Space of modular forms of level 9152, weight 2, and trivial character

• Label: 9152.2.a
• Level: $9152$
• Weight: $2$
• Character orbit: 9152.a
• Rep. character: $\chi_{9152}(1,\cdot)$
• Character field: $\Q$
• Dimension: $240$
• Newform subspaces: $80$
• Sturm bound: $2688$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 9152 = 2^{6} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9152.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 80 \)
Sturm bound:			\(2688\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(3\), \(5\), \(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9152))\).

	Total	New	Old
Modular forms	1368	240	1128
Cusp forms	1321	240	1081
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.

\(2\)	\(11\)	\(13\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(159\)	\(29\)	\(130\)		\(154\)	\(29\)	\(125\)		\(5\)	\(0\)	\(5\)
\(+\)	\(+\)	\(-\)	\(-\)		\(183\)	\(34\)	\(149\)		\(177\)	\(34\)	\(143\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)		\(179\)	\(31\)	\(148\)		\(173\)	\(31\)	\(142\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)		\(163\)	\(26\)	\(137\)		\(157\)	\(26\)	\(131\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)		\(173\)	\(31\)	\(142\)		\(167\)	\(31\)	\(136\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)		\(169\)	\(26\)	\(143\)		\(163\)	\(26\)	\(137\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)		\(173\)	\(29\)	\(144\)		\(167\)	\(29\)	\(138\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)		\(169\)	\(34\)	\(135\)		\(163\)	\(34\)	\(129\)		\(6\)	\(0\)	\(6\)
Plus space			\(+\)		\(664\)	\(110\)	\(554\)		\(641\)	\(110\)	\(531\)		\(23\)	\(0\)	\(23\)
Minus space			\(-\)		\(704\)	\(130\)	\(574\)		\(680\)	\(130\)	\(550\)		\(24\)	\(0\)	\(24\)

Trace form

\( 240 q + 240 q^{9} + 240 q^{25} - 48 q^{45} + 240 q^{49} - 48 q^{53} + 64 q^{61} + 16 q^{69} + 304 q^{81} + 64 q^{85} + 64 q^{89} - 48 q^{93}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9152))\) 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	11	13
9152.2.a.a	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				1144.2.a.d	$1$	$2$	\(0\)	\(-3\)	\(-3\)	\(-3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-3q^{5}-3q^{7}+6q^{9}-q^{11}+\cdots\)
9152.2.a.b	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				4576.2.a.a	$1$	$1$	\(0\)	\(-3\)	\(-1\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-q^{5}-4q^{7}+6q^{9}+q^{11}+\cdots\)
9152.2.a.c	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				286.2.a.a	$1$	$0$	\(0\)	\(-2\)	\(-3\)	\(1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-3q^{5}+q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
9152.2.a.d	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				1144.2.a.c	$1$	$1$	\(0\)	\(-2\)	\(-3\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-3q^{5}+q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
9152.2.a.e	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				286.2.a.f	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}-3q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
9152.2.a.f	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				4576.2.a.b	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+5q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
9152.2.a.g	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				286.2.a.e	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}+q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
9152.2.a.h	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				4576.2.a.c	$1$	$2$	\(0\)	\(-1\)	\(-3\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}-q^{7}-2q^{9}-q^{11}+q^{13}+\cdots\)
9152.2.a.i	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				572.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+2q^{7}-2q^{9}-q^{11}+\cdots\)
9152.2.a.j	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				286.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-3q^{7}-2q^{9}+q^{11}-q^{13}+\cdots\)
9152.2.a.k	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				1144.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{7}-2q^{9}-q^{11}-q^{13}+\cdots\)
9152.2.a.l	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				1144.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{7}-2q^{9}-q^{11}+q^{13}+\cdots\)
9152.2.a.m	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				286.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}-2q^{9}-q^{11}+q^{13}+\cdots\)
9152.2.a.n	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				143.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+2q^{7}-2q^{9}-q^{11}+q^{13}+\cdots\)
9152.2.a.o	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				286.2.a.c	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}+5q^{7}-2q^{9}-q^{11}+\cdots\)
9152.2.a.p	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				4576.2.a.d	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-4q^{7}-3q^{9}-q^{11}+q^{13}+\cdots\)
9152.2.a.q	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				4576.2.a.d	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+4q^{7}-3q^{9}+q^{11}+q^{13}+\cdots\)
9152.2.a.r	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				572.2.a.a	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}-2q^{7}-2q^{9}+q^{11}+\cdots\)
9152.2.a.s	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				4576.2.a.c	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}+q^{7}-2q^{9}+q^{11}+q^{13}+\cdots\)
9152.2.a.t	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				286.2.a.d	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+3q^{7}-2q^{9}-q^{11}-q^{13}+\cdots\)
9152.2.a.u	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				143.2.a.a	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{7}-2q^{9}+q^{11}+q^{13}+\cdots\)
9152.2.a.v	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				286.2.a.b	$1$	$1$	\(0\)	\(1\)	\(1\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}-2q^{9}+q^{11}+q^{13}+\cdots\)
9152.2.a.w	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				1144.2.a.b	$1$	$1$	\(0\)	\(1\)	\(1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+2q^{7}-2q^{9}+q^{11}-q^{13}+\cdots\)
9152.2.a.x	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				1144.2.a.a	$1$	$0$	\(0\)	\(1\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+2q^{7}-2q^{9}+q^{11}+q^{13}+\cdots\)
9152.2.a.y	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				286.2.a.c	$1$	$0$	\(0\)	\(1\)	\(3\)	\(-5\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}-5q^{7}-2q^{9}+q^{11}+\cdots\)
9152.2.a.z	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				1144.2.a.c	$1$	$1$	\(0\)	\(2\)	\(-3\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-3q^{5}-q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
9152.2.a.ba	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				286.2.a.a	$1$	$0$	\(0\)	\(2\)	\(-3\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-3q^{5}-q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
9152.2.a.bb	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				4576.2.a.b	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(-5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}-5q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
9152.2.a.bc	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				286.2.a.f	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+3q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
9152.2.a.bd	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				286.2.a.e	$1$	$1$	\(0\)	\(2\)	\(1\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}-q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
9152.2.a.be	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				1144.2.a.d	$1$	$0$	\(0\)	\(3\)	\(-3\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-3q^{5}+3q^{7}+6q^{9}+q^{11}+\cdots\)
9152.2.a.bf	$9152$	$2$	9152.a	1.a	$1$	$1$	$1$	$73.079$	\(\Q\)	None	✓				4576.2.a.a	$1$	$0$	\(0\)	\(3\)	\(-1\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-q^{5}+4q^{7}+6q^{9}-q^{11}+\cdots\)
9152.2.a.bg	$9152$	$2$	9152.a	1.a	$1$	$2$	$2$	$73.079$	\(\Q(\sqrt{13}) \)	None	✓				572.2.a.b	$1$	$0$	\(0\)	\(-3\)	\(0\)	\(3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+(2-\beta )q^{7}+(1+3\beta )q^{9}+\cdots\)
9152.2.a.bh	$9152$	$2$	9152.a	1.a	$1$	$2$	$2$	$73.079$	\(\Q(\sqrt{5}) \)	None	✓				1144.2.a.g	$1$	$1$	\(0\)	\(-3\)	\(2\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+(2-2\beta )q^{5}+(-2+3\beta )q^{7}+\cdots\)
9152.2.a.bi	$9152$	$2$	9152.a	1.a	$1$	$2$	$2$	$73.079$	\(\Q(\sqrt{5}) \)	None	✓				1144.2.a.f	$1$	$0$	\(0\)	\(-3\)	\(2\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+2\beta q^{5}-\beta q^{7}+(-1+\cdots)q^{9}+\cdots\)
9152.2.a.bj	$9152$	$2$	9152.a	1.a	$1$	$2$	$2$	$73.079$	\(\Q(\sqrt{5}) \)	None	✓				1144.2.a.e	$1$	$1$	\(0\)	\(-3\)	\(2\)	\(5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+(2-2\beta )q^{5}+(2+\beta )q^{7}+\cdots\)
9152.2.a.bk	$9152$	$2$	9152.a	1.a	$1$	$2$	$2$	$73.079$	\(\Q(\sqrt{41}) \)	None	✓				4576.2.a.i	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+(-1-\beta )q^{7}-2q^{9}-q^{11}+\cdots\)
9152.2.a.bl	$9152$	$2$	9152.a	1.a	$1$	$2$	$2$	$73.079$	\(\Q(\sqrt{21}) \)	None	✓				572.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(-4\)	\(5\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-2q^{5}+(3-\beta )q^{7}+(2+\beta )q^{9}+\cdots\)
9152.2.a.bm	$9152$	$2$	9152.a	1.a	$1$	$2$	$2$	$73.079$	\(\Q(\sqrt{21}) \)	None	✓				572.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(4\)	\(3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+2q^{5}+(1+\beta )q^{7}+(2+\beta )q^{9}+\cdots\)
9152.2.a.bn	$9152$	$2$	9152.a	1.a	$1$	$2$	$2$	$73.079$	\(\Q(\sqrt{21}) \)	None	✓				572.2.a.d	$1$	$1$	\(0\)	\(1\)	\(-4\)	\(-5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-2q^{5}+(-3+\beta )q^{7}+(2+\beta )q^{9}+\cdots\)
9152.2.a.bo	$9152$	$2$	9152.a	1.a	$1$	$2$	$2$	$73.079$	\(\Q(\sqrt{21}) \)	None	✓				572.2.a.c	$1$	$1$	\(0\)	\(1\)	\(4\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+2q^{5}+(-1-\beta )q^{7}+(2+\beta )q^{9}+\cdots\)
9152.2.a.bp	$9152$	$2$	9152.a	1.a	$1$	$2$	$2$	$73.079$	\(\Q(\sqrt{41}) \)	None	✓				4576.2.a.i	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+(1+\beta )q^{7}-2q^{9}+q^{11}+\cdots\)
9152.2.a.bq	$9152$	$2$	9152.a	1.a	$1$	$2$	$2$	$73.079$	\(\Q(\sqrt{13}) \)	None	✓				572.2.a.b	$1$	$0$	\(0\)	\(3\)	\(0\)	\(-3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(-2+\beta )q^{7}+(1+3\beta )q^{9}+\cdots\)
9152.2.a.br	$9152$	$2$	9152.a	1.a	$1$	$2$	$2$	$73.079$	\(\Q(\sqrt{5}) \)	None	✓				1144.2.a.e	$1$	$1$	\(0\)	\(3\)	\(2\)	\(-5\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(2-2\beta )q^{5}+(-2-\beta )q^{7}+\cdots\)
9152.2.a.bs	$9152$	$2$	9152.a	1.a	$1$	$2$	$2$	$73.079$	\(\Q(\sqrt{5}) \)	None	✓				1144.2.a.g	$1$	$1$	\(0\)	\(3\)	\(2\)	\(1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(2-2\beta )q^{5}+(2-3\beta )q^{7}+\cdots\)
9152.2.a.bt	$9152$	$2$	9152.a	1.a	$1$	$2$	$2$	$73.079$	\(\Q(\sqrt{5}) \)	None	✓				1144.2.a.f	$1$	$0$	\(0\)	\(3\)	\(2\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+2\beta q^{5}+\beta q^{7}+(-1+3\beta )q^{9}+\cdots\)
9152.2.a.bu	$9152$	$2$	9152.a	1.a	$1$	$3$	$3$	$73.079$	3.3.229.1	None	✓				1144.2.a.j	$1$	$0$	\(0\)	\(-3\)	\(-1\)	\(6\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}+(-\beta _{1}+\beta _{2})q^{5}+(2+\cdots)q^{7}+\cdots\)
9152.2.a.bv	$9152$	$2$	9152.a	1.a	$1$	$3$	$3$	$73.079$	3.3.229.1	None	✓				572.2.a.e	$1$	$0$	\(0\)	\(-2\)	\(1\)	\(7\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(2+\cdots)q^{7}+\cdots\)
9152.2.a.bw	$9152$	$2$	9152.a	1.a	$1$	$3$	$3$	$73.079$	3.3.961.1	None	✓				286.2.a.g	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots\)
9152.2.a.bx	$9152$	$2$	9152.a	1.a	$1$	$3$	$3$	$73.079$	3.3.229.1	None	✓				1144.2.a.i	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
9152.2.a.by	$9152$	$2$	9152.a	1.a	$1$	$3$	$3$	$73.079$	3.3.229.1	None	✓				1144.2.a.i	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+(1-\beta _{2})q^{7}+\cdots\)
9152.2.a.bz	$9152$	$2$	9152.a	1.a	$1$	$3$	$3$	$73.079$	3.3.229.1	None	✓				1144.2.a.h	$1$	$0$	\(0\)	\(0\)	\(5\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(2-\beta _{1}+\beta _{2})q^{5}+(-1-\beta _{2})q^{7}+\cdots\)
9152.2.a.ca	$9152$	$2$	9152.a	1.a	$1$	$3$	$3$	$73.079$	3.3.229.1	None	✓				1144.2.a.h	$1$	$0$	\(0\)	\(0\)	\(5\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(2-\beta _{1}+\beta _{2})q^{5}+(1+\beta _{2})q^{7}+\cdots\)
9152.2.a.cb	$9152$	$2$	9152.a	1.a	$1$	$3$	$3$	$73.079$	3.3.961.1	None	✓				286.2.a.g	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots\)
9152.2.a.cc	$9152$	$2$	9152.a	1.a	$1$	$3$	$3$	$73.079$	3.3.229.1	None	✓				572.2.a.e	$1$	$0$	\(0\)	\(2\)	\(1\)	\(-7\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(-2+\cdots)q^{7}+\cdots\)
9152.2.a.cd	$9152$	$2$	9152.a	1.a	$1$	$3$	$3$	$73.079$	3.3.229.1	None	✓				1144.2.a.j	$1$	$0$	\(0\)	\(3\)	\(-1\)	\(-6\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+(-\beta _{1}+\beta _{2})q^{5}+(-2+\cdots)q^{7}+\cdots\)
9152.2.a.ce	$9152$	$2$	9152.a	1.a	$1$	$4$	$4$	$73.079$	4.4.2624.1	None	✓				4576.2.a.l	$1$	$1$	\(0\)	\(-2\)	\(4\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots\)
9152.2.a.cf	$9152$	$2$	9152.a	1.a	$1$	$4$	$4$	$73.079$	\(\Q(\sqrt{2}, \sqrt{5})\)	None	✓				4576.2.a.k	$1$	$0$	\(0\)	\(-2\)	\(8\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1}+\beta _{2})q^{3}+(2+\beta _{1}-\beta _{3})q^{5}+\cdots\)
9152.2.a.cg	$9152$	$2$	9152.a	1.a	$1$	$4$	$4$	$73.079$	4.4.1957.1	None	✓				143.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{5}+(-2+\beta _{3})q^{7}+\cdots\)
9152.2.a.ch	$9152$	$2$	9152.a	1.a	$1$	$4$	$4$	$73.079$	4.4.1957.1	None	✓				143.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(6\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{5}+(2-\beta _{3})q^{7}+\cdots\)
9152.2.a.ci	$9152$	$2$	9152.a	1.a	$1$	$4$	$4$	$73.079$	4.4.2624.1	None	✓				4576.2.a.l	$1$	$0$	\(0\)	\(2\)	\(4\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
9152.2.a.cj	$9152$	$2$	9152.a	1.a	$1$	$4$	$4$	$73.079$	\(\Q(\sqrt{2}, \sqrt{5})\)	None	✓				4576.2.a.k	$1$	$1$	\(0\)	\(2\)	\(8\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1}-\beta _{2})q^{3}+(2-\beta _{1}+\beta _{3})q^{5}+\cdots\)
9152.2.a.ck	$9152$	$2$	9152.a	1.a	$1$	$5$	$5$	$73.079$	5.5.7698829.1	None	✓				1144.2.a.k	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1+\beta _{3})q^{5}+(-1-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
9152.2.a.cl	$9152$	$2$	9152.a	1.a	$1$	$5$	$5$	$73.079$	5.5.7698829.1	None	✓				1144.2.a.k	$1$	$0$	\(0\)	\(0\)	\(4\)	\(6\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(1+\beta _{3})q^{5}+(1+\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
9152.2.a.cm	$9152$	$2$	9152.a	1.a	$1$	$6$	$6$	$73.079$	6.6.194616205.1	None	✓				143.2.a.c	$1$	$0$	\(0\)	\(-3\)	\(-1\)	\(4\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}-\beta _{4}q^{5}+(1+\beta _{5})q^{7}+\cdots\)
9152.2.a.cn	$9152$	$2$	9152.a	1.a	$1$	$6$	$6$	$73.079$	6.6.16371248.1	None	✓				4576.2.a.o	$1$	$1$	\(0\)	\(-3\)	\(2\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{4}q^{3}-\beta _{2}q^{5}+\beta _{5}q^{7}+(1-2\beta _{1}+\cdots)q^{9}+\cdots\)
9152.2.a.co	$9152$	$2$	9152.a	1.a	$1$	$6$	$6$	$73.079$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓				1144.2.a.l	$1$	$1$	\(0\)	\(-1\)	\(-5\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1+\beta _{2})q^{5}-\beta _{5}q^{7}+(2+\cdots)q^{9}+\cdots\)
9152.2.a.cp	$9152$	$2$	9152.a	1.a	$1$	$6$	$6$	$73.079$	6.6.106740016.1	None	✓				4576.2.a.p	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(-5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{5}q^{5}+(-1-\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
9152.2.a.cq	$9152$	$2$	9152.a	1.a	$1$	$6$	$6$	$73.079$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓				1144.2.a.l	$1$	$1$	\(0\)	\(1\)	\(-5\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1+\beta _{2})q^{5}+\beta _{5}q^{7}+(2+\cdots)q^{9}+\cdots\)
9152.2.a.cr	$9152$	$2$	9152.a	1.a	$1$	$6$	$6$	$73.079$	6.6.106740016.1	None	✓				4576.2.a.p	$1$	$0$	\(0\)	\(1\)	\(2\)	\(5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{5}q^{5}+(1+\beta _{1}-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
9152.2.a.cs	$9152$	$2$	9152.a	1.a	$1$	$6$	$6$	$73.079$	6.6.194616205.1	None	✓				143.2.a.c	$1$	$0$	\(0\)	\(3\)	\(-1\)	\(-4\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}-\beta _{4}q^{5}+(-1-\beta _{5})q^{7}+\cdots\)
9152.2.a.ct	$9152$	$2$	9152.a	1.a	$1$	$6$	$6$	$73.079$	6.6.16371248.1	None	✓				4576.2.a.o	$1$	$0$	\(0\)	\(3\)	\(2\)	\(1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{3}-\beta _{2}q^{5}-\beta _{5}q^{7}+(1-2\beta _{1}+\cdots)q^{9}+\cdots\)
9152.2.a.cu	$9152$	$2$	9152.a	1.a	$1$	$8$	$8$	$73.079$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		4576.2.a.s	$1$	$1$	\(0\)	\(-5\)	\(2\)	\(-1\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}-\beta _{5}q^{5}+(\beta _{5}+\beta _{6}+\cdots)q^{7}+\cdots\)
9152.2.a.cv	$9152$	$2$	9152.a	1.a	$1$	$8$	$8$	$73.079$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		4576.2.a.t	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-4\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{6}q^{5}+(-1-\beta _{3})q^{7}+(1+\cdots)q^{9}+\cdots\)
9152.2.a.cw	$9152$	$2$	9152.a	1.a	$1$	$8$	$8$	$73.079$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		4576.2.a.t	$1$	$0$	\(0\)	\(1\)	\(1\)	\(4\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{6}q^{5}+(1+\beta _{3})q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
9152.2.a.cx	$9152$	$2$	9152.a	1.a	$1$	$8$	$8$	$73.079$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		4576.2.a.s	$1$	$0$	\(0\)	\(5\)	\(2\)	\(1\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}-\beta _{5}q^{5}+(-\beta _{5}-\beta _{6}+\cdots)q^{7}+\cdots\)
9152.2.a.cy	$9152$	$2$	9152.a	1.a	$1$	$9$	$9$	$73.079$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓		✓		4576.2.a.x	$1$	$1$	\(0\)	\(-2\)	\(-8\)	\(-5\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1+\beta _{7})q^{5}+(-1+\beta _{6}+\cdots)q^{7}+\cdots\)
9152.2.a.cz	$9152$	$2$	9152.a	1.a	$1$	$9$	$9$	$73.079$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓		✓		4576.2.a.w	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-5\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{2}q^{5}+(-1+\beta _{8})q^{7}+(2+\cdots)q^{9}+\cdots\)
9152.2.a.da	$9152$	$2$	9152.a	1.a	$1$	$9$	$9$	$73.079$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓		✓		4576.2.a.x	$1$	$0$	\(0\)	\(2\)	\(-8\)	\(5\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1+\beta _{7})q^{5}+(1-\beta _{6})q^{7}+\cdots\)
9152.2.a.db	$9152$	$2$	9152.a	1.a	$1$	$9$	$9$	$73.079$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓		✓		4576.2.a.w	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(5\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(1-\beta _{8})q^{7}+(2-\beta _{4}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9152))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9152)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(286))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(352))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(416))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(572))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(704))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(832))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2288))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4576))\)\(^{\oplus 2}\)