Space of modular forms of level 8670, weight 2, and trivial character

• Label: 8670.2.a
• Level: $8670$
• Weight: $2$
• Character orbit: 8670.a
• Rep. character: $\chi_{8670}(1,\cdot)$
• Character field: $\Q$
• Dimension: $182$
• Newform subspaces: $65$
• Sturm bound: $3672$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 8670 = 2 \cdot 3 \cdot 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8670.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 65 \)
Sturm bound:			\(3672\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8670))\).

	Total	New	Old
Modular forms	1908	182	1726
Cusp forms	1765	182	1583
Eisenstein series	143	0	143

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

\(2\)	\(3\)	\(5\)	\(17\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(11\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(12\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(10\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(12\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(16\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(7\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(8\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(15\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(10\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(12\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(11\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(12\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(8\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(15\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(16\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(7\)
Plus space				\(+\)	\(76\)
Minus space				\(-\)	\(106\)

Trace form

182 * q + 2 * q^3 + 182 * q^4 + 4 * q^7 + 182 * q^9 + 2 * q^10 - 4 * q^11 + 2 * q^12 - 8 * q^13 - 4 * q^14 + 182 * q^16 + 4 * q^21 - 4 * q^22 - 8 * q^23 + 182 * q^25 + 12 * q^26 + 2 * q^27 + 4 * q^28 - 24 * q^29 - 2 * q^30 - 16 * q^31 - 12 * q^33 - 4 * q^35 + 182 * q^36 - 8 * q^37 + 8 * q^38 + 8 * q^39 + 2 * q^40 + 4 * q^41 - 12 * q^42 - 4 * q^44 - 16 * q^47 + 2 * q^48 + 150 * q^49 - 8 * q^52 - 16 * q^53 - 12 * q^55 - 4 * q^56 + 16 * q^57 + 4 * q^58 - 20 * q^59 + 4 * q^61 + 8 * q^62 + 4 * q^63 + 182 * q^64 + 12 * q^65 + 4 * q^66 - 8 * q^67 - 8 * q^69 - 4 * q^70 + 24 * q^71 + 44 * q^73 + 20 * q^74 + 2 * q^75 - 16 * q^77 - 4 * q^78 - 16 * q^79 + 182 * q^81 + 32 * q^82 + 16 * q^83 + 4 * q^84 + 16 * q^86 + 8 * q^87 - 4 * q^88 - 36 * q^89 + 2 * q^90 + 40 * q^91 - 8 * q^92 + 32 * q^93 - 8 * q^94 - 24 * q^95 + 4 * q^97 + 48 * q^98 - 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8670))\) 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	5	17
8670.2.a.a	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	\(\Q\)	None	✓	✓			8670.2.a.a	$1$	$1$	\(-1\)	\(-1\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
8670.2.a.b	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	\(\Q\)	None	✓	✓			8670.2.a.b	$1$	$0$	\(-1\)	\(-1\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
8670.2.a.c	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	\(\Q\)	None	✓				510.2.a.b	$1$	$1$	\(-1\)	\(-1\)	\(-1\)	\(2\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
8670.2.a.d	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	\(\Q\)	None	✓				510.2.c.b	$1$	$1$	\(-1\)	\(-1\)	\(-1\)	\(2\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
8670.2.a.e	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	\(\Q\)	None	✓	✓			8670.2.a.e	$1$	$1$	\(-1\)	\(-1\)	\(1\)	\(-3\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-3q^{7}+\cdots\)
8670.2.a.f	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	\(\Q\)	None	✓	✓			8670.2.a.f	$1$	$1$	\(-1\)	\(-1\)	\(1\)	\(3\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+3q^{7}+\cdots\)
8670.2.a.g	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	\(\Q\)	None	✓				30.2.a.a	$1$	$0$	\(-1\)	\(-1\)	\(1\)	\(4\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots\)
8670.2.a.h	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	\(\Q\)	None	✓	✓			8670.2.a.f	$1$	$2$	\(-1\)	\(1\)	\(-1\)	\(-3\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-3q^{7}+\cdots\)
8670.2.a.i	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	\(\Q\)	None	✓	✓			8670.2.a.e	$1$	$0$	\(-1\)	\(1\)	\(-1\)	\(3\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+3q^{7}+\cdots\)
8670.2.a.j	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	\(\Q\)	None	✓				510.2.c.b	$1$	$1$	\(-1\)	\(1\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
8670.2.a.k	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	\(\Q\)	None	✓				510.2.a.a	$1$	$1$	\(-1\)	\(1\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
8670.2.a.l	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	\(\Q\)	None	✓	✓			8670.2.a.b	$1$	$1$	\(-1\)	\(1\)	\(1\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
8670.2.a.m	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	\(\Q\)	None	✓	✓			8670.2.a.a	$1$	$0$	\(-1\)	\(1\)	\(1\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
8670.2.a.n	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	\(\Q\)	None	✓				510.2.a.g	$1$	$0$	\(1\)	\(-1\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-2q^{7}+\cdots\)
8670.2.a.o	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	\(\Q\)	None	✓	✓			8670.2.a.o	$1$	$1$	\(1\)	\(-1\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
8670.2.a.p	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	\(\Q\)	None	✓	✓			8670.2.a.p	$1$	$1$	\(1\)	\(-1\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
8670.2.a.q	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	\(\Q\)	None	✓	✓			8670.2.a.q	$1$	$1$	\(1\)	\(-1\)	\(1\)	\(-3\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-3q^{7}+\cdots\)
8670.2.a.r	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	\(\Q\)	None	✓				510.2.a.f	$1$	$1$	\(1\)	\(-1\)	\(1\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
8670.2.a.s	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	\(\Q\)	None	✓				510.2.c.a	$1$	$1$	\(1\)	\(-1\)	\(1\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
8670.2.a.t	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	\(\Q\)	None	✓	✓			8670.2.a.t	$1$	$0$	\(1\)	\(-1\)	\(1\)	\(3\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+3q^{7}+\cdots\)
8670.2.a.u	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	\(\Q\)	None	✓	✓			8670.2.a.t	$1$	$1$	\(1\)	\(1\)	\(-1\)	\(-3\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-3q^{7}+\cdots\)
8670.2.a.v	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	\(\Q\)	None	✓				510.2.a.e	$1$	$1$	\(1\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
8670.2.a.w	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	\(\Q\)	None	✓				510.2.c.a	$1$	$1$	\(1\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
8670.2.a.x	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	\(\Q\)	None	✓	✓			8670.2.a.q	$1$	$0$	\(1\)	\(1\)	\(-1\)	\(3\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+3q^{7}+\cdots\)
8670.2.a.y	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	\(\Q\)	None	✓				510.2.a.d	$1$	$0$	\(1\)	\(1\)	\(1\)	\(-2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
8670.2.a.z	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	\(\Q\)	None	✓	✓			8670.2.a.p	$1$	$0$	\(1\)	\(1\)	\(1\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
8670.2.a.ba	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	\(\Q\)	None	✓	✓			8670.2.a.o	$1$	$0$	\(1\)	\(1\)	\(1\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
8670.2.a.bb	$8670$	$2$	8670.a	1.a	$1$	$1$	$1$	$69.230$	\(\Q\)	None	✓				510.2.a.c	$1$	$0$	\(1\)	\(1\)	\(1\)	\(4\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots\)
8670.2.a.bc	$8670$	$2$	8670.a	1.a	$1$	$2$	$2$	$69.230$	\(\Q(\sqrt{2}) \)	None	✓				510.2.p.b	$1$	$1$	\(-2\)	\(-2\)	\(-2\)	\(4\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(2+2\beta )q^{7}+\cdots\)
8670.2.a.bd	$8670$	$2$	8670.a	1.a	$1$	$2$	$2$	$69.230$	\(\Q(\sqrt{2}) \)	None	✓				510.2.c.d	$1$	$0$	\(-2\)	\(-2\)	\(2\)	\(-4\)		$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots\)
8670.2.a.be	$8670$	$2$	8670.a	1.a	$1$	$2$	$2$	$69.230$	\(\Q(\sqrt{6}) \)	None	✓				510.2.a.h	$1$	$0$	\(-2\)	\(2\)	\(-2\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+\beta q^{7}+\cdots\)
8670.2.a.bf	$8670$	$2$	8670.a	1.a	$1$	$2$	$2$	$69.230$	\(\Q(\sqrt{2}) \)	None	✓				510.2.c.d	$1$	$0$	\(-2\)	\(2\)	\(-2\)	\(4\)		$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(2+\beta )q^{7}+\cdots\)
8670.2.a.bg	$8670$	$2$	8670.a	1.a	$1$	$2$	$2$	$69.230$	\(\Q(\sqrt{2}) \)	None	✓				510.2.p.b	$1$	$1$	\(-2\)	\(2\)	\(2\)	\(-4\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(-2+\cdots)q^{7}+\cdots\)
8670.2.a.bh	$8670$	$2$	8670.a	1.a	$1$	$2$	$2$	$69.230$	\(\Q(\sqrt{13}) \)	None	✓				510.2.c.c	$1$	$0$	\(2\)	\(-2\)	\(-2\)	\(2\)		$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(1+\beta )q^{7}+\cdots\)
8670.2.a.bi	$8670$	$2$	8670.a	1.a	$1$	$2$	$2$	$69.230$	\(\Q(\sqrt{2}) \)	None	✓				510.2.p.a	$1$	$1$	\(2\)	\(-2\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+2\beta q^{7}+\cdots\)
8670.2.a.bj	$8670$	$2$	8670.a	1.a	$1$	$2$	$2$	$69.230$	\(\Q(\sqrt{2}) \)	None	✓				510.2.p.a	$1$	$1$	\(2\)	\(2\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+2\beta q^{7}+\cdots\)
8670.2.a.bk	$8670$	$2$	8670.a	1.a	$1$	$2$	$2$	$69.230$	\(\Q(\sqrt{13}) \)	None	✓				510.2.c.c	$1$	$0$	\(2\)	\(2\)	\(2\)	\(-2\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
8670.2.a.bl	$8670$	$2$	8670.a	1.a	$1$	$3$	$3$	$69.230$	\(\Q(\zeta_{18})^+\)	None	✓	✓			8670.2.a.bl	$1$	$0$	\(-3\)	\(-3\)	\(-3\)	\(0\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-\beta _{1}q^{7}+\cdots\)
8670.2.a.bm	$8670$	$2$	8670.a	1.a	$1$	$3$	$3$	$69.230$	\(\Q(\zeta_{18})^+\)	None	✓	✓			8670.2.a.bm	$1$	$0$	\(-3\)	\(-3\)	\(3\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+\beta _{1}q^{7}+\cdots\)
8670.2.a.bn	$8670$	$2$	8670.a	1.a	$1$	$3$	$3$	$69.230$	\(\Q(\zeta_{18})^+\)	None	✓	✓			8670.2.a.bm	$1$	$1$	\(-3\)	\(3\)	\(-3\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-\beta _{1}q^{7}+\cdots\)
8670.2.a.bo	$8670$	$2$	8670.a	1.a	$1$	$3$	$3$	$69.230$	\(\Q(\zeta_{18})^+\)	None	✓	✓	✓		8670.2.a.bl	$1$	$1$	\(-3\)	\(3\)	\(3\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+\beta _{1}q^{7}+\cdots\)
8670.2.a.bp	$8670$	$2$	8670.a	1.a	$1$	$3$	$3$	$69.230$	\(\Q(\zeta_{18})^+\)	None	✓	✓			8670.2.a.bp	$1$	$0$	\(3\)	\(-3\)	\(-3\)	\(6\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(2-\beta _{1}+\cdots)q^{7}+\cdots\)
8670.2.a.bq	$8670$	$2$	8670.a	1.a	$1$	$3$	$3$	$69.230$	\(\Q(\zeta_{18})^+\)	None	✓	✓			8670.2.a.bq	$1$	$0$	\(3\)	\(-3\)	\(3\)	\(6\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(2+\beta _{1}+\cdots)q^{7}+\cdots\)
8670.2.a.br	$8670$	$2$	8670.a	1.a	$1$	$3$	$3$	$69.230$	\(\Q(\zeta_{18})^+\)	None	✓	✓	✓		8670.2.a.bq	$1$	$1$	\(3\)	\(3\)	\(-3\)	\(-6\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots\)
8670.2.a.bs	$8670$	$2$	8670.a	1.a	$1$	$3$	$3$	$69.230$	\(\Q(\zeta_{18})^+\)	None	✓	✓			8670.2.a.bp	$1$	$1$	\(3\)	\(3\)	\(3\)	\(-6\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots\)
8670.2.a.bt	$8670$	$2$	8670.a	1.a	$1$	$4$	$4$	$69.230$	\(\Q(\zeta_{16})^+\)	None	✓		✓		510.2.p.d	$1$	$0$	\(-4\)	\(-4\)	\(4\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+\beta _{1}q^{7}+\cdots\)
8670.2.a.bu	$8670$	$2$	8670.a	1.a	$1$	$4$	$4$	$69.230$	\(\Q(\zeta_{16})^+\)	None	✓				510.2.u.b	$1$	$1$	\(-4\)	\(-4\)	\(4\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(\beta _{1}+\beta _{3})q^{7}+\cdots\)
8670.2.a.bv	$8670$	$2$	8670.a	1.a	$1$	$4$	$4$	$69.230$	\(\Q(\zeta_{16})^+\)	None	✓		✓		510.2.u.b	$1$	$1$	\(-4\)	\(4\)	\(-4\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(\beta _{1}+\beta _{3})q^{7}+\cdots\)
8670.2.a.bw	$8670$	$2$	8670.a	1.a	$1$	$4$	$4$	$69.230$	\(\Q(\zeta_{16})^+\)	None	✓				510.2.p.d	$1$	$0$	\(-4\)	\(4\)	\(-4\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+\beta _{1}q^{7}+\cdots\)
8670.2.a.bx	$8670$	$2$	8670.a	1.a	$1$	$4$	$4$	$69.230$	4.4.4352.1	None	✓		✓		510.2.p.c	$1$	$0$	\(4\)	\(-4\)	\(-4\)	\(-4\)		$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
8670.2.a.by	$8670$	$2$	8670.a	1.a	$1$	$4$	$4$	$69.230$	\(\Q(\zeta_{16})^+\)	None	✓				510.2.u.a	$1$	$1$	\(4\)	\(-4\)	\(-4\)	\(8\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(2+\beta _{1}+\cdots)q^{7}+\cdots\)
8670.2.a.bz	$8670$	$2$	8670.a	1.a	$1$	$4$	$4$	$69.230$	\(\Q(\zeta_{16})^+\)	None	✓		✓		510.2.u.a	$1$	$1$	\(4\)	\(4\)	\(4\)	\(-8\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots\)
8670.2.a.ca	$8670$	$2$	8670.a	1.a	$1$	$4$	$4$	$69.230$	4.4.4352.1	None	✓				510.2.p.c	$1$	$0$	\(4\)	\(4\)	\(4\)	\(4\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(1+\beta _{3})q^{7}+\cdots\)
8670.2.a.cb	$8670$	$2$	8670.a	1.a	$1$	$6$	$6$	$69.230$	6.6.204493248.1	None	✓	✓	✓		8670.2.a.cb	$1$	$1$	\(-6\)	\(-6\)	\(-6\)	\(0\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+\beta _{1}q^{7}+\cdots\)
8670.2.a.cc	$8670$	$2$	8670.a	1.a	$1$	$6$	$6$	$69.230$	6.6.46609344.1	None	✓	✓	✓		8670.2.a.cc	$1$	$1$	\(-6\)	\(-6\)	\(6\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+\beta _{5}q^{7}+\cdots\)
8670.2.a.cd	$8670$	$2$	8670.a	1.a	$1$	$6$	$6$	$69.230$	6.6.46609344.1	None	✓	✓	✓		8670.2.a.cc	$1$	$0$	\(-6\)	\(6\)	\(-6\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+\beta _{5}q^{7}+\cdots\)
8670.2.a.ce	$8670$	$2$	8670.a	1.a	$1$	$6$	$6$	$69.230$	6.6.204493248.1	None	✓	✓			8670.2.a.cb	$1$	$0$	\(-6\)	\(6\)	\(6\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+\beta _{1}q^{7}+\cdots\)
8670.2.a.cf	$8670$	$2$	8670.a	1.a	$1$	$6$	$6$	$69.230$	6.6.30652992.1	None	✓	✓	✓		8670.2.a.cf	$1$	$1$	\(6\)	\(-6\)	\(-6\)	\(-6\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
8670.2.a.cg	$8670$	$2$	8670.a	1.a	$1$	$6$	$6$	$69.230$	6.6.45769536.1	None	✓	✓	✓		8670.2.a.cg	$1$	$1$	\(6\)	\(-6\)	\(6\)	\(-6\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
8670.2.a.ch	$8670$	$2$	8670.a	1.a	$1$	$6$	$6$	$69.230$	6.6.45769536.1	None	✓	✓			8670.2.a.cg	$1$	$0$	\(6\)	\(6\)	\(-6\)	\(6\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+(1+\beta _{3}+\cdots)q^{7}+\cdots\)
8670.2.a.ci	$8670$	$2$	8670.a	1.a	$1$	$6$	$6$	$69.230$	6.6.30652992.1	None	✓	✓	✓		8670.2.a.cf	$1$	$0$	\(6\)	\(6\)	\(6\)	\(6\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(1+\beta _{3}+\cdots)q^{7}+\cdots\)
8670.2.a.cj	$8670$	$2$	8670.a	1.a	$1$	$8$	$8$	$69.230$	8.8.\(\cdots\).1	None	✓		✓		510.2.u.c	$1$	$0$	\(-8\)	\(-8\)	\(-8\)	\(-8\)		$+$	$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
8670.2.a.ck	$8670$	$2$	8670.a	1.a	$1$	$8$	$8$	$69.230$	8.8.\(\cdots\).1	None	✓		✓		510.2.u.c	$1$	$0$	\(-8\)	\(8\)	\(8\)	\(8\)		$+$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
8670.2.a.cl	$8670$	$2$	8670.a	1.a	$1$	$8$	$8$	$69.230$	8.8.\(\cdots\).1	None	✓		✓		510.2.u.d	$1$	$0$	\(8\)	\(-8\)	\(8\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
8670.2.a.cm	$8670$	$2$	8670.a	1.a	$1$	$8$	$8$	$69.230$	8.8.\(\cdots\).1	None	✓		✓		510.2.u.d	$1$	$0$	\(8\)	\(8\)	\(-8\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+(\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8670))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8670)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(170))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(255))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(510))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(578))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(867))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1445))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1734))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2890))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4335))\)\(^{\oplus 2}\)