Space of modular forms of level 9522, weight 2, and trivial character

• Label: 9522.2.a
• Level: $9522$
• Weight: $2$
• Character orbit: 9522.a
• Rep. character: $\chi_{9522}(1,\cdot)$
• Character field: $\Q$
• Dimension: $210$
• Newform subspaces: $62$
• Sturm bound: $3312$
• Trace bound: $29$

Defining parameters

Level:	\( N \)	\(=\)	\( 9522 = 2 \cdot 3^{2} \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9522.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 62 \)
Sturm bound:			\(3312\)
Trace bound:			\(29\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9522))\).

	Total	New	Old
Modular forms	1752	210	1542
Cusp forms	1561	210	1351
Eisenstein series	191	0	191

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

\(2\)	\(3\)	\(23\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(210\)	\(24\)	\(186\)		\(187\)	\(24\)	\(163\)		\(23\)	\(0\)	\(23\)
\(+\)	\(+\)	\(-\)	\(-\)		\(228\)	\(18\)	\(210\)		\(204\)	\(18\)	\(186\)		\(24\)	\(0\)	\(24\)
\(+\)	\(-\)	\(+\)	\(-\)		\(222\)	\(33\)	\(189\)		\(198\)	\(33\)	\(165\)		\(24\)	\(0\)	\(24\)
\(+\)	\(-\)	\(-\)	\(+\)		\(216\)	\(30\)	\(186\)		\(192\)	\(30\)	\(162\)		\(24\)	\(0\)	\(24\)
\(-\)	\(+\)	\(+\)	\(-\)		\(222\)	\(24\)	\(198\)		\(198\)	\(24\)	\(174\)		\(24\)	\(0\)	\(24\)
\(-\)	\(+\)	\(-\)	\(+\)		\(216\)	\(18\)	\(198\)		\(192\)	\(18\)	\(174\)		\(24\)	\(0\)	\(24\)
\(-\)	\(-\)	\(+\)	\(+\)		\(222\)	\(27\)	\(195\)		\(198\)	\(27\)	\(171\)		\(24\)	\(0\)	\(24\)
\(-\)	\(-\)	\(-\)	\(-\)		\(216\)	\(36\)	\(180\)		\(192\)	\(36\)	\(156\)		\(24\)	\(0\)	\(24\)
Plus space			\(+\)		\(864\)	\(99\)	\(765\)		\(769\)	\(99\)	\(670\)		\(95\)	\(0\)	\(95\)
Minus space			\(-\)		\(888\)	\(111\)	\(777\)		\(792\)	\(111\)	\(681\)		\(96\)	\(0\)	\(96\)

Trace form

210 * q + 210 * q^4 + 2 * q^5 - 4 * q^7 - 2 * q^10 - 10 * q^11 + 4 * q^13 + 4 * q^14 + 210 * q^16 - 8 * q^17 - 2 * q^19 + 2 * q^20 + 6 * q^22 + 202 * q^25 - 4 * q^28 - 4 * q^29 - 20 * q^31 + 12 * q^34 - 36 * q^35 - 2 * q^37 - 10 * q^38 - 2 * q^40 + 12 * q^41 - 6 * q^43 - 10 * q^44 + 4 * q^47 + 206 * q^49 - 8 * q^50 + 4 * q^52 + 18 * q^53 + 12 * q^55 + 4 * q^56 + 20 * q^58 + 4 * q^59 - 6 * q^61 - 12 * q^62 + 210 * q^64 + 12 * q^65 + 22 * q^67 - 8 * q^68 + 8 * q^70 - 8 * q^71 + 24 * q^73 + 34 * q^74 - 2 * q^76 + 40 * q^77 + 28 * q^79 + 2 * q^80 + 24 * q^82 + 34 * q^83 + 64 * q^85 - 6 * q^86 + 6 * q^88 + 12 * q^89 + 24 * q^91 + 8 * q^94 + 20 * q^95 - 8 * q^97 + 16 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9522))\) 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	23
9522.2.a.a	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	\(\Q\)	None	✓	✓			9522.2.a.a	$1$	$0$	\(-1\)	\(0\)	\(-2\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{5}-q^{7}-q^{8}+2q^{10}+\cdots\)
9522.2.a.b	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	\(\Q\)	None	✓				3174.2.a.f	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-5q^{13}+\cdots\)
9522.2.a.c	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	\(\Q\)	None	✓				3174.2.a.f	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-5q^{13}+\cdots\)
9522.2.a.d	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	\(\Q\)	None	✓				138.2.a.c	$1$	$1$	\(-1\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}-2q^{13}+\cdots\)
9522.2.a.e	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	\(\Q\)	None	✓	✓			9522.2.a.a	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-2q^{10}+\cdots\)
9522.2.a.f	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	\(\Q\)	None	✓				1058.2.a.a	$1$	$0$	\(1\)	\(0\)	\(-3\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{5}+2q^{7}+q^{8}-3q^{10}+\cdots\)
9522.2.a.g	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	\(\Q\)	None	✓				1058.2.a.d	$1$	$0$	\(1\)	\(0\)	\(-2\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{5}-2q^{7}+q^{8}-2q^{10}+\cdots\)
9522.2.a.h	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	\(\Q\)	None	✓	✓			9522.2.a.a	$1$	$1$	\(1\)	\(0\)	\(-2\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{5}+q^{7}+q^{8}-2q^{10}+\cdots\)
9522.2.a.i	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	\(\Q\)	None	✓				138.2.a.a	$1$	$0$	\(1\)	\(0\)	\(-2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{5}+2q^{7}+q^{8}-2q^{10}+\cdots\)
9522.2.a.j	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	\(\Q\)	None	✓				3174.2.a.a	$1$	$0$	\(1\)	\(0\)	\(-2\)	\(5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{5}+5q^{7}+q^{8}-2q^{10}+\cdots\)
9522.2.a.k	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	\(\Q\)	None	✓				138.2.a.b	$1$	$0$	\(1\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{7}+q^{8}+2q^{13}-2q^{14}+\cdots\)
9522.2.a.l	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	\(\Q\)	None	✓				3174.2.a.a	$1$	$0$	\(1\)	\(0\)	\(2\)	\(-5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}-5q^{7}+q^{8}+2q^{10}+\cdots\)
9522.2.a.m	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	\(\Q\)	None	✓	✓			9522.2.a.a	$1$	$1$	\(1\)	\(0\)	\(2\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}+2q^{10}+\cdots\)
9522.2.a.n	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	\(\Q\)	None	✓				1058.2.a.d	$1$	$0$	\(1\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}+2q^{7}+q^{8}+2q^{10}+\cdots\)
9522.2.a.o	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	\(\Q\)	None	✓				1058.2.a.a	$1$	$0$	\(1\)	\(0\)	\(3\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+3q^{5}-2q^{7}+q^{8}+3q^{10}+\cdots\)
9522.2.a.p	$9522$	$2$	9522.a	1.a	$1$	$1$	$1$	$76.034$	\(\Q\)	None	✓				46.2.a.a	$1$	$0$	\(1\)	\(0\)	\(4\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+4q^{5}+4q^{7}+q^{8}+4q^{10}+\cdots\)
9522.2.a.q	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	\(\Q(\sqrt{5}) \)	None	✓				138.2.a.d	$1$	$1$	\(-2\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-1-\beta )q^{5}-2\beta q^{7}+\cdots\)
9522.2.a.r	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	\(\Q(\sqrt{41}) \)	None	✓				3174.2.a.o	$1$	$1$	\(-2\)	\(0\)	\(-1\)	\(3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-\beta q^{5}+(1+\beta )q^{7}-q^{8}+\cdots\)
9522.2.a.s	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	\(\Q(\sqrt{2}) \)	None	✓				3174.2.a.m	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3\beta q^{5}-\beta q^{7}-q^{8}-3\beta q^{10}+\cdots\)
9522.2.a.t	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	\(\Q(\sqrt{3}) \)	None	✓				1058.2.a.g	$2$	$1$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta q^{5}+2\beta q^{7}-q^{8}-\beta q^{10}+\cdots\)
9522.2.a.u	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	\(\Q(\sqrt{3}) \)	None	✓	✓			9522.2.a.u	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta q^{7}-q^{8}+3\beta q^{11}+\cdots\)
9522.2.a.v	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	\(\Q(\sqrt{6}) \)	None	✓	✓			9522.2.a.v	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}-\beta q^{11}+\cdots\)
9522.2.a.w	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	\(\Q(\sqrt{3}) \)	None	✓				3174.2.a.p	$2$	$1$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}+\beta q^{11}+\cdots\)
9522.2.a.x	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	\(\Q(\sqrt{3}) \)	None	✓				3174.2.a.q	$2$	$1$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta q^{7}-q^{8}-\beta q^{11}+4q^{13}+\cdots\)
9522.2.a.y	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	\(\Q(\sqrt{2}) \)	None	✓				3174.2.a.n	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2\beta q^{5}+\beta q^{7}-q^{8}-2\beta q^{10}+\cdots\)
9522.2.a.z	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	\(\Q(\sqrt{2}) \)	None	✓				1058.2.a.h	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2\beta q^{7}-q^{8}+3\beta q^{11}+\cdots\)
9522.2.a.ba	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	\(\Q(\sqrt{41}) \)	None	✓				3174.2.a.o	$1$	$1$	\(-2\)	\(0\)	\(1\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta q^{5}+(-1-\beta )q^{7}-q^{8}+\cdots\)
9522.2.a.bb	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	\(\Q(\sqrt{7}) \)	None	✓				414.2.a.e	$1$	$0$	\(-2\)	\(0\)	\(2\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(1+\beta )q^{5}-2q^{7}-q^{8}+\cdots\)
9522.2.a.bc	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	\(\Q(\sqrt{7}) \)	None	✓				414.2.a.e	$1$	$1$	\(2\)	\(0\)	\(-2\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-1+\beta )q^{5}-2q^{7}+q^{8}+\cdots\)
9522.2.a.bd	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	\(\Q(\sqrt{3}) \)	None	✓				3174.2.a.j	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}-5q^{13}+\cdots\)
9522.2.a.be	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	\(\Q(\sqrt{3}) \)	None	✓	✓			9522.2.a.u	$2$	$1$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta q^{7}+q^{8}-3\beta q^{11}+\cdots\)
9522.2.a.bf	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	\(\Q(\sqrt{6}) \)	None	✓				3174.2.a.k	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-\beta q^{7}+q^{8}-\beta q^{11}-2q^{13}+\cdots\)
9522.2.a.bg	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	\(\Q(\sqrt{2}) \)	None	✓				3174.2.a.l	$2$	$1$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta q^{5}-3\beta q^{7}+q^{8}+\beta q^{10}+\cdots\)
9522.2.a.bh	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	\(\Q(\sqrt{6}) \)	None	✓	✓			9522.2.a.v	$2$	$1$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}-\beta q^{11}+\cdots\)
9522.2.a.bi	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	\(\Q(\sqrt{2}) \)	None	✓				3174.2.a.h	$2$	$1$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta q^{7}+q^{8}+\beta q^{14}+q^{16}+\cdots\)
9522.2.a.bj	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	\(\Q(\sqrt{3}) \)	None	✓				1058.2.a.f	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2\beta q^{5}-2\beta q^{7}+q^{8}+\cdots\)
9522.2.a.bk	$9522$	$2$	9522.a	1.a	$1$	$2$	$2$	$76.034$	\(\Q(\sqrt{2}) \)	None	✓				3174.2.a.i	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta q^{5}+\beta q^{7}+q^{8}+\beta q^{10}+\cdots\)
9522.2.a.bl	$9522$	$2$	9522.a	1.a	$1$	$4$	$4$	$76.034$	\(\Q(\zeta_{24})^+\)	None	✓				3174.2.a.v	$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-\beta _{1}-\beta _{3})q^{5}+(3\beta _{1}+\cdots)q^{7}+\cdots\)
9522.2.a.bm	$9522$	$2$	9522.a	1.a	$1$	$4$	$4$	$76.034$	\(\Q(\zeta_{24})^+\)	None	✓				1058.2.a.i	$2$	$1$	\(4\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(2\beta _{1}+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
9522.2.a.bn	$9522$	$2$	9522.a	1.a	$1$	$4$	$4$	$76.034$	\(\Q(\zeta_{24})^+\)	None	✓				3174.2.a.u	$2$	$1$	\(4\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots\)
9522.2.a.bo	$9522$	$2$	9522.a	1.a	$1$	$4$	$4$	$76.034$	\(\Q(\sqrt{3}, \sqrt{35})\)	None	✓				3174.2.a.t	$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots\)
9522.2.a.bp	$9522$	$2$	9522.a	1.a	$1$	$5$	$5$	$76.034$	\(\Q(\zeta_{22})^+\)	None	✓				46.2.c.a	$1$	$0$	\(-5\)	\(0\)	\(-8\)	\(7\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-2+\beta _{1}-\beta _{4})q^{5}+(1+\cdots)q^{7}+\cdots\)
9522.2.a.bq	$9522$	$2$	9522.a	1.a	$1$	$5$	$5$	$76.034$	\(\Q(\zeta_{22})^+\)	None	✓				138.2.e.a	$1$	$1$	\(-5\)	\(0\)	\(-7\)	\(7\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-1-\beta _{3}+\beta _{4})q^{5}+(2+\cdots)q^{7}+\cdots\)
9522.2.a.br	$9522$	$2$	9522.a	1.a	$1$	$5$	$5$	$76.034$	\(\Q(\zeta_{22})^+\)	None	✓				138.2.e.b	$1$	$1$	\(-5\)	\(0\)	\(-1\)	\(-11\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(\beta _{2}+\beta _{3}+\beta _{4})q^{5}+(-3+\cdots)q^{7}+\cdots\)
9522.2.a.bs	$9522$	$2$	9522.a	1.a	$1$	$5$	$5$	$76.034$	\(\Q(\zeta_{22})^+\)	None	✓				138.2.e.b	$1$	$0$	\(-5\)	\(0\)	\(1\)	\(11\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(1-2\beta _{1}+\beta _{2}+\beta _{4})q^{5}+\cdots\)
9522.2.a.bt	$9522$	$2$	9522.a	1.a	$1$	$5$	$5$	$76.034$	\(\Q(\zeta_{22})^+\)	None	✓				138.2.e.a	$1$	$0$	\(-5\)	\(0\)	\(7\)	\(-7\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(1+\beta _{3}-\beta _{4})q^{5}+(-2+\cdots)q^{7}+\cdots\)
9522.2.a.bu	$9522$	$2$	9522.a	1.a	$1$	$5$	$5$	$76.034$	\(\Q(\zeta_{22})^+\)	None	✓				46.2.c.a	$1$	$1$	\(-5\)	\(0\)	\(8\)	\(-7\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(1+\beta _{1}+\beta _{3}-\beta _{4})q^{5}+\cdots\)
9522.2.a.bv	$9522$	$2$	9522.a	1.a	$1$	$5$	$5$	$76.034$	\(\Q(\zeta_{22})^+\)	None	✓				138.2.e.c	$1$	$1$	\(5\)	\(0\)	\(-11\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-3-\beta _{2}+2\beta _{3}-\beta _{4})q^{5}+\cdots\)
9522.2.a.bw	$9522$	$2$	9522.a	1.a	$1$	$5$	$5$	$76.034$	\(\Q(\zeta_{22})^+\)	None	✓				46.2.c.b	$1$	$0$	\(5\)	\(0\)	\(-2\)	\(9\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-\beta _{1}-\beta _{3})q^{5}+(3-2\beta _{1}+\cdots)q^{7}+\cdots\)
9522.2.a.bx	$9522$	$2$	9522.a	1.a	$1$	$5$	$5$	$76.034$	\(\Q(\zeta_{22})^+\)	None	✓				138.2.e.d	$1$	$1$	\(5\)	\(0\)	\(-1\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(\beta _{2}-\beta _{3}-\beta _{4})q^{5}+(1+\cdots)q^{7}+\cdots\)
9522.2.a.by	$9522$	$2$	9522.a	1.a	$1$	$5$	$5$	$76.034$	\(\Q(\zeta_{22})^+\)	None	✓				138.2.e.d	$1$	$0$	\(5\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(\beta _{1}+\beta _{2}-\beta _{4})q^{5}+(1+\cdots)q^{7}+\cdots\)
9522.2.a.bz	$9522$	$2$	9522.a	1.a	$1$	$5$	$5$	$76.034$	\(\Q(\zeta_{22})^+\)	None	✓				46.2.c.b	$1$	$1$	\(5\)	\(0\)	\(2\)	\(-9\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(\beta _{1}-\beta _{4})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
9522.2.a.ca	$9522$	$2$	9522.a	1.a	$1$	$5$	$5$	$76.034$	\(\Q(\zeta_{22})^+\)	None	✓				138.2.e.c	$1$	$0$	\(5\)	\(0\)	\(11\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(2-\beta _{1}-\beta _{2}-\beta _{4})q^{5}+\cdots\)
9522.2.a.cb	$9522$	$2$	9522.a	1.a	$1$	$6$	$6$	$76.034$	6.6.197448192.1	None	✓	✓			9522.2.a.cb	$2$	$1$	\(-6\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-\beta _{3}q^{5}+\beta _{4}q^{7}-q^{8}+\cdots\)
9522.2.a.cc	$9522$	$2$	9522.a	1.a	$1$	$6$	$6$	$76.034$	6.6.197448192.1	None	✓	✓			9522.2.a.cb	$2$	$0$	\(6\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-\beta _{3}q^{5}-\beta _{4}q^{7}+q^{8}+\cdots\)
9522.2.a.cd	$9522$	$2$	9522.a	1.a	$1$	$8$	$8$	$76.034$	8.8.\(\cdots\).1	None	✓	✓			9522.2.a.cd	$2$	$1$	\(-8\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(\beta _{1}+\beta _{4})q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
9522.2.a.ce	$9522$	$2$	9522.a	1.a	$1$	$8$	$8$	$76.034$	8.8.\(\cdots\).1	None	✓		✓		1058.2.a.n	$2$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(\beta _{2}+\beta _{4})q^{5}+(-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
9522.2.a.cf	$9522$	$2$	9522.a	1.a	$1$	$8$	$8$	$76.034$	8.8.\(\cdots\).1	None	✓	✓			9522.2.a.cd	$2$	$0$	\(8\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(\beta _{1}+\beta _{4})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
9522.2.a.cg	$9522$	$2$	9522.a	1.a	$1$	$10$	$10$	$76.034$	10.10.\(\cdots\).1	None	✓		✓		414.2.i.g	$1$	$1$	\(-10\)	\(0\)	\(-10\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-1+\beta _{2})q^{5}+(\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)
9522.2.a.ch	$9522$	$2$	9522.a	1.a	$1$	$10$	$10$	$76.034$	10.10.\(\cdots\).1	None	✓		✓		414.2.i.g	$1$	$0$	\(-10\)	\(0\)	\(10\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(1+\beta _{2})q^{5}+(\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)
9522.2.a.ci	$9522$	$2$	9522.a	1.a	$1$	$10$	$10$	$76.034$	10.10.\(\cdots\).1	None	✓		✓		414.2.i.g	$1$	$1$	\(10\)	\(0\)	\(-10\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-1+\beta _{2})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
9522.2.a.cj	$9522$	$2$	9522.a	1.a	$1$	$10$	$10$	$76.034$	10.10.\(\cdots\).1	None	✓		✓		414.2.i.g	$1$	$0$	\(10\)	\(0\)	\(10\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(1+\beta _{2})q^{5}+(-\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9522))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9522)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(207))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(414))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(529))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1058))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1587))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3174))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4761))\)\(^{\oplus 2}\)