7840, weight 2, and trivial character

• Label: 7840.2.a
• Level: $7840$
• Weight: $2$
• Character orbit: 7840.a
• Rep. character: $\chi_{7840}(1,\cdot)$
• Character field: $\Q$
• Dimension: $164$
• Newform subspaces: $61$
• Sturm bound: $2688$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 7840 = 2^{5} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7840.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 61 \)
Sturm bound:			\(2688\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(3\), \(11\), \(13\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7840))\).

	Total	New	Old
Modular forms	1408	164	1244
Cusp forms	1281	164	1117
Eisenstein series	127	0	127

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
\(+\)	\(+\)	\(+\)	\(+\)	\(21\)
\(+\)	\(+\)	\(-\)	\(-\)	\(21\)
\(+\)	\(-\)	\(+\)	\(-\)	\(23\)
\(+\)	\(-\)	\(-\)	\(+\)	\(18\)
\(-\)	\(+\)	\(+\)	\(-\)	\(19\)
\(-\)	\(+\)	\(-\)	\(+\)	\(21\)
\(-\)	\(-\)	\(+\)	\(+\)	\(17\)
\(-\)	\(-\)	\(-\)	\(-\)	\(24\)
Plus space			\(+\)	\(77\)
Minus space			\(-\)	\(87\)

Trace form

\( 164 q + 172 q^{9} + 16 q^{13} + 8 q^{17} + 164 q^{25} - 8 q^{29} - 16 q^{33} + 16 q^{37} - 32 q^{41} - 8 q^{45} - 16 q^{53} - 8 q^{65} - 40 q^{69} + 40 q^{73} + 188 q^{81} + 40 q^{89} - 16 q^{93} + 56 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7840))\) 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
7840.2.a.a	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	\(\Q\)	None	✓				1120.2.a.b	$1$	$1$	\(0\)	\(-3\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-q^{5}+6q^{9}+3q^{11}-q^{13}+\cdots\)
7840.2.a.b	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	\(\Q\)	None	✓				1120.2.a.a	$1$	$1$	\(0\)	\(-3\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+q^{5}+6q^{9}+q^{11}+q^{13}+\cdots\)
7840.2.a.c	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	\(\Q\)	None	✓				1120.2.q.a	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+q^{9}+3q^{11}+q^{13}+\cdots\)
7840.2.a.d	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	\(\Q\)	None	✓				1120.2.q.a	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}+q^{9}-3q^{11}-q^{13}+\cdots\)
7840.2.a.e	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	\(\Q\)	None	✓				160.2.a.a	$1$	$0$	\(0\)	\(-2\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots\)
7840.2.a.f	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	\(\Q\)	None	✓				1120.2.a.f	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{9}-3q^{11}+7q^{13}+\cdots\)
7840.2.a.g	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	\(\Q\)	None	✓				1120.2.q.b	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{9}-2q^{11}+2q^{13}+\cdots\)
7840.2.a.h	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	\(\Q\)	None	✓				1120.2.a.e	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{9}+5q^{11}-5q^{13}+\cdots\)
7840.2.a.i	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	\(\Q\)	None	✓				1120.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{9}-q^{11}-3q^{13}+\cdots\)
7840.2.a.j	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	\(\Q\)	None	✓				1120.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{9}-q^{11}+q^{13}-q^{15}+\cdots\)
7840.2.a.k	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	\(\Q\)	None	✓				1120.2.q.b	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{9}+2q^{11}-2q^{13}+\cdots\)
7840.2.a.l	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	\(\Q\)	None	✓				1120.2.a.i	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{9}+2q^{13}-2q^{17}-8q^{19}+\cdots\)
7840.2.a.m	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	\(\Q\)	None	✓				1120.2.a.i	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{9}+2q^{13}-2q^{17}+8q^{19}+\cdots\)
7840.2.a.n	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	\(\Q\)	None	✓				1120.2.a.g	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-3q^{9}-4q^{11}-2q^{13}-6q^{17}+\cdots\)
7840.2.a.o	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	\(\Q\)	None	✓				1120.2.a.g	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-3q^{9}+4q^{11}-2q^{13}-6q^{17}+\cdots\)
7840.2.a.p	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	\(\Q\)	None	✓				1120.2.a.e	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{9}-5q^{11}-5q^{13}+\cdots\)
7840.2.a.q	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	\(\Q\)	None	✓				1120.2.q.b	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{9}+2q^{11}+2q^{13}+\cdots\)
7840.2.a.r	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	\(\Q\)	None	✓				1120.2.a.f	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{9}+3q^{11}+7q^{13}+\cdots\)
7840.2.a.s	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	\(\Q\)	None	✓				1120.2.q.b	$1$	$1$	\(0\)	\(1\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{9}-2q^{11}-2q^{13}+\cdots\)
7840.2.a.t	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	\(\Q\)	None	✓				1120.2.a.d	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{9}+q^{11}-3q^{13}+\cdots\)
7840.2.a.u	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	\(\Q\)	None	✓				1120.2.a.c	$1$	$1$	\(0\)	\(1\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{9}+q^{11}+q^{13}+q^{15}+\cdots\)
7840.2.a.v	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	\(\Q\)	None	✓				1120.2.q.a	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+q^{9}-3q^{11}+q^{13}+\cdots\)
7840.2.a.w	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	\(\Q\)	None	✓				160.2.a.a	$1$	$1$	\(0\)	\(2\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}+q^{9}-4q^{11}+6q^{13}+\cdots\)
7840.2.a.x	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	\(\Q\)	None	✓				1120.2.q.a	$1$	$0$	\(0\)	\(2\)	\(1\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}+q^{9}+3q^{11}-q^{13}+\cdots\)
7840.2.a.y	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	\(\Q\)	None	✓				1120.2.a.b	$1$	$1$	\(0\)	\(3\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-q^{5}+6q^{9}-3q^{11}-q^{13}+\cdots\)
7840.2.a.z	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	\(\Q\)	None	✓				1120.2.a.a	$1$	$0$	\(0\)	\(3\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+q^{5}+6q^{9}-q^{11}+q^{13}+\cdots\)
7840.2.a.ba	$7840$	$2$	7840.a	1.a	$1$	$2$	$2$	$62.603$	\(\Q(\sqrt{2}) \)	None	✓				1120.2.q.e	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}-q^{5}-2\beta q^{9}+(-2+\cdots)q^{11}+\cdots\)
7840.2.a.bb	$7840$	$2$	7840.a	1.a	$1$	$2$	$2$	$62.603$	\(\Q(\sqrt{2}) \)	None	✓				1120.2.q.e	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+q^{5}-2\beta q^{9}+(2-2\beta )q^{11}+\cdots\)
7840.2.a.bc	$7840$	$2$	7840.a	1.a	$1$	$2$	$2$	$62.603$	\(\Q(\sqrt{17}) \)	None	✓				1120.2.a.r	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-q^{5}+(1+\beta )q^{9}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
7840.2.a.bd	$7840$	$2$	7840.a	1.a	$1$	$2$	$2$	$62.603$	\(\Q(\sqrt{17}) \)	None	✓				1120.2.a.q	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+q^{5}+(1+\beta )q^{9}+(4-\beta )q^{11}+\cdots\)
7840.2.a.be	$7840$	$2$	7840.a	1.a	$1$	$2$	$2$	$62.603$	\(\Q(\sqrt{5}) \)	None	✓	✓			7840.2.a.be	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-q^{5}+2q^{9}-\beta q^{11}+q^{13}+\cdots\)
7840.2.a.bf	$7840$	$2$	7840.a	1.a	$1$	$2$	$2$	$62.603$	\(\Q(\sqrt{2}) \)	None	✓				160.2.a.c	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}+5q^{9}+2\beta q^{11}+2q^{13}+\cdots\)
7840.2.a.bg	$7840$	$2$	7840.a	1.a	$1$	$2$	$2$	$62.603$	\(\Q(\sqrt{5}) \)	None	✓	✓			7840.2.a.be	$2$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+q^{5}+2q^{9}+\beta q^{11}-q^{13}+\cdots\)
7840.2.a.bh	$7840$	$2$	7840.a	1.a	$1$	$2$	$2$	$62.603$	\(\Q(\sqrt{17}) \)	None	✓				1120.2.a.r	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}+(1+\beta )q^{9}-\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
7840.2.a.bi	$7840$	$2$	7840.a	1.a	$1$	$2$	$2$	$62.603$	\(\Q(\sqrt{17}) \)	None	✓				1120.2.a.q	$1$	$0$	\(0\)	\(1\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}+(1+\beta )q^{9}+(-4+\beta )q^{11}+\cdots\)
7840.2.a.bj	$7840$	$2$	7840.a	1.a	$1$	$2$	$2$	$62.603$	\(\Q(\sqrt{2}) \)	None	✓				1120.2.q.e	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-q^{5}+2\beta q^{9}+(2+2\beta )q^{11}+\cdots\)
7840.2.a.bk	$7840$	$2$	7840.a	1.a	$1$	$2$	$2$	$62.603$	\(\Q(\sqrt{2}) \)	None	✓				1120.2.q.e	$1$	$1$	\(0\)	\(2\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+q^{5}+2\beta q^{9}+(-2-2\beta )q^{11}+\cdots\)
7840.2.a.bl	$7840$	$2$	7840.a	1.a	$1$	$3$	$3$	$62.603$	3.3.229.1	None	✓	✓			7840.2.a.bl	$1$	$1$	\(0\)	\(-2\)	\(-3\)	\(0\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}-q^{5}+(2-\beta _{1}+2\beta _{2})q^{9}+\cdots\)
7840.2.a.bm	$7840$	$2$	7840.a	1.a	$1$	$3$	$3$	$62.603$	3.3.229.1	None	✓	✓			7840.2.a.bl	$1$	$1$	\(0\)	\(-2\)	\(3\)	\(0\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+q^{5}+(2-\beta _{1}+2\beta _{2})q^{9}+\cdots\)
7840.2.a.bn	$7840$	$2$	7840.a	1.a	$1$	$3$	$3$	$62.603$	3.3.229.1	None	✓	✓			7840.2.a.bl	$1$	$0$	\(0\)	\(2\)	\(-3\)	\(0\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}-q^{5}+(2-\beta _{1}+2\beta _{2})q^{9}+\cdots\)
7840.2.a.bo	$7840$	$2$	7840.a	1.a	$1$	$3$	$3$	$62.603$	3.3.229.1	None	✓	✓			7840.2.a.bl	$1$	$0$	\(0\)	\(2\)	\(3\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}+q^{5}+(2-\beta _{1}+2\beta _{2})q^{9}+\cdots\)
7840.2.a.bp	$7840$	$2$	7840.a	1.a	$1$	$4$	$4$	$62.603$	\(\Q(\sqrt{3}, \sqrt{7})\)	None	✓				1120.2.q.g	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+2\beta _{1}q^{11}+(-1-\beta _{3})q^{13}+\cdots\)
7840.2.a.bq	$7840$	$2$	7840.a	1.a	$1$	$4$	$4$	$62.603$	\(\Q(\zeta_{24})^+\)	None	✓	✓			7840.2.a.bq	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+(\beta _{1}+\beta _{3})q^{11}+(3-\beta _{2}+\cdots)q^{13}+\cdots\)
7840.2.a.br	$7840$	$2$	7840.a	1.a	$1$	$4$	$4$	$62.603$	\(\Q(\sqrt{5}, \sqrt{13})\)	None	✓	✓			7840.2.a.br	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+(2+\beta _{2})q^{9}+\beta _{3}q^{11}+\cdots\)
7840.2.a.bs	$7840$	$2$	7840.a	1.a	$1$	$4$	$4$	$62.603$	\(\Q(\sqrt{5}, \sqrt{13})\)	None	✓				1120.2.q.h	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+(2+\beta _{2})q^{9}-\beta _{3}q^{11}+\cdots\)
7840.2.a.bt	$7840$	$2$	7840.a	1.a	$1$	$4$	$4$	$62.603$	\(\Q(\zeta_{24})^+\)	None	✓	✓			7840.2.a.bq	$2$	$1$	\(0\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+(\beta _{1}-\beta _{3})q^{11}+(-3+\cdots)q^{13}+\cdots\)
7840.2.a.bu	$7840$	$2$	7840.a	1.a	$1$	$4$	$4$	$62.603$	\(\Q(\sqrt{3}, \sqrt{7})\)	None	✓				1120.2.q.g	$2$	$1$	\(0\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}-2\beta _{1}q^{11}+(1-\beta _{3})q^{13}+\cdots\)
7840.2.a.bv	$7840$	$2$	7840.a	1.a	$1$	$4$	$4$	$62.603$	\(\Q(\sqrt{5}, \sqrt{13})\)	None	✓				1120.2.q.h	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+(2+\beta _{2})q^{9}+\beta _{3}q^{11}+\cdots\)
7840.2.a.bw	$7840$	$2$	7840.a	1.a	$1$	$4$	$4$	$62.603$	\(\Q(\sqrt{5}, \sqrt{13})\)	None	✓	✓			7840.2.a.br	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+(2+\beta _{2})q^{9}-\beta _{3}q^{11}+\cdots\)
7840.2.a.bx	$7840$	$2$	7840.a	1.a	$1$	$5$	$5$	$62.603$	5.5.1686096.1	None	✓				1120.2.q.i	$1$	$1$	\(0\)	\(0\)	\(-5\)	\(0\)		$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+(2+\beta _{2})q^{9}+(-1-\beta _{4})q^{11}+\cdots\)
7840.2.a.by	$7840$	$2$	7840.a	1.a	$1$	$5$	$5$	$62.603$	5.5.1686096.1	None	✓				1120.2.q.i	$1$	$0$	\(0\)	\(0\)	\(-5\)	\(0\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+(2+\beta _{2})q^{9}+(1+\beta _{4})q^{11}+\cdots\)
7840.2.a.bz	$7840$	$2$	7840.a	1.a	$1$	$5$	$5$	$62.603$	5.5.1686096.1	None	✓		✓		1120.2.q.i	$1$	$1$	\(0\)	\(0\)	\(5\)	\(0\)		$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+(2+\beta _{2})q^{9}+(-1-\beta _{4})q^{11}+\cdots\)
7840.2.a.ca	$7840$	$2$	7840.a	1.a	$1$	$5$	$5$	$62.603$	5.5.1686096.1	None	✓		✓		1120.2.q.i	$1$	$0$	\(0\)	\(0\)	\(5\)	\(0\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+(2+\beta _{2})q^{9}+(1+\beta _{4})q^{11}+\cdots\)
7840.2.a.cb	$7840$	$2$	7840.a	1.a	$1$	$6$	$6$	$62.603$	6.6.28198912.1	None	✓	✓			7840.2.a.cb	$1$	$1$	\(0\)	\(-4\)	\(-6\)	\(0\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}-q^{5}+(2-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
7840.2.a.cc	$7840$	$2$	7840.a	1.a	$1$	$6$	$6$	$62.603$	6.6.28198912.1	None	✓	✓	✓		7840.2.a.cb	$1$	$1$	\(0\)	\(-4\)	\(6\)	\(0\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+q^{5}+(2-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
7840.2.a.cd	$7840$	$2$	7840.a	1.a	$1$	$6$	$6$	$62.603$	6.6.170145936.1	None	✓		✓		1120.2.q.k	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)		$+$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}-q^{5}+(2-\beta _{5})q^{9}+\beta _{2}q^{11}+\cdots\)
7840.2.a.ce	$7840$	$2$	7840.a	1.a	$1$	$6$	$6$	$62.603$	6.6.170145936.1	None	✓				1120.2.q.k	$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$+$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}+q^{5}+(2-\beta _{5})q^{9}-\beta _{2}q^{11}+\cdots\)
7840.2.a.cf	$7840$	$2$	7840.a	1.a	$1$	$6$	$6$	$62.603$	6.6.28198912.1	None	✓	✓	✓		7840.2.a.cb	$1$	$0$	\(0\)	\(4\)	\(-6\)	\(0\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}-q^{5}+(2-\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{9}+\cdots\)
7840.2.a.cg	$7840$	$2$	7840.a	1.a	$1$	$6$	$6$	$62.603$	6.6.28198912.1	None	✓	✓			7840.2.a.cb	$1$	$0$	\(0\)	\(4\)	\(6\)	\(0\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+q^{5}+(2-\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{9}+\cdots\)
7840.2.a.ch	$7840$	$2$	7840.a	1.a	$1$	$8$	$8$	$62.603$	8.8.\(\cdots\).1	None	✓	✓	✓		7840.2.a.ch	$2$	$1$	\(0\)	\(0\)	\(-8\)	\(0\)		$+$	$+$	$+$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{6}q^{3}-q^{5}+(1-\beta _{2})q^{9}+(-\beta _{4}+\cdots)q^{11}+\cdots\)
7840.2.a.ci	$7840$	$2$	7840.a	1.a	$1$	$8$	$8$	$62.603$	8.8.\(\cdots\).1	None	✓	✓	✓		7840.2.a.ch	$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)		$+$	$-$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{6}q^{3}+q^{5}+(1-\beta _{2})q^{9}+(\beta _{4}+\beta _{6}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7840))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7840)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(490))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(560))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(784))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(980))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1568))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1960))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3920))\)\(^{\oplus 2}\)