Space of modular forms of level 9576, weight 2, and trivial character

• Label: 9576.2.a
• Level: $9576$
• Weight: $2$
• Character orbit: 9576.a
• Rep. character: $\chi_{9576}(1,\cdot)$
• Character field: $\Q$
• Dimension: $134$
• Newform subspaces: $67$
• Sturm bound: $3840$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 9576 = 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9576.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 67 \)
Sturm bound:			\(3840\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9576))\).

	Total	New	Old
Modular forms	1952	134	1818
Cusp forms	1889	134	1755
Eisenstein series	63	0	63

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

\(2\)	\(3\)	\(7\)	\(19\)	Fricke		Total				Cusp				Eisenstein
						All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)		\(112\)	\(6\)	\(106\)		\(109\)	\(6\)	\(103\)		\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)		\(128\)	\(7\)	\(121\)		\(124\)	\(7\)	\(117\)		\(4\)	\(0\)	\(4\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)		\(126\)	\(7\)	\(119\)		\(122\)	\(7\)	\(115\)		\(4\)	\(0\)	\(4\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)		\(122\)	\(6\)	\(116\)		\(118\)	\(6\)	\(112\)		\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)		\(122\)	\(12\)	\(110\)		\(118\)	\(12\)	\(106\)		\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)		\(122\)	\(9\)	\(113\)		\(118\)	\(9\)	\(109\)		\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)		\(122\)	\(9\)	\(113\)		\(118\)	\(9\)	\(109\)		\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)		\(122\)	\(12\)	\(110\)		\(118\)	\(12\)	\(106\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)		\(132\)	\(6\)	\(126\)		\(128\)	\(6\)	\(122\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)		\(116\)	\(7\)	\(109\)		\(112\)	\(7\)	\(105\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)		\(118\)	\(7\)	\(111\)		\(114\)	\(7\)	\(107\)		\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)		\(122\)	\(6\)	\(116\)		\(118\)	\(6\)	\(112\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)		\(122\)	\(9\)	\(113\)		\(118\)	\(9\)	\(109\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)		\(122\)	\(11\)	\(111\)		\(118\)	\(11\)	\(107\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)		\(122\)	\(11\)	\(111\)		\(118\)	\(11\)	\(107\)		\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)		\(122\)	\(9\)	\(113\)		\(118\)	\(9\)	\(109\)		\(4\)	\(0\)	\(4\)
Plus space				\(+\)		\(956\)	\(62\)	\(894\)		\(925\)	\(62\)	\(863\)		\(31\)	\(0\)	\(31\)
Minus space				\(-\)		\(996\)	\(72\)	\(924\)		\(964\)	\(72\)	\(892\)		\(32\)	\(0\)	\(32\)

Trace form

134 * q + 4 * q^5 - 12 * q^11 + 4 * q^13 + 4 * q^17 + 134 * q^25 - 4 * q^29 + 16 * q^31 - 12 * q^35 + 4 * q^37 - 4 * q^41 + 20 * q^43 + 134 * q^49 - 20 * q^53 + 16 * q^55 + 16 * q^59 + 4 * q^61 + 8 * q^65 - 24 * q^71 + 12 * q^73 + 8 * q^77 + 40 * q^79 + 32 * q^83 - 24 * q^85 - 20 * q^89 + 8 * q^91 - 4 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9576))\) 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	19
9576.2.a.a	$9576$	$2$	9576.a	1.a	$1$	$1$	$1$	$76.465$	\(\Q\)	None	✓	✓			9576.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}-q^{7}+2q^{11}+2q^{13}+q^{19}+\cdots\)
9576.2.a.b	$9576$	$2$	9576.a	1.a	$1$	$1$	$1$	$76.465$	\(\Q\)	None	✓				3192.2.a.j	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-q^{7}-6q^{11}-2q^{13}+8q^{17}+\cdots\)
9576.2.a.c	$9576$	$2$	9576.a	1.a	$1$	$1$	$1$	$76.465$	\(\Q\)	None	✓				3192.2.a.i	$1$	$2$	\(0\)	\(0\)	\(-2\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-q^{7}-4q^{11}-6q^{13}-6q^{17}+\cdots\)
9576.2.a.d	$9576$	$2$	9576.a	1.a	$1$	$1$	$1$	$76.465$	\(\Q\)	None	✓	✓			9576.2.a.d	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-q^{7}+2q^{11}-4q^{13}+4q^{17}+\cdots\)
9576.2.a.e	$9576$	$2$	9576.a	1.a	$1$	$1$	$1$	$76.465$	\(\Q\)	None	✓				3192.2.a.h	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-q^{7}+4q^{11}-6q^{13}-2q^{17}+\cdots\)
9576.2.a.f	$9576$	$2$	9576.a	1.a	$1$	$1$	$1$	$76.465$	\(\Q\)	None	✓				3192.2.a.p	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-q^{7}+6q^{11}-2q^{13}+q^{19}+\cdots\)
9576.2.a.g	$9576$	$2$	9576.a	1.a	$1$	$1$	$1$	$76.465$	\(\Q\)	None	✓	✓			9576.2.a.g	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{7}-2q^{11}+2q^{13}+2q^{17}+\cdots\)
9576.2.a.h	$9576$	$2$	9576.a	1.a	$1$	$1$	$1$	$76.465$	\(\Q\)	None	✓	✓			9576.2.a.h	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{7}+6q^{11}-4q^{17}-q^{19}+\cdots\)
9576.2.a.i	$9576$	$2$	9576.a	1.a	$1$	$1$	$1$	$76.465$	\(\Q\)	None	✓				3192.2.a.n	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}-6q^{11}+4q^{13}-q^{19}+2q^{23}+\cdots\)
9576.2.a.j	$9576$	$2$	9576.a	1.a	$1$	$1$	$1$	$76.465$	\(\Q\)	None	✓				3192.2.a.e	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}-2q^{13}+q^{19}-4q^{23}-5q^{25}+\cdots\)
9576.2.a.k	$9576$	$2$	9576.a	1.a	$1$	$1$	$1$	$76.465$	\(\Q\)	None	✓	✓			9576.2.a.k	$1$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-4q^{11}+2q^{13}+2q^{17}+q^{19}+\cdots\)
9576.2.a.l	$9576$	$2$	9576.a	1.a	$1$	$1$	$1$	$76.465$	\(\Q\)	None	✓				3192.2.a.g	$1$	$1$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-2q^{11}-4q^{13}+q^{19}+6q^{23}+\cdots\)
9576.2.a.m	$9576$	$2$	9576.a	1.a	$1$	$1$	$1$	$76.465$	\(\Q\)	None	✓	✓			9576.2.a.m	$1$	$1$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-2q^{11}+6q^{13}-q^{19}-6q^{23}+\cdots\)
9576.2.a.n	$9576$	$2$	9576.a	1.a	$1$	$1$	$1$	$76.465$	\(\Q\)	None	✓				3192.2.a.o	$1$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-2q^{13}+8q^{17}-q^{19}+4q^{23}+\cdots\)
9576.2.a.o	$9576$	$2$	9576.a	1.a	$1$	$1$	$1$	$76.465$	\(\Q\)	None	✓	✓			9576.2.a.m	$1$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}+2q^{11}+6q^{13}-q^{19}+6q^{23}+\cdots\)
9576.2.a.p	$9576$	$2$	9576.a	1.a	$1$	$1$	$1$	$76.465$	\(\Q\)	None	✓	✓			9576.2.a.k	$1$	$1$	\(0\)	\(0\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}+4q^{11}+2q^{13}-2q^{17}+q^{19}+\cdots\)
9576.2.a.q	$9576$	$2$	9576.a	1.a	$1$	$1$	$1$	$76.465$	\(\Q\)	None	✓				3192.2.a.f	$1$	$1$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}+4q^{11}+2q^{13}+q^{19}-5q^{25}+\cdots\)
9576.2.a.r	$9576$	$2$	9576.a	1.a	$1$	$1$	$1$	$76.465$	\(\Q\)	None	✓	✓			9576.2.a.d	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-q^{7}-2q^{11}-4q^{13}-4q^{17}+\cdots\)
9576.2.a.s	$9576$	$2$	9576.a	1.a	$1$	$1$	$1$	$76.465$	\(\Q\)	None	✓				3192.2.a.c	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-q^{7}-2q^{13}-2q^{17}+q^{19}+\cdots\)
9576.2.a.t	$9576$	$2$	9576.a	1.a	$1$	$1$	$1$	$76.465$	\(\Q\)	None	✓				3192.2.a.b	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-q^{7}+4q^{11}+2q^{13}+6q^{17}+\cdots\)
9576.2.a.u	$9576$	$2$	9576.a	1.a	$1$	$1$	$1$	$76.465$	\(\Q\)	None	✓	✓			9576.2.a.h	$1$	$0$	\(0\)	\(0\)	\(2\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+q^{7}-6q^{11}+4q^{17}-q^{19}+\cdots\)
9576.2.a.v	$9576$	$2$	9576.a	1.a	$1$	$1$	$1$	$76.465$	\(\Q\)	None	✓				3192.2.a.d	$1$	$1$	\(0\)	\(0\)	\(2\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+q^{7}-2q^{13}-6q^{17}-q^{19}+\cdots\)
9576.2.a.w	$9576$	$2$	9576.a	1.a	$1$	$1$	$1$	$76.465$	\(\Q\)	None	✓	✓			9576.2.a.g	$1$	$0$	\(0\)	\(0\)	\(2\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+q^{7}+2q^{11}+2q^{13}-2q^{17}+\cdots\)
9576.2.a.x	$9576$	$2$	9576.a	1.a	$1$	$1$	$1$	$76.465$	\(\Q\)	None	✓				3192.2.a.m	$1$	$0$	\(0\)	\(0\)	\(2\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+q^{7}+4q^{11}+2q^{13}-2q^{17}+\cdots\)
9576.2.a.y	$9576$	$2$	9576.a	1.a	$1$	$1$	$1$	$76.465$	\(\Q\)	None	✓				3192.2.a.k	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}-q^{7}-4q^{11}+2q^{13}+4q^{17}+\cdots\)
9576.2.a.z	$9576$	$2$	9576.a	1.a	$1$	$1$	$1$	$76.465$	\(\Q\)	None	✓	✓			9576.2.a.a	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}-q^{7}-2q^{11}+2q^{13}+q^{19}+\cdots\)
9576.2.a.ba	$9576$	$2$	9576.a	1.a	$1$	$1$	$1$	$76.465$	\(\Q\)	None	✓				3192.2.a.a	$1$	$1$	\(0\)	\(0\)	\(4\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}-q^{7}-2q^{13}-4q^{17}+q^{19}+\cdots\)
9576.2.a.bb	$9576$	$2$	9576.a	1.a	$1$	$1$	$1$	$76.465$	\(\Q\)	None	✓				3192.2.a.l	$1$	$0$	\(0\)	\(0\)	\(4\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}+q^{7}-2q^{11}-4q^{13}-4q^{17}+\cdots\)
9576.2.a.bc	$9576$	$2$	9576.a	1.a	$1$	$2$	$2$	$76.465$	\(\Q(\sqrt{5}) \)	None	✓				1064.2.a.e	$1$	$0$	\(0\)	\(0\)	\(-5\)	\(2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-2-\beta )q^{5}+q^{7}+(1+3\beta )q^{11}+\cdots\)
9576.2.a.bd	$9576$	$2$	9576.a	1.a	$1$	$2$	$2$	$76.465$	\(\Q(\sqrt{17}) \)	None	✓	✓			9576.2.a.bd	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-2q^{5}-q^{7}+2q^{11}+(1+\beta )q^{13}+\cdots\)
9576.2.a.be	$9576$	$2$	9576.a	1.a	$1$	$2$	$2$	$76.465$	\(\Q(\sqrt{5}) \)	None	✓	✓			9576.2.a.be	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{5}-q^{7}+2\beta q^{11}+2\beta q^{13}+\cdots\)
9576.2.a.bf	$9576$	$2$	9576.a	1.a	$1$	$2$	$2$	$76.465$	\(\Q(\sqrt{3}) \)	None	✓	✓			9576.2.a.bf	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{5}-q^{7}+2\beta q^{11}+4q^{13}+\cdots\)
9576.2.a.bg	$9576$	$2$	9576.a	1.a	$1$	$2$	$2$	$76.465$	\(\Q(\sqrt{5}) \)	None	✓	✓			9576.2.a.bg	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{5}-q^{7}+(3-\beta )q^{11}+(-3+\cdots)q^{13}+\cdots\)
9576.2.a.bh	$9576$	$2$	9576.a	1.a	$1$	$2$	$2$	$76.465$	\(\Q(\sqrt{7}) \)	None	✓	✓			9576.2.a.bh	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(2\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{5}+q^{7}-2q^{11}-4q^{13}+\cdots\)
9576.2.a.bi	$9576$	$2$	9576.a	1.a	$1$	$2$	$2$	$76.465$	\(\Q(\sqrt{5}) \)	None	✓	✓			9576.2.a.bi	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(2\)		$-$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{5}+q^{7}-2q^{11}+2\beta q^{13}+\cdots\)
9576.2.a.bj	$9576$	$2$	9576.a	1.a	$1$	$2$	$2$	$76.465$	\(\Q(\sqrt{3}) \)	None	✓				3192.2.a.q	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{5}+q^{7}+(-2+2\beta )q^{13}+\cdots\)
9576.2.a.bk	$9576$	$2$	9576.a	1.a	$1$	$2$	$2$	$76.465$	\(\Q(\sqrt{3}) \)	None	✓				3192.2.a.t	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-q^{7}-2q^{13}-\beta q^{17}-q^{19}+\cdots\)
9576.2.a.bl	$9576$	$2$	9576.a	1.a	$1$	$2$	$2$	$76.465$	\(\Q(\sqrt{2}) \)	None	✓	✓			9576.2.a.bl	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+q^{7}-2q^{11}+(2-\beta )q^{13}+\cdots\)
9576.2.a.bm	$9576$	$2$	9576.a	1.a	$1$	$2$	$2$	$76.465$	\(\Q(\sqrt{5}) \)	None	✓				1064.2.a.a	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-2\beta )q^{5}+q^{7}+(-1+3\beta )q^{11}+\cdots\)
9576.2.a.bn	$9576$	$2$	9576.a	1.a	$1$	$2$	$2$	$76.465$	\(\Q(\sqrt{5}) \)	None	✓				1064.2.a.c	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-2\beta )q^{5}+q^{7}+(-1+3\beta )q^{11}+\cdots\)
9576.2.a.bo	$9576$	$2$	9576.a	1.a	$1$	$2$	$2$	$76.465$	\(\Q(\sqrt{2}) \)	None	✓	✓			9576.2.a.bl	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+q^{7}+2q^{11}+(2+\beta )q^{13}+\cdots\)
9576.2.a.bp	$9576$	$2$	9576.a	1.a	$1$	$2$	$2$	$76.465$	\(\Q(\sqrt{5}) \)	None	✓	✓			9576.2.a.bg	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}-q^{7}+(-3+\beta )q^{11}+(-3+\cdots)q^{13}+\cdots\)
9576.2.a.bq	$9576$	$2$	9576.a	1.a	$1$	$2$	$2$	$76.465$	\(\Q(\sqrt{5}) \)	None	✓	✓			9576.2.a.be	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}-q^{7}-2\beta q^{11}+2\beta q^{13}+\cdots\)
9576.2.a.br	$9576$	$2$	9576.a	1.a	$1$	$2$	$2$	$76.465$	\(\Q(\sqrt{3}) \)	None	✓	✓			9576.2.a.bf	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}-q^{7}+2\beta q^{11}+4q^{13}+\cdots\)
9576.2.a.bs	$9576$	$2$	9576.a	1.a	$1$	$2$	$2$	$76.465$	\(\Q(\sqrt{13}) \)	None	✓				1064.2.a.b	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-2\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}+\beta q^{11}+(1-2\beta )q^{13}+\cdots\)
9576.2.a.bt	$9576$	$2$	9576.a	1.a	$1$	$2$	$2$	$76.465$	\(\Q(\sqrt{5}) \)	None	✓				1064.2.a.d	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}+(-1+3\beta )q^{11}+(3-4\beta )q^{13}+\cdots\)
9576.2.a.bu	$9576$	$2$	9576.a	1.a	$1$	$2$	$2$	$76.465$	\(\Q(\sqrt{7}) \)	None	✓	✓			9576.2.a.bh	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}+q^{7}+2q^{11}-4q^{13}+\cdots\)
9576.2.a.bv	$9576$	$2$	9576.a	1.a	$1$	$2$	$2$	$76.465$	\(\Q(\sqrt{5}) \)	None	✓	✓			9576.2.a.bi	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}+q^{7}+2q^{11}+2\beta q^{13}+\cdots\)
9576.2.a.bw	$9576$	$2$	9576.a	1.a	$1$	$2$	$2$	$76.465$	\(\Q(\sqrt{3}) \)	None	✓				3192.2.a.s	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}+q^{7}+4q^{11}+(2+2\beta )q^{13}+\cdots\)
9576.2.a.bx	$9576$	$2$	9576.a	1.a	$1$	$2$	$2$	$76.465$	\(\Q(\sqrt{17}) \)	None	✓	✓			9576.2.a.bd	$1$	$1$	\(0\)	\(0\)	\(4\)	\(-2\)		$+$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+2q^{5}-q^{7}-2q^{11}+(1+\beta )q^{13}+\cdots\)
9576.2.a.by	$9576$	$2$	9576.a	1.a	$1$	$2$	$2$	$76.465$	\(\Q(\sqrt{2}) \)	None	✓				3192.2.a.r	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(2+\beta )q^{5}-q^{7}+2\beta q^{11}+4\beta q^{13}+\cdots\)
9576.2.a.bz	$9576$	$2$	9576.a	1.a	$1$	$3$	$3$	$76.465$	3.3.316.1	None	✓	✓	✓		9576.2.a.bz	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(-3\)		$+$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{2})q^{5}-q^{7}+2\beta _{2}q^{11}+(1+\cdots)q^{17}+\cdots\)
9576.2.a.ca	$9576$	$2$	9576.a	1.a	$1$	$3$	$3$	$76.465$	3.3.1101.1	None	✓				1064.2.a.f	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(3\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{5}+q^{7}+(-3+\beta _{1}-\beta _{2})q^{11}+\cdots\)
9576.2.a.cb	$9576$	$2$	9576.a	1.a	$1$	$3$	$3$	$76.465$	3.3.568.1	None	✓				3192.2.a.u	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-3\)		$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}-q^{7}+(1+\beta _{1}+\beta _{2})q^{11}+\cdots\)
9576.2.a.cc	$9576$	$2$	9576.a	1.a	$1$	$3$	$3$	$76.465$	3.3.316.1	None	✓				3192.2.a.v	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-3\)		$+$	$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{7}+(1-\beta _{1})q^{11}+(-2-\beta _{2})q^{13}+\cdots\)
9576.2.a.cd	$9576$	$2$	9576.a	1.a	$1$	$3$	$3$	$76.465$	3.3.1772.1	None	✓	✓	✓		9576.2.a.cd	$1$	$1$	\(0\)	\(0\)	\(0\)	\(3\)		$-$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{5}+q^{7}-2q^{11}+(-3+\beta _{1}+\cdots)q^{17}+\cdots\)
9576.2.a.ce	$9576$	$2$	9576.a	1.a	$1$	$3$	$3$	$76.465$	3.3.1772.1	None	✓	✓	✓		9576.2.a.cd	$1$	$0$	\(0\)	\(0\)	\(0\)	\(3\)		$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{5}+q^{7}+2q^{11}+(3-\beta _{1})q^{17}+\cdots\)
9576.2.a.cf	$9576$	$2$	9576.a	1.a	$1$	$3$	$3$	$76.465$	3.3.316.1	None	✓	✓	✓		9576.2.a.bz	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-3\)		$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{2})q^{5}-q^{7}-2\beta _{2}q^{11}+(-1+\cdots)q^{17}+\cdots\)
9576.2.a.cg	$9576$	$2$	9576.a	1.a	$1$	$4$	$4$	$76.465$	4.4.7232.1	None	✓		✓		3192.2.a.y	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(-4\)		$+$	$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{5}-q^{7}+\beta _{2}q^{11}+(1+\cdots)q^{13}+\cdots\)
9576.2.a.ch	$9576$	$2$	9576.a	1.a	$1$	$4$	$4$	$76.465$	4.4.2225.1	None	✓		✓		3192.2.a.z	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(4\)		$+$	$-$	$-$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{2})q^{5}+q^{7}+(-1+\beta _{3})q^{11}+\cdots\)
9576.2.a.ci	$9576$	$2$	9576.a	1.a	$1$	$4$	$4$	$76.465$	4.4.25857.1	None	✓				1064.2.a.h	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(4\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{5}+q^{7}+(-\beta _{1}+\beta _{2}+\beta _{3})q^{11}+\cdots\)
9576.2.a.cj	$9576$	$2$	9576.a	1.a	$1$	$4$	$4$	$76.465$	4.4.9248.1	None	✓		✓		3192.2.a.x	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}-q^{7}+(-\beta _{1}+\beta _{2})q^{11}+(1+\cdots)q^{17}+\cdots\)
9576.2.a.ck	$9576$	$2$	9576.a	1.a	$1$	$4$	$4$	$76.465$	4.4.18097.1	None	✓		✓		1064.2.a.g	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-4\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2}-\beta _{3})q^{5}-q^{7}+(-1-\beta _{1}+\cdots)q^{11}+\cdots\)
9576.2.a.cl	$9576$	$2$	9576.a	1.a	$1$	$4$	$4$	$76.465$	4.4.13068.1	None	✓		✓		3192.2.a.w	$1$	$0$	\(0\)	\(0\)	\(4\)	\(4\)		$-$	$-$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{2})q^{5}+q^{7}+(-\beta _{1}-\beta _{3})q^{11}+\cdots\)
9576.2.a.cm	$9576$	$2$	9576.a	1.a	$1$	$5$	$5$	$76.465$	5.5.10463409.1	None	✓		✓		1064.2.a.i	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(-5\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{4})q^{5}-q^{7}+(-1+\beta _{1}-\beta _{3}+\cdots)q^{11}+\cdots\)
9576.2.a.cn	$9576$	$2$	9576.a	1.a	$1$	$5$	$5$	$76.465$	5.5.401584.1	None	✓		✓		3192.2.a.bb	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(5\)		$-$	$-$	$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}+q^{7}+(-1+\beta _{2}-\beta _{3})q^{11}+\cdots\)
9576.2.a.co	$9576$	$2$	9576.a	1.a	$1$	$5$	$5$	$76.465$	5.5.135076.1	None	✓		✓		3192.2.a.ba	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(5\)		$+$	$-$	$-$	$-$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{5}+q^{7}+\beta _{4}q^{11}+(2-\beta _{3})q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9576))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9576)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(171))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(228))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(252))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(266))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(342))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(399))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(456))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(504))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(532))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(684))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(798))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1064))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1197))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1368))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1596))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2394))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4788))\)\(^{\oplus 2}\)