Space of modular forms of level 7728, weight 2, and trivial character

• Label: 7728.2.a
• Level: $7728$
• Weight: $2$
• Character orbit: 7728.a
• Rep. character: $\chi_{7728}(1,\cdot)$
• Character field: $\Q$
• Dimension: $132$
• Newform subspaces: $60$
• Sturm bound: $3072$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 7728 = 2^{4} \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7728.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 60 \)
Sturm bound:			\(3072\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7728))\).

	Total	New	Old
Modular forms	1560	132	1428
Cusp forms	1513	132	1381
Eisenstein series	47	0	47

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

\(2\)	\(3\)	\(7\)	\(23\)	Fricke		Total				Cusp				Eisenstein
						All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)		\(89\)	\(7\)	\(82\)		\(87\)	\(7\)	\(80\)		\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)		\(104\)	\(10\)	\(94\)		\(101\)	\(10\)	\(91\)		\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)		\(102\)	\(10\)	\(92\)		\(99\)	\(10\)	\(89\)		\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)		\(95\)	\(7\)	\(88\)		\(92\)	\(7\)	\(85\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)		\(98\)	\(10\)	\(88\)		\(95\)	\(10\)	\(85\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)		\(99\)	\(7\)	\(92\)		\(96\)	\(7\)	\(89\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)		\(101\)	\(7\)	\(94\)		\(98\)	\(7\)	\(91\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)		\(92\)	\(10\)	\(82\)		\(89\)	\(10\)	\(79\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)		\(106\)	\(8\)	\(98\)		\(103\)	\(8\)	\(95\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)		\(91\)	\(8\)	\(83\)		\(88\)	\(8\)	\(80\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)		\(93\)	\(8\)	\(85\)		\(90\)	\(8\)	\(82\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)		\(100\)	\(8\)	\(92\)		\(97\)	\(8\)	\(89\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)		\(97\)	\(8\)	\(89\)		\(94\)	\(8\)	\(86\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)		\(96\)	\(8\)	\(88\)		\(93\)	\(8\)	\(85\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)		\(94\)	\(8\)	\(86\)		\(91\)	\(8\)	\(83\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)		\(103\)	\(8\)	\(95\)		\(100\)	\(8\)	\(92\)		\(3\)	\(0\)	\(3\)
Plus space				\(+\)		\(768\)	\(60\)	\(708\)		\(745\)	\(60\)	\(685\)		\(23\)	\(0\)	\(23\)
Minus space				\(-\)		\(792\)	\(72\)	\(720\)		\(768\)	\(72\)	\(696\)		\(24\)	\(0\)	\(24\)

Trace form

132 * q - 8 * q^5 + 132 * q^9 - 8 * q^13 + 8 * q^17 + 140 * q^25 - 8 * q^29 - 8 * q^37 - 16 * q^39 + 8 * q^41 - 32 * q^43 - 8 * q^45 + 132 * q^49 - 8 * q^53 - 32 * q^55 - 8 * q^61 + 48 * q^65 + 40 * q^73 - 32 * q^75 + 132 * q^81 - 16 * q^85 + 40 * q^89 + 8 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7728))\) 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	23
7728.2.a.a	$7728$	$2$	7728.a	1.a	$1$	$1$	$1$	$61.708$	\(\Q\)	None	✓				966.2.a.i	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}-q^{7}+q^{9}+5q^{13}+3q^{15}+\cdots\)
7728.2.a.b	$7728$	$2$	7728.a	1.a	$1$	$1$	$1$	$61.708$	\(\Q\)	None	✓				966.2.a.j	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
7728.2.a.c	$7728$	$2$	7728.a	1.a	$1$	$1$	$1$	$61.708$	\(\Q\)	None	✓				966.2.a.f	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{7}+q^{9}-6q^{11}+2q^{13}+\cdots\)
7728.2.a.d	$7728$	$2$	7728.a	1.a	$1$	$1$	$1$	$61.708$	\(\Q\)	None	✓				1932.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{7}+q^{9}-3q^{11}+2q^{13}+\cdots\)
7728.2.a.e	$7728$	$2$	7728.a	1.a	$1$	$1$	$1$	$61.708$	\(\Q\)	None	✓				483.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{7}+q^{9}-q^{11}+2q^{13}+4q^{17}+\cdots\)
7728.2.a.f	$7728$	$2$	7728.a	1.a	$1$	$1$	$1$	$61.708$	\(\Q\)	None	✓				3864.2.a.c	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}+q^{9}-q^{11}-6q^{13}-7q^{19}+\cdots\)
7728.2.a.g	$7728$	$2$	7728.a	1.a	$1$	$1$	$1$	$61.708$	\(\Q\)	None	✓				966.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}+q^{9}+2q^{11}-6q^{13}+\cdots\)
7728.2.a.h	$7728$	$2$	7728.a	1.a	$1$	$1$	$1$	$61.708$	\(\Q\)	None	✓				3864.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots\)
7728.2.a.i	$7728$	$2$	7728.a	1.a	$1$	$1$	$1$	$61.708$	\(\Q\)	None	✓				3864.2.a.d	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-q^{7}+q^{9}+6q^{13}-2q^{15}+\cdots\)
7728.2.a.j	$7728$	$2$	7728.a	1.a	$1$	$1$	$1$	$61.708$	\(\Q\)	None	✓				966.2.a.k	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}+q^{7}+q^{9}-4q^{11}-3q^{13}+\cdots\)
7728.2.a.k	$7728$	$2$	7728.a	1.a	$1$	$1$	$1$	$61.708$	\(\Q\)	None	✓				3864.2.a.f	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}-q^{7}+q^{9}-3q^{11}-2q^{13}+\cdots\)
7728.2.a.l	$7728$	$2$	7728.a	1.a	$1$	$1$	$1$	$61.708$	\(\Q\)	None	✓				483.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}+q^{7}+q^{9}+5q^{11}-2q^{13}+\cdots\)
7728.2.a.m	$7728$	$2$	7728.a	1.a	$1$	$1$	$1$	$61.708$	\(\Q\)	None	✓				966.2.a.a	$1$	$1$	\(0\)	\(1\)	\(-4\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{5}-q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
7728.2.a.n	$7728$	$2$	7728.a	1.a	$1$	$1$	$1$	$61.708$	\(\Q\)	None	✓				3864.2.a.a	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}+q^{7}+q^{9}-q^{13}-3q^{15}+\cdots\)
7728.2.a.o	$7728$	$2$	7728.a	1.a	$1$	$1$	$1$	$61.708$	\(\Q\)	None	✓				966.2.a.g	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
7728.2.a.p	$7728$	$2$	7728.a	1.a	$1$	$1$	$1$	$61.708$	\(\Q\)	None	✓				966.2.a.b	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{7}+q^{9}+4q^{13}-2q^{15}+\cdots\)
7728.2.a.q	$7728$	$2$	7728.a	1.a	$1$	$1$	$1$	$61.708$	\(\Q\)	None	✓				3864.2.a.b	$1$	$1$	\(0\)	\(1\)	\(0\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}+q^{9}+2q^{11}-6q^{13}+\cdots\)
7728.2.a.r	$7728$	$2$	7728.a	1.a	$1$	$1$	$1$	$61.708$	\(\Q\)	None	✓				1932.2.a.a	$1$	$1$	\(0\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}+q^{9}+5q^{11}-6q^{13}+\cdots\)
7728.2.a.s	$7728$	$2$	7728.a	1.a	$1$	$1$	$1$	$61.708$	\(\Q\)	None	✓				966.2.a.h	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}-q^{13}+q^{15}+\cdots\)
7728.2.a.t	$7728$	$2$	7728.a	1.a	$1$	$1$	$1$	$61.708$	\(\Q\)	None	✓				966.2.a.c	$1$	$1$	\(0\)	\(1\)	\(2\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}-4q^{13}+\cdots\)
7728.2.a.u	$7728$	$2$	7728.a	1.a	$1$	$1$	$1$	$61.708$	\(\Q\)	None	✓				966.2.a.d	$1$	$0$	\(0\)	\(1\)	\(3\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}-q^{7}+q^{9}-4q^{11}+3q^{13}+\cdots\)
7728.2.a.v	$7728$	$2$	7728.a	1.a	$1$	$2$	$2$	$61.708$	\(\Q(\sqrt{5}) \)	None	✓				483.2.a.c	$1$	$1$	\(0\)	\(-2\)	\(-5\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-2-\beta )q^{5}-q^{7}+q^{9}+(3+\cdots)q^{11}+\cdots\)
7728.2.a.w	$7728$	$2$	7728.a	1.a	$1$	$2$	$2$	$61.708$	\(\Q(\sqrt{5}) \)	None	✓				1932.2.a.f	$1$	$0$	\(0\)	\(-2\)	\(-5\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-2-\beta )q^{5}-q^{7}+q^{9}+q^{11}+\cdots\)
7728.2.a.x	$7728$	$2$	7728.a	1.a	$1$	$2$	$2$	$61.708$	\(\Q(\sqrt{13}) \)	None	✓				483.2.a.f	$1$	$1$	\(0\)	\(-2\)	\(-5\)	\(2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-2-\beta )q^{5}+q^{7}+q^{9}+5q^{11}+\cdots\)
7728.2.a.y	$7728$	$2$	7728.a	1.a	$1$	$2$	$2$	$61.708$	\(\Q(\sqrt{5}) \)	None	✓				3864.2.a.j	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta q^{5}-q^{7}+q^{9}+(3-2\beta )q^{11}+\cdots\)
7728.2.a.z	$7728$	$2$	7728.a	1.a	$1$	$2$	$2$	$61.708$	\(\Q(\sqrt{41}) \)	None	✓				966.2.a.m	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta q^{5}+q^{7}+q^{9}+(2+\beta )q^{13}+\cdots\)
7728.2.a.ba	$7728$	$2$	7728.a	1.a	$1$	$2$	$2$	$61.708$	\(\Q(\sqrt{5}) \)	None	✓				1932.2.a.g	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta q^{5}+q^{7}+q^{9}+3q^{11}+(-1+\cdots)q^{13}+\cdots\)
7728.2.a.bb	$7728$	$2$	7728.a	1.a	$1$	$2$	$2$	$61.708$	\(\Q(\sqrt{5}) \)	None	✓				1932.2.a.h	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+3\beta )q^{5}-q^{7}+q^{9}-3q^{11}+\cdots\)
7728.2.a.bc	$7728$	$2$	7728.a	1.a	$1$	$2$	$2$	$61.708$	\(\Q(\sqrt{41}) \)	None	✓				966.2.a.n	$1$	$0$	\(0\)	\(-2\)	\(1\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}-q^{7}+q^{9}+4q^{11}+(2+\cdots)q^{13}+\cdots\)
7728.2.a.bd	$7728$	$2$	7728.a	1.a	$1$	$2$	$2$	$61.708$	\(\Q(\sqrt{5}) \)	None	✓				966.2.a.p	$1$	$1$	\(0\)	\(-2\)	\(4\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-q^{7}+q^{9}-\beta q^{13}-2q^{15}+\cdots\)
7728.2.a.be	$7728$	$2$	7728.a	1.a	$1$	$2$	$2$	$61.708$	\(\Q(\sqrt{5}) \)	None	✓				483.2.a.e	$1$	$0$	\(0\)	\(-2\)	\(5\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(3-\beta )q^{5}-q^{7}+q^{9}-q^{11}+\cdots\)
7728.2.a.bf	$7728$	$2$	7728.a	1.a	$1$	$2$	$2$	$61.708$	\(\Q(\sqrt{13}) \)	None	✓				1932.2.a.c	$1$	$1$	\(0\)	\(2\)	\(-5\)	\(2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-2-\beta )q^{5}+q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
7728.2.a.bg	$7728$	$2$	7728.a	1.a	$1$	$2$	$2$	$61.708$	\(\Q(\sqrt{5}) \)	None	✓				483.2.a.g	$1$	$1$	\(0\)	\(2\)	\(-3\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta )q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
7728.2.a.bh	$7728$	$2$	7728.a	1.a	$1$	$2$	$2$	$61.708$	\(\Q(\sqrt{33}) \)	None	✓				966.2.a.o	$1$	$1$	\(0\)	\(2\)	\(-3\)	\(2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta )q^{5}+q^{7}+q^{9}-4q^{11}+\cdots\)
7728.2.a.bi	$7728$	$2$	7728.a	1.a	$1$	$2$	$2$	$61.708$	\(\Q(\sqrt{41}) \)	None	✓				3864.2.a.g	$1$	$0$	\(0\)	\(2\)	\(0\)	\(-2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}+q^{9}+\beta q^{11}+2q^{13}+\cdots\)
7728.2.a.bj	$7728$	$2$	7728.a	1.a	$1$	$2$	$2$	$61.708$	\(\Q(\sqrt{33}) \)	None	✓				3864.2.a.i	$1$	$0$	\(0\)	\(2\)	\(1\)	\(-2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}-q^{7}+q^{9}+(-1+\beta )q^{11}+\cdots\)
7728.2.a.bk	$7728$	$2$	7728.a	1.a	$1$	$2$	$2$	$61.708$	\(\Q(\sqrt{13}) \)	None	✓				1932.2.a.e	$1$	$0$	\(0\)	\(2\)	\(1\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}-q^{7}+q^{9}+(-1+2\beta )q^{11}+\cdots\)
7728.2.a.bl	$7728$	$2$	7728.a	1.a	$1$	$2$	$2$	$61.708$	\(\Q(\sqrt{29}) \)	None	✓				3864.2.a.h	$1$	$1$	\(0\)	\(2\)	\(1\)	\(2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+q^{7}+q^{9}-5q^{11}+(1+\cdots)q^{13}+\cdots\)
7728.2.a.bm	$7728$	$2$	7728.a	1.a	$1$	$2$	$2$	$61.708$	\(\Q(\sqrt{17}) \)	None	✓				966.2.a.l	$1$	$0$	\(0\)	\(2\)	\(1\)	\(2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+q^{7}+q^{9}+(-2+2\beta )q^{11}+\cdots\)
7728.2.a.bn	$7728$	$2$	7728.a	1.a	$1$	$2$	$2$	$61.708$	\(\Q(\sqrt{5}) \)	None	✓				483.2.a.d	$1$	$1$	\(0\)	\(2\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+q^{7}+q^{9}+(-1+2\beta )q^{11}+\cdots\)
7728.2.a.bo	$7728$	$2$	7728.a	1.a	$1$	$2$	$2$	$61.708$	\(\Q(\sqrt{5}) \)	None	✓				1932.2.a.d	$1$	$0$	\(0\)	\(2\)	\(1\)	\(2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+q^{7}+q^{9}+(1+2\beta )q^{11}+\cdots\)
7728.2.a.bp	$7728$	$2$	7728.a	1.a	$1$	$3$	$3$	$61.708$	3.3.229.1	None	✓				3864.2.a.p	$1$	$0$	\(0\)	\(-3\)	\(-3\)	\(-3\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta _{1})q^{5}-q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
7728.2.a.bq	$7728$	$2$	7728.a	1.a	$1$	$3$	$3$	$61.708$	3.3.733.1	None	✓				3864.2.a.o	$1$	$0$	\(0\)	\(-3\)	\(-3\)	\(3\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta _{2})q^{5}+q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
7728.2.a.br	$7728$	$2$	7728.a	1.a	$1$	$3$	$3$	$61.708$	3.3.1101.1	None	✓		✓		1932.2.a.j	$1$	$1$	\(0\)	\(-3\)	\(1\)	\(3\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{1}q^{5}+q^{7}+q^{9}-q^{11}+(-1+\cdots)q^{13}+\cdots\)
7728.2.a.bs	$7728$	$2$	7728.a	1.a	$1$	$3$	$3$	$61.708$	3.3.229.1	None	✓				3864.2.a.q	$1$	$1$	\(0\)	\(-3\)	\(1\)	\(3\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{2}q^{5}+q^{7}+q^{9}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
7728.2.a.bt	$7728$	$2$	7728.a	1.a	$1$	$3$	$3$	$61.708$	3.3.837.1	None	✓		✓		483.2.a.h	$1$	$0$	\(0\)	\(-3\)	\(3\)	\(3\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{1})q^{5}+q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
7728.2.a.bu	$7728$	$2$	7728.a	1.a	$1$	$3$	$3$	$61.708$	3.3.621.1	None	✓				3864.2.a.k	$1$	$0$	\(0\)	\(3\)	\(-3\)	\(-3\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta _{1}+\beta _{2})q^{5}-q^{7}+q^{9}+\cdots\)
7728.2.a.bv	$7728$	$2$	7728.a	1.a	$1$	$3$	$3$	$61.708$	3.3.1509.1	None	✓		✓		1932.2.a.i	$1$	$1$	\(0\)	\(3\)	\(-1\)	\(-3\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{1}q^{5}-q^{7}+q^{9}+(-1+2\beta _{1}+\cdots)q^{11}+\cdots\)
7728.2.a.bw	$7728$	$2$	7728.a	1.a	$1$	$3$	$3$	$61.708$	3.3.229.1	None	✓		✓		3864.2.a.l	$1$	$1$	\(0\)	\(3\)	\(-1\)	\(3\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{2}q^{5}+q^{7}+q^{9}+(-1-\beta _{1}+\cdots)q^{11}+\cdots\)
7728.2.a.bx	$7728$	$2$	7728.a	1.a	$1$	$3$	$3$	$61.708$	3.3.837.1	None	✓				3864.2.a.m	$1$	$1$	\(0\)	\(3\)	\(0\)	\(-3\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{5}-q^{7}+q^{9}+(-2+\beta _{1}+\cdots)q^{11}+\cdots\)
7728.2.a.by	$7728$	$2$	7728.a	1.a	$1$	$3$	$3$	$61.708$	3.3.1229.1	None	✓				3864.2.a.n	$1$	$0$	\(0\)	\(3\)	\(1\)	\(-3\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{5}-q^{7}+q^{9}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
7728.2.a.bz	$7728$	$2$	7728.a	1.a	$1$	$4$	$4$	$61.708$	4.4.39605.1	None	✓		✓		3864.2.a.t	$1$	$1$	\(0\)	\(-4\)	\(-2\)	\(4\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta _{1})q^{5}+q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
7728.2.a.ca	$7728$	$2$	7728.a	1.a	$1$	$4$	$4$	$61.708$	4.4.256549.1	None	✓		✓		3864.2.a.u	$1$	$1$	\(0\)	\(-4\)	\(2\)	\(-4\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{1}q^{5}-q^{7}+q^{9}+(1+\beta _{2}+\cdots)q^{11}+\cdots\)
7728.2.a.cb	$7728$	$2$	7728.a	1.a	$1$	$4$	$4$	$61.708$	4.4.2225.1	None	✓		✓		3864.2.a.r	$1$	$1$	\(0\)	\(4\)	\(-3\)	\(-4\)		$+$	$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta _{3})q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
7728.2.a.cc	$7728$	$2$	7728.a	1.a	$1$	$4$	$4$	$61.708$	4.4.75645.1	None	✓				3864.2.a.s	$1$	$0$	\(0\)	\(4\)	\(1\)	\(4\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{5}+q^{7}+q^{9}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
7728.2.a.cd	$7728$	$2$	7728.a	1.a	$1$	$4$	$4$	$61.708$	4.4.24197.1	None	✓		✓		483.2.a.i	$1$	$0$	\(0\)	\(4\)	\(5\)	\(-4\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-\beta _{3})q^{5}-q^{7}+q^{9}+(1+\beta _{2}+\cdots)q^{11}+\cdots\)
7728.2.a.ce	$7728$	$2$	7728.a	1.a	$1$	$4$	$4$	$61.708$	4.4.15317.1	None	✓		✓		483.2.a.j	$1$	$0$	\(0\)	\(4\)	\(5\)	\(4\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta _{3})q^{5}+q^{7}+q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
7728.2.a.cf	$7728$	$2$	7728.a	1.a	$1$	$5$	$5$	$61.708$	5.5.17679757.1	None	✓		✓		3864.2.a.v	$1$	$0$	\(0\)	\(-5\)	\(-6\)	\(-5\)		$+$	$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta _{1})q^{5}-q^{7}+q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
7728.2.a.cg	$7728$	$2$	7728.a	1.a	$1$	$6$	$6$	$61.708$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓		✓		3864.2.a.x	$1$	$0$	\(0\)	\(-6\)	\(0\)	\(6\)		$+$	$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{5}q^{5}+q^{7}+q^{9}+(-1-\beta _{4}+\cdots)q^{11}+\cdots\)
7728.2.a.ch	$7728$	$2$	7728.a	1.a	$1$	$6$	$6$	$61.708$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓		✓		3864.2.a.w	$1$	$0$	\(0\)	\(6\)	\(2\)	\(6\)		$+$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{3}q^{5}+q^{7}+q^{9}-\beta _{4}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7728))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7728)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(276))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(322))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(368))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(483))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(552))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(644))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(966))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1104))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1288))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1932))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2576))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3864))\)\(^{\oplus 2}\)