Space of modular forms of level 9680, weight 2, and trivial character

• Label: 9680.2.a
• Level: $9680$
• Weight: $2$
• Character orbit: 9680.a
• Rep. character: $\chi_{9680}(1,\cdot)$
• Character field: $\Q$
• Dimension: $218$
• Newform subspaces: $84$
• Sturm bound: $3168$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 9680 = 2^{4} \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9680.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 84 \)
Sturm bound:			\(3168\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(3\), \(7\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9680))\).

	Total	New	Old
Modular forms	1656	218	1438
Cusp forms	1513	218	1295
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.

\(2\)	\(5\)	\(11\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(198\)	\(24\)	\(174\)		\(181\)	\(24\)	\(157\)		\(17\)	\(0\)	\(17\)
\(+\)	\(+\)	\(-\)	\(-\)		\(216\)	\(30\)	\(186\)		\(198\)	\(30\)	\(168\)		\(18\)	\(0\)	\(18\)
\(+\)	\(-\)	\(+\)	\(-\)		\(210\)	\(30\)	\(180\)		\(192\)	\(30\)	\(162\)		\(18\)	\(0\)	\(18\)
\(+\)	\(-\)	\(-\)	\(+\)		\(204\)	\(25\)	\(179\)		\(186\)	\(25\)	\(161\)		\(18\)	\(0\)	\(18\)
\(-\)	\(+\)	\(+\)	\(-\)		\(216\)	\(30\)	\(186\)		\(198\)	\(30\)	\(168\)		\(18\)	\(0\)	\(18\)
\(-\)	\(+\)	\(-\)	\(+\)		\(198\)	\(25\)	\(173\)		\(180\)	\(25\)	\(155\)		\(18\)	\(0\)	\(18\)
\(-\)	\(-\)	\(+\)	\(+\)		\(204\)	\(24\)	\(180\)		\(186\)	\(24\)	\(162\)		\(18\)	\(0\)	\(18\)
\(-\)	\(-\)	\(-\)	\(-\)		\(210\)	\(30\)	\(180\)		\(192\)	\(30\)	\(162\)		\(18\)	\(0\)	\(18\)
Plus space			\(+\)		\(804\)	\(98\)	\(706\)		\(733\)	\(98\)	\(635\)		\(71\)	\(0\)	\(71\)
Minus space			\(-\)		\(852\)	\(120\)	\(732\)		\(780\)	\(120\)	\(660\)		\(72\)	\(0\)	\(72\)

Trace form

218 * q + 2 * q^3 + 6 * q^7 + 222 * q^9 - 2 * q^15 + 4 * q^17 - 4 * q^21 - 2 * q^23 + 218 * q^25 - 4 * q^27 - 12 * q^29 + 12 * q^31 - 6 * q^35 - 8 * q^37 - 20 * q^39 + 14 * q^43 - 4 * q^45 - 22 * q^47 + 230 * q^49 - 36 * q^51 + 8 * q^57 - 16 * q^59 + 16 * q^61 + 6 * q^63 + 4 * q^65 + 30 * q^67 + 20 * q^69 + 12 * q^71 + 20 * q^73 + 2 * q^75 + 8 * q^79 + 230 * q^81 - 26 * q^83 + 8 * q^85 - 36 * q^87 + 20 * q^89 + 52 * q^91 + 40 * q^93 + 8 * q^95 + 28 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9680))\) 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	11
9680.2.a.a	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				440.2.a.d	$1$	$1$	\(0\)	\(-3\)	\(1\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+q^{5}+q^{7}+6q^{9}+6q^{13}+\cdots\)
9680.2.a.b	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				1210.2.a.g	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+q^{9}-6q^{13}+2q^{15}+\cdots\)
9680.2.a.c	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				1210.2.a.g	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+q^{9}+6q^{13}+2q^{15}+\cdots\)
9680.2.a.d	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				220.2.a.b	$1$	$0$	\(0\)	\(-2\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}+q^{9}-2q^{15}+4q^{17}+\cdots\)
9680.2.a.e	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				4840.2.a.g	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-3q^{7}-2q^{9}-4q^{13}+\cdots\)
9680.2.a.f	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				2420.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}-2q^{9}-2q^{13}+q^{15}+\cdots\)
9680.2.a.g	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				110.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}-2q^{9}-2q^{13}+q^{15}+\cdots\)
9680.2.a.h	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				2420.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}-2q^{9}+2q^{13}+q^{15}+\cdots\)
9680.2.a.i	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				4840.2.a.g	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+3q^{7}-2q^{9}+4q^{13}+\cdots\)
9680.2.a.j	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				110.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+5q^{7}-2q^{9}-2q^{13}+\cdots\)
9680.2.a.k	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				1210.2.a.f	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}-2q^{9}+4q^{13}-q^{15}+\cdots\)
9680.2.a.l	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				1210.2.a.f	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}-2q^{9}-4q^{13}-q^{15}+\cdots\)
9680.2.a.m	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				2420.2.a.c	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-4q^{7}-3q^{9}+4q^{13}-4q^{17}+\cdots\)
9680.2.a.n	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				440.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}-3q^{9}-8q^{19}+8q^{23}+\cdots\)
9680.2.a.o	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				440.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}-3q^{9}+4q^{13}+4q^{17}+\cdots\)
9680.2.a.p	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				2420.2.a.c	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{7}-3q^{9}-4q^{13}+4q^{17}+\cdots\)
9680.2.a.q	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				40.2.a.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{7}-3q^{9}+2q^{13}-2q^{17}+\cdots\)
9680.2.a.r	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				55.2.a.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-3q^{9}-2q^{13}-6q^{17}-4q^{19}+\cdots\)
9680.2.a.s	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				440.2.a.c	$1$	$1$	\(0\)	\(0\)	\(1\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{7}-3q^{9}-6q^{13}+6q^{17}+\cdots\)
9680.2.a.t	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				1210.2.a.c	$1$	$0$	\(0\)	\(1\)	\(1\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-3q^{7}-2q^{9}+q^{15}-8q^{17}+\cdots\)
9680.2.a.u	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				1210.2.a.d	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-3q^{7}-2q^{9}+q^{15}+3q^{17}+\cdots\)
9680.2.a.v	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				1210.2.a.d	$1$	$1$	\(0\)	\(1\)	\(1\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+3q^{7}-2q^{9}+q^{15}-3q^{17}+\cdots\)
9680.2.a.w	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				1210.2.a.c	$1$	$0$	\(0\)	\(1\)	\(1\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+3q^{7}-2q^{9}+q^{15}+8q^{17}+\cdots\)
9680.2.a.x	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				110.2.a.b	$1$	$0$	\(0\)	\(1\)	\(1\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+3q^{7}-2q^{9}+6q^{13}+\cdots\)
9680.2.a.y	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				4840.2.a.a	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+q^{9}-2q^{13}-2q^{15}+\cdots\)
9680.2.a.z	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				4840.2.a.a	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+q^{9}+2q^{13}-2q^{15}+\cdots\)
9680.2.a.ba	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				20.2.a.a	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+2q^{7}+q^{9}-2q^{13}+\cdots\)
9680.2.a.bb	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				220.2.a.a	$1$	$0$	\(0\)	\(2\)	\(1\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}-4q^{7}+q^{9}+4q^{13}+\cdots\)
9680.2.a.bc	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				1210.2.a.a	$1$	$0$	\(0\)	\(3\)	\(-1\)	\(-5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-q^{5}-5q^{7}+6q^{9}-4q^{13}+\cdots\)
9680.2.a.bd	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				1210.2.a.a	$1$	$0$	\(0\)	\(3\)	\(-1\)	\(5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-q^{5}+5q^{7}+6q^{9}+4q^{13}+\cdots\)
9680.2.a.be	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				605.2.a.a	$1$	$0$	\(0\)	\(3\)	\(1\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+q^{5}-3q^{7}+6q^{9}-4q^{13}+\cdots\)
9680.2.a.bf	$9680$	$2$	9680.a	1.a	$1$	$1$	$1$	$77.295$	\(\Q\)	None	✓				605.2.a.a	$1$	$0$	\(0\)	\(3\)	\(1\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+q^{5}+3q^{7}+6q^{9}+4q^{13}+\cdots\)
9680.2.a.bg	$9680$	$2$	9680.a	1.a	$1$	$2$	$2$	$77.295$	\(\Q(\sqrt{3}) \)	None	✓				605.2.a.f	$2$	$1$	\(0\)	\(-4\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}+\beta q^{7}+q^{9}-2q^{15}+\cdots\)
9680.2.a.bh	$9680$	$2$	9680.a	1.a	$1$	$2$	$2$	$77.295$	\(\Q(\sqrt{5}) \)	None	✓				110.2.g.a	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2\beta q^{3}-q^{5}+(-1-\beta )q^{7}+(1+4\beta )q^{9}+\cdots\)
9680.2.a.bi	$9680$	$2$	9680.a	1.a	$1$	$2$	$2$	$77.295$	\(\Q(\sqrt{5}) \)	None	✓				110.2.g.a	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2\beta q^{3}-q^{5}+(1+\beta )q^{7}+(1+4\beta )q^{9}+\cdots\)
9680.2.a.bj	$9680$	$2$	9680.a	1.a	$1$	$2$	$2$	$77.295$	\(\Q(\sqrt{2}) \)	None	✓				4840.2.a.o	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+q^{5}+(-1+\beta )q^{7}+\cdots\)
9680.2.a.bk	$9680$	$2$	9680.a	1.a	$1$	$2$	$2$	$77.295$	\(\Q(\sqrt{2}) \)	None	✓				4840.2.a.o	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+q^{5}+(1-\beta )q^{7}-2\beta q^{9}+\cdots\)
9680.2.a.bl	$9680$	$2$	9680.a	1.a	$1$	$2$	$2$	$77.295$	\(\Q(\sqrt{17}) \)	None	✓				440.2.a.f	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-q^{5}+(2-\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
9680.2.a.bm	$9680$	$2$	9680.a	1.a	$1$	$2$	$2$	$77.295$	\(\Q(\sqrt{17}) \)	None	✓				440.2.a.g	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(5\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-q^{5}+(2+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
9680.2.a.bn	$9680$	$2$	9680.a	1.a	$1$	$2$	$2$	$77.295$	\(\Q(\sqrt{2}) \)	None	✓				55.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-4\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}-2q^{7}+5q^{9}+(4-\beta )q^{13}+\cdots\)
9680.2.a.bo	$9680$	$2$	9680.a	1.a	$1$	$2$	$2$	$77.295$	\(\Q(\sqrt{3}) \)	None	✓				1210.2.a.o	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}+(-1-2\beta )q^{7}+(-2+\cdots)q^{13}+\cdots\)
9680.2.a.bp	$9680$	$2$	9680.a	1.a	$1$	$2$	$2$	$77.295$	\(\Q(\sqrt{3}) \)	None	✓				1210.2.a.o	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}+(1+2\beta )q^{7}+(2+2\beta )q^{13}+\cdots\)
9680.2.a.bq	$9680$	$2$	9680.a	1.a	$1$	$2$	$2$	$77.295$	\(\Q(\sqrt{3}) \)	None	✓				4840.2.a.k	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}+(-2+\beta )q^{7}+2\beta q^{13}+\cdots\)
9680.2.a.br	$9680$	$2$	9680.a	1.a	$1$	$2$	$2$	$77.295$	\(\Q(\sqrt{3}) \)	None	✓				4840.2.a.k	$1$	$1$	\(0\)	\(0\)	\(2\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}+(2-\beta )q^{7}-2\beta q^{13}+\cdots\)
9680.2.a.bs	$9680$	$2$	9680.a	1.a	$1$	$2$	$2$	$77.295$	\(\Q(\sqrt{17}) \)	None	✓				440.2.a.e	$1$	$1$	\(0\)	\(1\)	\(2\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}-\beta q^{7}+(1+\beta )q^{9}-2q^{13}+\cdots\)
9680.2.a.bt	$9680$	$2$	9680.a	1.a	$1$	$2$	$2$	$77.295$	\(\Q(\sqrt{33}) \)	None	✓				110.2.a.d	$1$	$0$	\(0\)	\(1\)	\(2\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}+\beta q^{7}+(5+\beta )q^{9}-2q^{13}+\cdots\)
9680.2.a.bu	$9680$	$2$	9680.a	1.a	$1$	$2$	$2$	$77.295$	\(\Q(\sqrt{3}) \)	None	✓				605.2.a.e	$2$	$0$	\(0\)	\(2\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-\beta q^{7}-2q^{9}-2\beta q^{13}+\cdots\)
9680.2.a.bv	$9680$	$2$	9680.a	1.a	$1$	$2$	$2$	$77.295$	\(\Q(\sqrt{3}) \)	None	✓				2420.2.a.h	$2$	$1$	\(0\)	\(2\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-\beta q^{7}-2q^{9}+q^{15}+4\beta q^{19}+\cdots\)
9680.2.a.bw	$9680$	$2$	9680.a	1.a	$1$	$2$	$2$	$77.295$	\(\Q(\sqrt{5}) \)	None	✓				110.2.g.b	$1$	$1$	\(0\)	\(3\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-q^{5}+(-1+3\beta )q^{9}+(-4+\cdots)q^{13}+\cdots\)
9680.2.a.bx	$9680$	$2$	9680.a	1.a	$1$	$2$	$2$	$77.295$	\(\Q(\sqrt{5}) \)	None	✓				110.2.g.b	$1$	$0$	\(0\)	\(3\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-q^{5}+(-1+3\beta )q^{9}+(4+\cdots)q^{13}+\cdots\)
9680.2.a.by	$9680$	$2$	9680.a	1.a	$1$	$3$	$3$	$77.295$	3.3.788.1	None	✓				4840.2.a.s	$1$	$0$	\(0\)	\(-1\)	\(-3\)	\(-3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+(-1-\beta _{1}+\beta _{2})q^{7}+\cdots\)
9680.2.a.bz	$9680$	$2$	9680.a	1.a	$1$	$3$	$3$	$77.295$	3.3.404.1	None	✓				605.2.a.g	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+(-2\beta _{1}+\beta _{2})q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)
9680.2.a.ca	$9680$	$2$	9680.a	1.a	$1$	$3$	$3$	$77.295$	3.3.404.1	None	✓				4840.2.a.t	$1$	$0$	\(0\)	\(-1\)	\(-3\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}-q^{5}-\beta _{1}q^{7}+(2+\beta _{1}-\beta _{2})q^{9}+\cdots\)
9680.2.a.cb	$9680$	$2$	9680.a	1.a	$1$	$3$	$3$	$77.295$	3.3.404.1	None	✓				605.2.a.g	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+(2\beta _{1}-\beta _{2})q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)
9680.2.a.cc	$9680$	$2$	9680.a	1.a	$1$	$3$	$3$	$77.295$	3.3.404.1	None	✓				4840.2.a.t	$1$	$0$	\(0\)	\(-1\)	\(-3\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}-q^{5}+\beta _{1}q^{7}+(2+\beta _{1}-\beta _{2})q^{9}+\cdots\)
9680.2.a.cd	$9680$	$2$	9680.a	1.a	$1$	$3$	$3$	$77.295$	3.3.788.1	None	✓				4840.2.a.s	$1$	$0$	\(0\)	\(-1\)	\(-3\)	\(3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+(1+\beta _{1}-\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots\)
9680.2.a.ce	$9680$	$2$	9680.a	1.a	$1$	$3$	$3$	$77.295$	3.3.1524.1	None	✓				2420.2.a.i	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+\beta _{2}q^{7}+(2+\beta _{1}+\beta _{2})q^{9}+\cdots\)
9680.2.a.cf	$9680$	$2$	9680.a	1.a	$1$	$3$	$3$	$77.295$	3.3.1524.1	None	✓				2420.2.a.i	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}-\beta _{2}q^{7}+(2+\beta _{1}+\beta _{2})q^{9}+\cdots\)
9680.2.a.cg	$9680$	$2$	9680.a	1.a	$1$	$3$	$3$	$77.295$	3.3.568.1	None	✓				4840.2.a.q	$1$	$0$	\(0\)	\(1\)	\(3\)	\(-1\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+q^{5}+\beta _{2}q^{7}+(3-\beta _{1})q^{9}+\cdots\)
9680.2.a.ch	$9680$	$2$	9680.a	1.a	$1$	$3$	$3$	$77.295$	3.3.568.1	None	✓				4840.2.a.q	$1$	$0$	\(0\)	\(1\)	\(3\)	\(1\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+q^{5}-\beta _{2}q^{7}+(3-\beta _{1})q^{9}+\cdots\)
9680.2.a.ci	$9680$	$2$	9680.a	1.a	$1$	$4$	$4$	$77.295$	4.4.5225.1	None	✓				110.2.g.c	$1$	$0$	\(0\)	\(-3\)	\(4\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+q^{5}+(-1-\beta _{1}+\beta _{3})q^{7}+\cdots\)
9680.2.a.cj	$9680$	$2$	9680.a	1.a	$1$	$4$	$4$	$77.295$	4.4.5225.1	None	✓				110.2.g.c	$1$	$1$	\(0\)	\(-3\)	\(4\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+q^{5}+(1+\beta _{1}-\beta _{3})q^{7}+\cdots\)
9680.2.a.ck	$9680$	$2$	9680.a	1.a	$1$	$4$	$4$	$77.295$	4.4.5125.1	None	✓				220.2.m.a	$1$	$0$	\(0\)	\(-2\)	\(-4\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\cdots\)
9680.2.a.cl	$9680$	$2$	9680.a	1.a	$1$	$4$	$4$	$77.295$	4.4.5125.1	None	✓				220.2.m.a	$1$	$1$	\(0\)	\(-2\)	\(-4\)	\(3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+(\beta _{1}-\beta _{2}+\beta _{3})q^{7}+\cdots\)
9680.2.a.cm	$9680$	$2$	9680.a	1.a	$1$	$4$	$4$	$77.295$	4.4.725.1	None	✓				55.2.g.b	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{2}-\beta _{3})q^{3}-q^{5}+(-2+\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots\)
9680.2.a.cn	$9680$	$2$	9680.a	1.a	$1$	$4$	$4$	$77.295$	4.4.725.1	None	✓				55.2.g.b	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{2}-\beta _{3})q^{3}-q^{5}+(2-\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)
9680.2.a.co	$9680$	$2$	9680.a	1.a	$1$	$4$	$4$	$77.295$	4.4.2525.1	None	✓				220.2.m.b	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{2})q^{3}+q^{5}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
9680.2.a.cp	$9680$	$2$	9680.a	1.a	$1$	$4$	$4$	$77.295$	4.4.2525.1	None	✓				220.2.m.b	$1$	$1$	\(0\)	\(0\)	\(4\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{2})q^{3}+q^{5}+(1-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
9680.2.a.cq	$9680$	$2$	9680.a	1.a	$1$	$4$	$4$	$77.295$	4.4.4752.1	None	✓				4840.2.a.w	$1$	$1$	\(0\)	\(2\)	\(-4\)	\(-6\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}-q^{5}+(-2-\beta _{2}+\beta _{3})q^{7}+\cdots\)
9680.2.a.cr	$9680$	$2$	9680.a	1.a	$1$	$4$	$4$	$77.295$	4.4.4752.1	None	✓				4840.2.a.w	$1$	$1$	\(0\)	\(2\)	\(-4\)	\(6\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}-q^{5}+(2+\beta _{2}-\beta _{3})q^{7}+\cdots\)
9680.2.a.cs	$9680$	$2$	9680.a	1.a	$1$	$4$	$4$	$77.295$	4.4.2525.1	None	✓				55.2.g.a	$1$	$1$	\(0\)	\(2\)	\(4\)	\(-11\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+(-3-\beta _{2}+\beta _{3})q^{7}+\cdots\)
9680.2.a.ct	$9680$	$2$	9680.a	1.a	$1$	$4$	$4$	$77.295$	4.4.725.1	None	✓				440.2.y.a	$1$	$1$	\(0\)	\(2\)	\(4\)	\(-7\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+q^{5}+(-2+\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\cdots\)
9680.2.a.cu	$9680$	$2$	9680.a	1.a	$1$	$4$	$4$	$77.295$	4.4.725.1	None	✓				440.2.y.a	$1$	$0$	\(0\)	\(2\)	\(4\)	\(7\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+q^{5}+(2-\beta _{1}-\beta _{2}+\beta _{3})q^{7}+\cdots\)
9680.2.a.cv	$9680$	$2$	9680.a	1.a	$1$	$4$	$4$	$77.295$	4.4.2525.1	None	✓				55.2.g.a	$1$	$0$	\(0\)	\(2\)	\(4\)	\(11\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+(3+\beta _{2}-\beta _{3})q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)
9680.2.a.cw	$9680$	$2$	9680.a	1.a	$1$	$6$	$6$	$77.295$	6.6.27433728.1	None	✓		✓		605.2.a.m	$2$	$1$	\(0\)	\(-6\)	\(6\)	\(0\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{3})q^{3}+q^{5}-\beta _{1}q^{7}+(2-\beta _{2}+\cdots)q^{9}+\cdots\)
9680.2.a.cx	$9680$	$2$	9680.a	1.a	$1$	$6$	$6$	$77.295$	6.6.45753625.1	None	✓				440.2.y.b	$1$	$1$	\(0\)	\(-2\)	\(-6\)	\(-6\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}-q^{5}+(-1+\beta _{2}+\beta _{5})q^{7}+\cdots\)
9680.2.a.cy	$9680$	$2$	9680.a	1.a	$1$	$6$	$6$	$77.295$	6.6.45753625.1	None	✓				440.2.y.b	$1$	$0$	\(0\)	\(-2\)	\(-6\)	\(6\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}-q^{5}+(1-\beta _{2}-\beta _{5})q^{7}+(-2\beta _{2}+\cdots)q^{9}+\cdots\)
9680.2.a.cz	$9680$	$2$	9680.a	1.a	$1$	$6$	$6$	$77.295$	6.6.507624192.1	None	✓		✓		2420.2.a.o	$2$	$0$	\(0\)	\(2\)	\(-6\)	\(0\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{4}q^{3}-q^{5}+(-\beta _{1}+\beta _{2})q^{7}+(3+\cdots)q^{9}+\cdots\)
9680.2.a.da	$9680$	$2$	9680.a	1.a	$1$	$6$	$6$	$77.295$	6.6.22733568.1	None	✓				4840.2.a.bc	$1$	$0$	\(0\)	\(2\)	\(6\)	\(-4\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+(-\beta _{3}-\beta _{4})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
9680.2.a.db	$9680$	$2$	9680.a	1.a	$1$	$6$	$6$	$77.295$	6.6.22733568.1	None	✓				4840.2.a.bc	$1$	$0$	\(0\)	\(2\)	\(6\)	\(4\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+(\beta _{3}+\beta _{4})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
9680.2.a.dc	$9680$	$2$	9680.a	1.a	$1$	$6$	$6$	$77.295$	6.6.25903625.1	None	✓				440.2.y.c	$1$	$1$	\(0\)	\(3\)	\(-6\)	\(-7\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+(-1+\beta _{2}-\beta _{3}+\beta _{5})q^{7}+\cdots\)
9680.2.a.dd	$9680$	$2$	9680.a	1.a	$1$	$6$	$6$	$77.295$	6.6.25903625.1	None	✓				440.2.y.c	$1$	$0$	\(0\)	\(3\)	\(-6\)	\(7\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+(1-\beta _{2}+\beta _{3}-\beta _{5})q^{7}+\cdots\)
9680.2.a.de	$9680$	$2$	9680.a	1.a	$1$	$8$	$8$	$77.295$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		440.2.y.d	$1$	$1$	\(0\)	\(-1\)	\(8\)	\(-6\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+(-1-\beta _{4})q^{7}+(3+\beta _{4}+\cdots)q^{9}+\cdots\)
9680.2.a.df	$9680$	$2$	9680.a	1.a	$1$	$8$	$8$	$77.295$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		440.2.y.d	$1$	$0$	\(0\)	\(-1\)	\(8\)	\(6\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+(1+\beta _{4})q^{7}+(3+\beta _{4}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9680))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9680)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(220))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(440))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(484))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(605))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(880))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(968))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1936))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2420))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4840))\)\(^{\oplus 2}\)