Space of modular forms of level 7056, weight 2, and trivial character

• Label: 7056.2.a
• Level: $7056$
• Weight: $2$
• Character orbit: 7056.a
• Rep. character: $\chi_{7056}(1,\cdot)$
• Character field: $\Q$
• Dimension: $100$
• Newform subspaces: $77$
• Sturm bound: $2688$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 7056 = 2^{4} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7056.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 77 \)
Sturm bound:			\(2688\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\), \(17\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7056))\).

	Total	New	Old
Modular forms	1440	105	1335
Cusp forms	1249	100	1149
Eisenstein series	191	5	186

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(3\)	\(7\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(176\)	\(8\)	\(168\)		\(153\)	\(8\)	\(145\)		\(23\)	\(0\)	\(23\)
\(+\)	\(+\)	\(-\)	\(-\)		\(184\)	\(12\)	\(172\)		\(160\)	\(12\)	\(148\)		\(24\)	\(0\)	\(24\)
\(+\)	\(-\)	\(+\)	\(-\)		\(184\)	\(16\)	\(168\)		\(160\)	\(16\)	\(144\)		\(24\)	\(0\)	\(24\)
\(+\)	\(-\)	\(-\)	\(+\)		\(176\)	\(15\)	\(161\)		\(152\)	\(15\)	\(137\)		\(24\)	\(0\)	\(24\)
\(-\)	\(+\)	\(+\)	\(-\)		\(184\)	\(12\)	\(172\)		\(160\)	\(12\)	\(148\)		\(24\)	\(0\)	\(24\)
\(-\)	\(+\)	\(-\)	\(+\)		\(176\)	\(9\)	\(167\)		\(152\)	\(9\)	\(143\)		\(24\)	\(0\)	\(24\)
\(-\)	\(-\)	\(+\)	\(+\)		\(176\)	\(15\)	\(161\)		\(152\)	\(13\)	\(139\)		\(24\)	\(2\)	\(22\)
\(-\)	\(-\)	\(-\)	\(-\)		\(184\)	\(18\)	\(166\)		\(160\)	\(15\)	\(145\)		\(24\)	\(3\)	\(21\)
Plus space			\(+\)		\(704\)	\(47\)	\(657\)		\(609\)	\(45\)	\(564\)		\(95\)	\(2\)	\(93\)
Minus space			\(-\)		\(736\)	\(58\)	\(678\)		\(640\)	\(55\)	\(585\)		\(96\)	\(3\)	\(93\)

Trace form

100 * q + 2 * q^11 + 2 * q^13 - 4 * q^17 - 4 * q^19 + 2 * q^23 + 94 * q^25 + 14 * q^29 - 4 * q^31 + 6 * q^37 - 4 * q^41 - 4 * q^43 - 28 * q^59 + 6 * q^61 - 8 * q^65 - 2 * q^67 - 40 * q^71 + 2 * q^73 - 22 * q^79 + 12 * q^83 + 18 * q^85 - 12 * q^89 - 34 * q^95 + 2 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7056))\) 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	7
7056.2.a.a	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				294.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}-4q^{11}+4q^{13}-4q^{19}+11q^{25}+\cdots\)
7056.2.a.b	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				504.2.s.a	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}-3q^{13}+4q^{17}-7q^{19}+4q^{23}+\cdots\)
7056.2.a.c	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				56.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}-2q^{17}-2q^{19}+8q^{23}+11q^{25}+\cdots\)
7056.2.a.d	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				504.2.s.a	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}+3q^{13}+4q^{17}+7q^{19}-4q^{23}+\cdots\)
7056.2.a.e	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				126.2.g.a	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-3q^{11}+2q^{13}-6q^{17}-2q^{19}+\cdots\)
7056.2.a.f	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				28.2.e.a	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-3q^{11}+2q^{13}-3q^{17}+q^{19}+\cdots\)
7056.2.a.g	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				42.2.e.b	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+3q^{11}-4q^{13}+4q^{19}+4q^{25}+\cdots\)
7056.2.a.h	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				126.2.g.a	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+3q^{11}-2q^{13}-6q^{17}+2q^{19}+\cdots\)
7056.2.a.i	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				168.2.q.b	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-6q^{11}-3q^{13}-4q^{17}+5q^{19}+\cdots\)
7056.2.a.j	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				504.2.a.d	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-6q^{11}+6q^{13}+2q^{17}+4q^{19}+\cdots\)
7056.2.a.k	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				42.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-4q^{11}-6q^{13}+2q^{17}-4q^{19}+\cdots\)
7056.2.a.l	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				504.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-2q^{11}-2q^{13}-6q^{17}-4q^{19}+\cdots\)
7056.2.a.m	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				21.2.e.a	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-2q^{11}-q^{13}+q^{19}-q^{25}+\cdots\)
7056.2.a.n	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				588.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+2q^{11}-4q^{13}-6q^{17}-8q^{19}+\cdots\)
7056.2.a.o	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				84.2.i.a	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+2q^{11}+3q^{13}+8q^{17}-q^{19}+\cdots\)
7056.2.a.p	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				21.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+4q^{11}+2q^{13}-6q^{17}+4q^{19}+\cdots\)
7056.2.a.q	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				24.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+4q^{11}+2q^{13}+2q^{17}-4q^{19}+\cdots\)
7056.2.a.r	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				504.2.s.b	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-5q^{11}+2q^{13}+6q^{17}-2q^{19}+\cdots\)
7056.2.a.s	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				56.2.i.a	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{11}-2q^{13}+3q^{17}+5q^{19}+\cdots\)
7056.2.a.t	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				168.2.q.a	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+3q^{11}-4q^{13}-4q^{19}+8q^{23}+\cdots\)
7056.2.a.u	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				56.2.i.b	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+3q^{11}+6q^{13}-5q^{17}+q^{19}+\cdots\)
7056.2.a.v	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				504.2.s.b	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+5q^{11}-2q^{13}+6q^{17}+2q^{19}+\cdots\)
7056.2.a.w	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				42.2.e.a	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+5q^{11}+4q^{17}-8q^{19}-4q^{23}+\cdots\)
7056.2.a.x	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				84.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-6q^{11}-2q^{13}-4q^{19}-6q^{23}+\cdots\)
7056.2.a.y	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓				63.2.e.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-7q^{13}+7q^{19}-5q^{25}+7q^{31}+\cdots\)
7056.2.a.z	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓				252.2.k.b	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-5q^{13}-q^{19}-5q^{25}+11q^{31}+\cdots\)
7056.2.a.ba	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				1176.2.a.b	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{13}+4q^{17}-4q^{19}+4q^{23}+\cdots\)
7056.2.a.bb	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓				36.2.a.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{13}+8q^{19}-5q^{25}-4q^{31}+\cdots\)
7056.2.a.bc	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				1176.2.a.b	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{13}-4q^{17}+4q^{19}+4q^{23}+\cdots\)
7056.2.a.bd	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				14.2.a.a	$1$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{13}+6q^{17}+2q^{19}-5q^{25}+\cdots\)
7056.2.a.be	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓				252.2.k.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+5q^{13}+q^{19}-5q^{25}-11q^{31}+\cdots\)
7056.2.a.bf	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓				63.2.e.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	\(q+7q^{13}-7q^{19}-5q^{25}-7q^{31}+\cdots\)
7056.2.a.bg	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	\(\Q(\sqrt{-7}) \)	✓				49.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+4q^{11}+8q^{23}-5q^{25}-2q^{29}+\cdots\)
7056.2.a.bh	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				504.2.s.b	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-5q^{11}-2q^{13}-6q^{17}+2q^{19}+\cdots\)
7056.2.a.bi	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				56.2.i.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{11}+2q^{13}-3q^{17}-5q^{19}+\cdots\)
7056.2.a.bj	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				56.2.i.b	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+3q^{11}-6q^{13}+5q^{17}-q^{19}+\cdots\)
7056.2.a.bk	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				168.2.q.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+3q^{11}+4q^{13}+4q^{19}+8q^{23}+\cdots\)
7056.2.a.bl	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				42.2.e.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+5q^{11}-4q^{17}+8q^{19}-4q^{23}+\cdots\)
7056.2.a.bm	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				504.2.s.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+5q^{11}+2q^{13}-6q^{17}-2q^{19}+\cdots\)
7056.2.a.bn	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				168.2.q.b	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-6q^{11}+3q^{13}+4q^{17}-5q^{19}+\cdots\)
7056.2.a.bo	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				56.2.a.a	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-4q^{11}-2q^{13}-6q^{17}+8q^{19}+\cdots\)
7056.2.a.bp	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				21.2.e.a	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-2q^{11}+q^{13}-q^{19}-q^{25}+\cdots\)
7056.2.a.bq	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				168.2.a.a	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-6q^{13}-2q^{17}+4q^{19}-4q^{23}+\cdots\)
7056.2.a.br	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				168.2.a.b	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+2q^{13}+6q^{17}-4q^{19}-4q^{23}+\cdots\)
7056.2.a.bs	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				84.2.i.a	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+2q^{11}-3q^{13}-8q^{17}+q^{19}+\cdots\)
7056.2.a.bt	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				504.2.a.a	$1$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+2q^{11}-2q^{13}+6q^{17}-4q^{19}+\cdots\)
7056.2.a.bu	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				588.2.a.b	$1$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+2q^{11}+4q^{13}+6q^{17}+8q^{19}+\cdots\)
7056.2.a.bv	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				504.2.a.d	$1$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+6q^{11}+6q^{13}-2q^{17}+4q^{19}+\cdots\)
7056.2.a.bw	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				28.2.e.a	$1$	$0$	\(0\)	\(0\)	\(3\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-3q^{11}-2q^{13}+3q^{17}-q^{19}+\cdots\)
7056.2.a.bx	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				126.2.g.a	$1$	$1$	\(0\)	\(0\)	\(3\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-3q^{11}-2q^{13}+6q^{17}+2q^{19}+\cdots\)
7056.2.a.by	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				126.2.g.a	$1$	$0$	\(0\)	\(0\)	\(3\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+3q^{11}+2q^{13}+6q^{17}-2q^{19}+\cdots\)
7056.2.a.bz	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				42.2.e.b	$1$	$0$	\(0\)	\(0\)	\(3\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+3q^{11}+4q^{13}-4q^{19}+4q^{25}+\cdots\)
7056.2.a.ca	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				294.2.a.b	$1$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}-4q^{11}-4q^{13}+4q^{19}+11q^{25}+\cdots\)
7056.2.a.cb	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				504.2.s.a	$1$	$1$	\(0\)	\(0\)	\(4\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}-3q^{13}-4q^{17}-7q^{19}-4q^{23}+\cdots\)
7056.2.a.cc	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				504.2.s.a	$1$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}+3q^{13}-4q^{17}+7q^{19}+4q^{23}+\cdots\)
7056.2.a.cd	$7056$	$2$	7056.a	1.a	$1$	$1$	$1$	$56.342$	\(\Q\)	None	✓				84.2.a.a	$1$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}+2q^{11}+6q^{13}-4q^{17}-4q^{19}+\cdots\)
7056.2.a.ce	$7056$	$2$	7056.a	1.a	$1$	$2$	$2$	$56.342$	\(\Q(\sqrt{2}) \)	None	✓				1176.2.a.l	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-2+\beta )q^{5}+(-2-2\beta )q^{11}+3\beta q^{13}+\cdots\)
7056.2.a.cf	$7056$	$2$	7056.a	1.a	$1$	$2$	$2$	$56.342$	\(\Q(\sqrt{2}) \)	None	✓				147.2.a.d	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-2+\beta )q^{5}-2q^{11}+(4+\beta )q^{13}+\cdots\)
7056.2.a.cg	$7056$	$2$	7056.a	1.a	$1$	$2$	$2$	$56.342$	\(\Q(\sqrt{2}) \)	None	✓				1176.2.a.j	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-2+\beta )q^{5}+(2-2\beta )q^{11}-\beta q^{13}+\cdots\)
7056.2.a.ch	$7056$	$2$	7056.a	1.a	$1$	$2$	$2$	$56.342$	\(\Q(\sqrt{57}) \)	None	✓				168.2.q.c	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{5}-\beta q^{11}+(-3+\beta )q^{13}-4q^{17}+\cdots\)
7056.2.a.ci	$7056$	$2$	7056.a	1.a	$1$	$2$	$2$	$56.342$	\(\Q(\sqrt{2}) \)	None	✓				882.2.a.m	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-4q^{11}+3\beta q^{13}-5\beta q^{17}+\cdots\)
7056.2.a.cj	$7056$	$2$	7056.a	1.a	$1$	$2$	$2$	$56.342$	\(\Q(\sqrt{2}) \)	None	✓				392.2.a.h	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-4q^{11}+\beta q^{13}-2\beta q^{17}+\cdots\)
7056.2.a.ck	$7056$	$2$	7056.a	1.a	$1$	$2$	$2$	$56.342$	\(\Q(\sqrt{2}) \)	None	✓				3528.2.a.bf	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-2q^{11}+2\beta q^{13}+\beta q^{17}+\cdots\)
7056.2.a.cl	$7056$	$2$	7056.a	1.a	$1$	$2$	$2$	$56.342$	\(\Q(\sqrt{2}) \)	None	✓				98.2.a.b	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2\beta q^{5}-2q^{11}-\beta q^{17}-5\beta q^{19}+\cdots\)
7056.2.a.cm	$7056$	$2$	7056.a	1.a	$1$	$2$	$2$	$56.342$	\(\Q(\sqrt{3}) \)	None	✓				63.2.a.b	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-\beta q^{11}-2q^{13}-\beta q^{17}-4q^{19}+\cdots\)
7056.2.a.cn	$7056$	$2$	7056.a	1.a	$1$	$2$	$2$	$56.342$	\(\Q(\sqrt{2}) \)	None	✓				3528.2.a.bg	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+\beta q^{13}-\beta q^{17}-4q^{23}-3q^{25}+\cdots\)
7056.2.a.co	$7056$	$2$	7056.a	1.a	$1$	$2$	$2$	$56.342$	\(\Q(\sqrt{7}) \)	\(\Q(\sqrt{-7}) \)	✓				441.2.a.h	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$2$	$N(\mathrm{U}(1))$	\(q+\beta q^{11}-\beta q^{23}-5q^{25}-2\beta q^{29}+\cdots\)
7056.2.a.cp	$7056$	$2$	7056.a	1.a	$1$	$2$	$2$	$56.342$	\(\Q(\sqrt{2}) \)	None	✓				3528.2.a.bg	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-\beta q^{13}-\beta q^{17}+4q^{23}-3q^{25}+\cdots\)
7056.2.a.cq	$7056$	$2$	7056.a	1.a	$1$	$2$	$2$	$56.342$	\(\Q(\sqrt{2}) \)	None	✓				3528.2.a.bf	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+2q^{11}-2\beta q^{13}+\beta q^{17}+\cdots\)
7056.2.a.cr	$7056$	$2$	7056.a	1.a	$1$	$2$	$2$	$56.342$	\(\Q(\sqrt{2}) \)	None	✓				196.2.a.c	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+4q^{11}-3\beta q^{13}+\beta q^{17}+\cdots\)
7056.2.a.cs	$7056$	$2$	7056.a	1.a	$1$	$2$	$2$	$56.342$	\(\Q(\sqrt{2}) \)	None	✓				882.2.a.m	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+4q^{11}-3\beta q^{13}-5\beta q^{17}+\cdots\)
7056.2.a.ct	$7056$	$2$	7056.a	1.a	$1$	$2$	$2$	$56.342$	\(\Q(\sqrt{2}) \)	None	✓				392.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2\beta q^{5}+6q^{11}+4\beta q^{13}+\beta q^{17}+\cdots\)
7056.2.a.cu	$7056$	$2$	7056.a	1.a	$1$	$2$	$2$	$56.342$	\(\Q(\sqrt{57}) \)	None	✓				168.2.q.c	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-\beta q^{11}+(3-\beta )q^{13}+4q^{17}+\cdots\)
7056.2.a.cv	$7056$	$2$	7056.a	1.a	$1$	$2$	$2$	$56.342$	\(\Q(\sqrt{2}) \)	None	✓				147.2.a.d	$1$	$1$	\(0\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(2+\beta )q^{5}-2q^{11}+(-4+\beta )q^{13}+\cdots\)
7056.2.a.cw	$7056$	$2$	7056.a	1.a	$1$	$2$	$2$	$56.342$	\(\Q(\sqrt{2}) \)	None	✓				1176.2.a.l	$1$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(2+\beta )q^{5}+(-2+2\beta )q^{11}+3\beta q^{13}+\cdots\)
7056.2.a.cx	$7056$	$2$	7056.a	1.a	$1$	$2$	$2$	$56.342$	\(\Q(\sqrt{2}) \)	None	✓				1176.2.a.j	$1$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(2+\beta )q^{5}+(2+2\beta )q^{11}-\beta q^{13}+\cdots\)
7056.2.a.cy	$7056$	$2$	7056.a	1.a	$1$	$4$	$4$	$56.342$	\(\Q(\sqrt{2}, \sqrt{7})\)	None	✓		✓		1764.2.a.m	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{5}+\beta _{3}q^{11}-3\beta _{1}q^{13}+\beta _{2}q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7056))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7056)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(252))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(504))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(588))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(784))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(882))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1008))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1764))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2352))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3528))\)\(^{\oplus 2}\)