Space of modular forms of level 9537, weight 2, and trivial character

• Label: 9537.2.a
• Level: $9537$
• Weight: $2$
• Character orbit: 9537.a
• Rep. character: $\chi_{9537}(1,\cdot)$
• Character field: $\Q$
• Dimension: $452$
• Newform subspaces: $56$
• Sturm bound: $2448$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 9537 = 3 \cdot 11 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9537.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 56 \)
Sturm bound:			\(2448\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(2\), \(5\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9537))\).

	Total	New	Old
Modular forms	1260	452	808
Cusp forms	1189	452	737
Eisenstein series	71	0	71

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

\(3\)	\(11\)	\(17\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(54\)
\(+\)	\(+\)	\(-\)	\(-\)	\(60\)
\(+\)	\(-\)	\(+\)	\(-\)	\(61\)
\(+\)	\(-\)	\(-\)	\(+\)	\(52\)
\(-\)	\(+\)	\(+\)	\(-\)	\(55\)
\(-\)	\(+\)	\(-\)	\(+\)	\(57\)
\(-\)	\(-\)	\(+\)	\(+\)	\(48\)
\(-\)	\(-\)	\(-\)	\(-\)	\(65\)
Plus space			\(+\)	\(211\)
Minus space			\(-\)	\(241\)

Trace form

452 * q + 2 * q^2 - 2 * q^3 + 456 * q^4 + 8 * q^5 + 4 * q^6 - 4 * q^7 - 6 * q^8 + 452 * q^9 - 4 * q^10 - 6 * q^12 - 4 * q^14 + 4 * q^15 + 472 * q^16 + 2 * q^18 + 4 * q^19 + 16 * q^20 - 12 * q^21 - 2 * q^22 - 8 * q^23 + 12 * q^24 + 460 * q^25 + 36 * q^26 - 2 * q^27 + 12 * q^28 + 20 * q^29 + 16 * q^30 - 8 * q^31 + 10 * q^32 + 2 * q^33 - 8 * q^35 + 456 * q^36 + 12 * q^38 - 12 * q^39 - 4 * q^40 + 20 * q^41 - 12 * q^42 + 4 * q^43 + 8 * q^44 + 8 * q^45 + 8 * q^46 - 24 * q^47 + 2 * q^48 + 452 * q^49 - 2 * q^50 - 56 * q^52 + 8 * q^53 + 4 * q^54 + 8 * q^55 + 12 * q^56 - 20 * q^57 + 56 * q^58 + 32 * q^59 - 20 * q^60 + 8 * q^61 - 4 * q^63 + 496 * q^64 + 48 * q^65 + 4 * q^66 - 16 * q^67 + 24 * q^69 - 8 * q^70 + 40 * q^71 - 6 * q^72 + 32 * q^73 + 28 * q^74 + 2 * q^75 - 4 * q^76 + 4 * q^77 + 8 * q^78 - 20 * q^79 - 24 * q^80 + 452 * q^81 + 32 * q^82 + 16 * q^83 - 20 * q^84 + 12 * q^86 - 18 * q^88 + 56 * q^89 - 4 * q^90 - 56 * q^92 - 32 * q^94 - 32 * q^95 + 28 * q^96 - 16 * q^97 + 2 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9537))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	11	17
9537.2.a.a	$9537$	$2$	9537.a	1.a	$1$	$1$	$1$	$76.153$	\(\Q\)	None	✓				561.2.a.a	$1$	$1$	\(-2\)	\(-1\)	\(0\)	\(3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-q^{3}+2q^{4}+2q^{6}+3q^{7}+\cdots\)
9537.2.a.b	$9537$	$2$	9537.a	1.a	$1$	$1$	$1$	$76.153$	\(\Q\)	None	✓				561.2.a.b	$1$	$1$	\(-1\)	\(-1\)	\(-2\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+3q^{8}+\cdots\)
9537.2.a.c	$9537$	$2$	9537.a	1.a	$1$	$1$	$1$	$76.153$	\(\Q\)	None	✓	✓			9537.2.a.c	$1$	$1$	\(-1\)	\(-1\)	\(-2\)	\(3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+3q^{7}+\cdots\)
9537.2.a.d	$9537$	$2$	9537.a	1.a	$1$	$1$	$1$	$76.153$	\(\Q\)	None	✓	✓			9537.2.a.c	$1$	$0$	\(-1\)	\(1\)	\(2\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}+2q^{5}-q^{6}-3q^{7}+\cdots\)
9537.2.a.e	$9537$	$2$	9537.a	1.a	$1$	$1$	$1$	$76.153$	\(\Q\)	None	✓	✓			9537.2.a.e	$1$	$2$	\(0\)	\(-1\)	\(-3\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}-3q^{5}-2q^{7}+q^{9}+q^{11}+\cdots\)
9537.2.a.f	$9537$	$2$	9537.a	1.a	$1$	$1$	$1$	$76.153$	\(\Q\)	None	✓	✓			9537.2.a.f	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}-q^{5}-4q^{7}+q^{9}-q^{11}+\cdots\)
9537.2.a.g	$9537$	$2$	9537.a	1.a	$1$	$1$	$1$	$76.153$	\(\Q\)	None	✓	✓			9537.2.a.g	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}+q^{5}+q^{9}+q^{11}+2q^{12}+\cdots\)
9537.2.a.h	$9537$	$2$	9537.a	1.a	$1$	$1$	$1$	$76.153$	\(\Q\)	None	✓				561.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}+2q^{5}-q^{7}+q^{9}-q^{11}+\cdots\)
9537.2.a.i	$9537$	$2$	9537.a	1.a	$1$	$1$	$1$	$76.153$	\(\Q\)	None	✓	✓			9537.2.a.g	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}-q^{5}+q^{9}-q^{11}-2q^{12}+\cdots\)
9537.2.a.j	$9537$	$2$	9537.a	1.a	$1$	$1$	$1$	$76.153$	\(\Q\)	None	✓	✓			9537.2.a.f	$1$	$0$	\(0\)	\(1\)	\(1\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+q^{5}+4q^{7}+q^{9}+q^{11}+\cdots\)
9537.2.a.k	$9537$	$2$	9537.a	1.a	$1$	$1$	$1$	$76.153$	\(\Q\)	None	✓				561.2.a.c	$1$	$0$	\(0\)	\(1\)	\(2\)	\(3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+2q^{5}+3q^{7}+q^{9}-q^{11}+\cdots\)
9537.2.a.l	$9537$	$2$	9537.a	1.a	$1$	$1$	$1$	$76.153$	\(\Q\)	None	✓	✓			9537.2.a.e	$1$	$1$	\(0\)	\(1\)	\(3\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+3q^{5}+2q^{7}+q^{9}-q^{11}+\cdots\)
9537.2.a.m	$9537$	$2$	9537.a	1.a	$1$	$1$	$1$	$76.153$	\(\Q\)	None	✓				33.2.a.a	$1$	$0$	\(1\)	\(1\)	\(2\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}+2q^{5}+q^{6}-4q^{7}+\cdots\)
9537.2.a.n	$9537$	$2$	9537.a	1.a	$1$	$2$	$2$	$76.153$	\(\Q(\sqrt{2}) \)	None	✓				561.2.j.a	$1$	$1$	\(-2\)	\(-2\)	\(4\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}+(2-\beta )q^{5}+q^{6}+\cdots\)
9537.2.a.o	$9537$	$2$	9537.a	1.a	$1$	$2$	$2$	$76.153$	\(\Q(\sqrt{2}) \)	None	✓				561.2.j.b	$1$	$0$	\(-2\)	\(-2\)	\(4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}+(2+\beta )q^{5}+q^{6}+\cdots\)
9537.2.a.p	$9537$	$2$	9537.a	1.a	$1$	$2$	$2$	$76.153$	\(\Q(\sqrt{2}) \)	None	✓				561.2.j.b	$1$	$0$	\(-2\)	\(2\)	\(-4\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}+(-2-\beta )q^{5}-q^{6}+\cdots\)
9537.2.a.q	$9537$	$2$	9537.a	1.a	$1$	$2$	$2$	$76.153$	\(\Q(\sqrt{2}) \)	None	✓				561.2.j.a	$1$	$1$	\(-2\)	\(2\)	\(-4\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}+(-2-\beta )q^{5}-q^{6}+\cdots\)
9537.2.a.r	$9537$	$2$	9537.a	1.a	$1$	$2$	$2$	$76.153$	\(\Q(\sqrt{17}) \)	None	✓	✓			9537.2.a.r	$1$	$0$	\(-1\)	\(-2\)	\(3\)	\(5\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-q^{3}+(2+\beta )q^{4}+(1+\beta )q^{5}+\cdots\)
9537.2.a.s	$9537$	$2$	9537.a	1.a	$1$	$2$	$2$	$76.153$	\(\Q(\sqrt{17}) \)	None	✓	✓			9537.2.a.r	$1$	$1$	\(-1\)	\(2\)	\(-3\)	\(-5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+q^{3}+(2+\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
9537.2.a.t	$9537$	$2$	9537.a	1.a	$1$	$2$	$2$	$76.153$	\(\Q(\sqrt{2}) \)	None	✓				561.2.a.e	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(6\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}+(2+\beta )q^{5}-\beta q^{6}+3q^{7}+\cdots\)
9537.2.a.u	$9537$	$2$	9537.a	1.a	$1$	$2$	$2$	$76.153$	\(\Q(\sqrt{17}) \)	None	✓				561.2.a.f	$1$	$0$	\(1\)	\(2\)	\(-4\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+(2+\beta )q^{4}-2q^{5}+\beta q^{6}+\cdots\)
9537.2.a.v	$9537$	$2$	9537.a	1.a	$1$	$3$	$3$	$76.153$	3.3.148.1	None	✓				561.2.a.g	$1$	$1$	\(-2\)	\(3\)	\(2\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
9537.2.a.w	$9537$	$2$	9537.a	1.a	$1$	$3$	$3$	$76.153$	3.3.148.1	None	✓				561.2.a.h	$1$	$0$	\(0\)	\(3\)	\(4\)	\(7\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots\)
9537.2.a.x	$9537$	$2$	9537.a	1.a	$1$	$3$	$3$	$76.153$	3.3.316.1	None	✓				561.2.a.i	$1$	$1$	\(1\)	\(3\)	\(-4\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
9537.2.a.y	$9537$	$2$	9537.a	1.a	$1$	$4$	$4$	$76.153$	4.4.22676.1	None	✓				561.2.a.j	$1$	$1$	\(1\)	\(-4\)	\(4\)	\(-9\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{3})q^{5}+\cdots\)
9537.2.a.z	$9537$	$2$	9537.a	1.a	$1$	$5$	$5$	$76.153$	5.5.9338213.1	None	✓	✓			9537.2.a.z	$1$	$0$	\(0\)	\(-5\)	\(2\)	\(8\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
9537.2.a.ba	$9537$	$2$	9537.a	1.a	$1$	$5$	$5$	$76.153$	5.5.9338213.1	None	✓	✓			9537.2.a.z	$1$	$1$	\(0\)	\(5\)	\(-2\)	\(-8\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
9537.2.a.bb	$9537$	$2$	9537.a	1.a	$1$	$5$	$5$	$76.153$	5.5.81509.1	None	✓	✓			9537.2.a.bb	$1$	$1$	\(1\)	\(-5\)	\(-3\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{4})q^{2}-q^{3}+(1-\beta _{3})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
9537.2.a.bc	$9537$	$2$	9537.a	1.a	$1$	$5$	$5$	$76.153$	5.5.81509.1	None	✓	✓			9537.2.a.bb	$1$	$0$	\(1\)	\(5\)	\(3\)	\(3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{4})q^{2}+q^{3}+(1-\beta _{3})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
9537.2.a.bd	$9537$	$2$	9537.a	1.a	$1$	$6$	$6$	$76.153$	6.6.24366928.1	None	✓				561.2.g.a	$1$	$1$	\(-3\)	\(-6\)	\(6\)	\(1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}-q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
9537.2.a.be	$9537$	$2$	9537.a	1.a	$1$	$6$	$6$	$76.153$	6.6.24366928.1	None	✓				561.2.g.a	$1$	$1$	\(-3\)	\(6\)	\(-6\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
9537.2.a.bf	$9537$	$2$	9537.a	1.a	$1$	$6$	$6$	$76.153$	6.6.6754732.1	None	✓	✓			9537.2.a.bf	$1$	$0$	\(-1\)	\(-6\)	\(2\)	\(7\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{2}-q^{3}+(1-\beta _{4}-\beta _{5})q^{4}+(1+\cdots)q^{5}+\cdots\)
9537.2.a.bg	$9537$	$2$	9537.a	1.a	$1$	$6$	$6$	$76.153$	6.6.78067472.1	None	✓				561.2.a.k	$1$	$0$	\(-1\)	\(-6\)	\(-2\)	\(-7\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)
9537.2.a.bh	$9537$	$2$	9537.a	1.a	$1$	$6$	$6$	$76.153$	6.6.6754732.1	None	✓	✓			9537.2.a.bf	$1$	$1$	\(-1\)	\(6\)	\(-2\)	\(-7\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{2}+q^{3}+(1-\beta _{4}-\beta _{5})q^{4}+(-1+\cdots)q^{5}+\cdots\)
9537.2.a.bi	$9537$	$2$	9537.a	1.a	$1$	$6$	$6$	$76.153$	6.6.1690398989.1	None	✓	✓			9537.2.a.bi	$1$	$1$	\(2\)	\(-6\)	\(1\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots\)
9537.2.a.bj	$9537$	$2$	9537.a	1.a	$1$	$6$	$6$	$76.153$	6.6.1690398989.1	None	✓	✓			9537.2.a.bi	$1$	$0$	\(2\)	\(6\)	\(-1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots\)
9537.2.a.bk	$9537$	$2$	9537.a	1.a	$1$	$6$	$6$	$76.153$	6.6.7328637.1	None	✓	✓			9537.2.a.bk	$1$	$1$	\(3\)	\(-6\)	\(0\)	\(-6\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{4})q^{2}-q^{3}+(1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
9537.2.a.bl	$9537$	$2$	9537.a	1.a	$1$	$6$	$6$	$76.153$	6.6.7328637.1	None	✓	✓			9537.2.a.bk	$1$	$0$	\(3\)	\(6\)	\(0\)	\(6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{4})q^{2}+q^{3}+(1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
9537.2.a.bm	$9537$	$2$	9537.a	1.a	$1$	$8$	$8$	$76.153$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				561.2.g.b	$1$	$0$	\(1\)	\(-8\)	\(-2\)	\(-1\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\beta _{6}+\cdots)q^{5}+\cdots\)
9537.2.a.bn	$9537$	$2$	9537.a	1.a	$1$	$8$	$8$	$76.153$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				561.2.g.b	$1$	$0$	\(1\)	\(8\)	\(2\)	\(1\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
9537.2.a.bo	$9537$	$2$	9537.a	1.a	$1$	$10$	$10$	$76.153$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓				561.2.j.c	$1$	$1$	\(0\)	\(-10\)	\(8\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{6}+\cdots)q^{5}+\cdots\)
9537.2.a.bp	$9537$	$2$	9537.a	1.a	$1$	$10$	$10$	$76.153$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓				561.2.j.c	$1$	$1$	\(0\)	\(10\)	\(-8\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{6}+\cdots)q^{5}+\cdots\)
9537.2.a.bq	$9537$	$2$	9537.a	1.a	$1$	$14$	$14$	$76.153$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓				561.2.j.d	$1$	$0$	\(8\)	\(-14\)	\(-8\)	\(-2\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
9537.2.a.br	$9537$	$2$	9537.a	1.a	$1$	$14$	$14$	$76.153$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓				561.2.j.d	$1$	$0$	\(8\)	\(14\)	\(8\)	\(2\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
9537.2.a.bs	$9537$	$2$	9537.a	1.a	$1$	$15$	$15$	$76.153$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	✓	✓		9537.2.a.bs	$1$	$1$	\(0\)	\(-15\)	\(-6\)	\(-15\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{5}+\cdots)q^{5}+\cdots\)
9537.2.a.bt	$9537$	$2$	9537.a	1.a	$1$	$15$	$15$	$76.153$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	✓			9537.2.a.bs	$1$	$0$	\(0\)	\(15\)	\(6\)	\(15\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{5}+\cdots)q^{5}+\cdots\)
9537.2.a.bu	$9537$	$2$	9537.a	1.a	$1$	$18$	$18$	$76.153$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	✓			9537.2.a.bu	$1$	$0$	\(-3\)	\(-18\)	\(6\)	\(15\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{13}q^{5}+\cdots\)
9537.2.a.bv	$9537$	$2$	9537.a	1.a	$1$	$18$	$18$	$76.153$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	✓	✓		9537.2.a.bu	$1$	$1$	\(-3\)	\(18\)	\(-6\)	\(-15\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{13}q^{5}+\cdots\)
9537.2.a.bw	$9537$	$2$	9537.a	1.a	$1$	$18$	$18$	$76.153$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	✓			9537.2.a.bw	$1$	$1$	\(3\)	\(-18\)	\(-6\)	\(-15\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots\)
9537.2.a.bx	$9537$	$2$	9537.a	1.a	$1$	$18$	$18$	$76.153$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	✓	✓		9537.2.a.bw	$1$	$0$	\(3\)	\(18\)	\(6\)	\(15\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots\)
9537.2.a.by	$9537$	$2$	9537.a	1.a	$1$	$21$	$21$	$76.153$		None	✓	✓	✓		9537.2.a.by	$1$	$0$	\(-3\)	\(-21\)	\(6\)	\(21\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
9537.2.a.bz	$9537$	$2$	9537.a	1.a	$1$	$21$	$21$	$76.153$		None	✓	✓			9537.2.a.by	$1$	$1$	\(-3\)	\(21\)	\(-6\)	\(-21\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
9537.2.a.ca	$9537$	$2$	9537.a	1.a	$1$	$28$	$28$	$76.153$		None	✓		✓		561.2.o.a	$1$	$1$	\(-8\)	\(-28\)	\(8\)	\(-4\)		$+$	$-$	$-$	$+$		$\mathrm{SU}(2)$
9537.2.a.cb	$9537$	$2$	9537.a	1.a	$1$	$28$	$28$	$76.153$		None	✓		✓		561.2.o.a	$1$	$1$	\(-8\)	\(28\)	\(-8\)	\(4\)		$-$	$+$	$-$	$+$		$\mathrm{SU}(2)$
9537.2.a.cc	$9537$	$2$	9537.a	1.a	$1$	$36$	$36$	$76.153$		None	✓		✓		561.2.o.b	$1$	$0$	\(8\)	\(-36\)	\(-24\)	\(4\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
9537.2.a.cd	$9537$	$2$	9537.a	1.a	$1$	$36$	$36$	$76.153$		None	✓		✓		561.2.o.b	$1$	$0$	\(8\)	\(36\)	\(24\)	\(-4\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9537))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9537)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(187))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(561))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(867))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3179))\)\(^{\oplus 2}\)