Space of modular forms of level 8664, weight 2, and trivial character

• Label: 8664.2.a
• Level: $8664$
• Weight: $2$
• Character orbit: 8664.a
• Rep. character: $\chi_{8664}(1,\cdot)$
• Character field: $\Q$
• Dimension: $171$
• Newform subspaces: $45$
• Sturm bound: $3040$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 8664 = 2^{3} \cdot 3 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8664.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 45 \)
Sturm bound:			\(3040\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\), \(13\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8664))\).

	Total	New	Old
Modular forms	1600	171	1429
Cusp forms	1441	171	1270
Eisenstein series	159	0	159

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

\(2\)	\(3\)	\(19\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(22\)
\(+\)	\(+\)	\(-\)	\(-\)	\(20\)
\(+\)	\(-\)	\(+\)	\(-\)	\(23\)
\(+\)	\(-\)	\(-\)	\(+\)	\(20\)
\(-\)	\(+\)	\(+\)	\(-\)	\(27\)
\(-\)	\(+\)	\(-\)	\(+\)	\(16\)
\(-\)	\(-\)	\(+\)	\(+\)	\(18\)
\(-\)	\(-\)	\(-\)	\(-\)	\(25\)
Plus space			\(+\)	\(76\)
Minus space			\(-\)	\(95\)

Trace form

171 * q + q^3 - 2 * q^5 + 4 * q^7 + 171 * q^9 - 4 * q^11 - 2 * q^13 + 2 * q^15 - 6 * q^17 + 8 * q^23 + 161 * q^25 + q^27 - 2 * q^29 + 4 * q^31 - 8 * q^33 - 10 * q^37 + 6 * q^39 + 10 * q^41 - 8 * q^43 - 2 * q^45 - 24 * q^47 + 175 * q^49 + 10 * q^51 + 14 * q^53 + 24 * q^55 - 20 * q^59 + 18 * q^61 + 4 * q^63 + 28 * q^65 + 36 * q^67 - 8 * q^69 - 8 * q^71 - 18 * q^73 + 15 * q^75 + 40 * q^77 - 4 * q^79 + 171 * q^81 + 28 * q^83 + 20 * q^85 + 10 * q^87 + 42 * q^89 + 40 * q^91 + 12 * q^93 + 14 * q^97 - 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8664))\) 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	19
8664.2.a.a	$8664$	$2$	8664.a	1.a	$1$	$1$	$1$	$69.182$	\(\Q\)	None	✓				456.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}-3q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
8664.2.a.b	$8664$	$2$	8664.a	1.a	$1$	$1$	$1$	$69.182$	\(\Q\)	None	✓				456.2.q.c	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(-5\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}-5q^{7}+q^{9}-4q^{11}+\cdots\)
8664.2.a.c	$8664$	$2$	8664.a	1.a	$1$	$1$	$1$	$69.182$	\(\Q\)	None	✓	✓			8664.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}-4q^{7}+q^{9}+2q^{11}+\cdots\)
8664.2.a.d	$8664$	$2$	8664.a	1.a	$1$	$1$	$1$	$69.182$	\(\Q\)	None	✓				456.2.q.b	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{7}+q^{9}+2q^{11}-q^{13}+\cdots\)
8664.2.a.e	$8664$	$2$	8664.a	1.a	$1$	$1$	$1$	$69.182$	\(\Q\)	None	✓				456.2.q.a	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-3q^{7}+q^{9}-5q^{13}+\cdots\)
8664.2.a.f	$8664$	$2$	8664.a	1.a	$1$	$1$	$1$	$69.182$	\(\Q\)	None	✓				456.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{9}-2q^{13}-2q^{15}+\cdots\)
8664.2.a.g	$8664$	$2$	8664.a	1.a	$1$	$1$	$1$	$69.182$	\(\Q\)	None	✓	✓			8664.2.a.g	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{5}+q^{7}+q^{9}-3q^{11}-3q^{15}+\cdots\)
8664.2.a.h	$8664$	$2$	8664.a	1.a	$1$	$1$	$1$	$69.182$	\(\Q\)	None	✓				456.2.q.c	$1$	$2$	\(0\)	\(1\)	\(-2\)	\(-5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-5q^{7}+q^{9}-4q^{11}+\cdots\)
8664.2.a.i	$8664$	$2$	8664.a	1.a	$1$	$1$	$1$	$69.182$	\(\Q\)	None	✓	✓			8664.2.a.c	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-4q^{7}+q^{9}+2q^{11}+\cdots\)
8664.2.a.j	$8664$	$2$	8664.a	1.a	$1$	$1$	$1$	$69.182$	\(\Q\)	None	✓				24.2.a.a	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
8664.2.a.k	$8664$	$2$	8664.a	1.a	$1$	$1$	$1$	$69.182$	\(\Q\)	None	✓				456.2.q.b	$1$	$0$	\(0\)	\(1\)	\(0\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{7}+q^{9}+2q^{11}+q^{13}+\cdots\)
8664.2.a.l	$8664$	$2$	8664.a	1.a	$1$	$1$	$1$	$69.182$	\(\Q\)	None	✓				456.2.a.a	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-3\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-3q^{7}+q^{9}-5q^{11}+2q^{13}+\cdots\)
8664.2.a.m	$8664$	$2$	8664.a	1.a	$1$	$1$	$1$	$69.182$	\(\Q\)	None	✓				456.2.q.a	$1$	$0$	\(0\)	\(1\)	\(2\)	\(-3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-3q^{7}+q^{9}+5q^{13}+\cdots\)
8664.2.a.n	$8664$	$2$	8664.a	1.a	$1$	$1$	$1$	$69.182$	\(\Q\)	None	✓	✓			8664.2.a.g	$1$	$1$	\(0\)	\(1\)	\(3\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}+q^{7}+q^{9}-3q^{11}+3q^{15}+\cdots\)
8664.2.a.o	$8664$	$2$	8664.a	1.a	$1$	$1$	$1$	$69.182$	\(\Q\)	None	✓				456.2.a.b	$1$	$0$	\(0\)	\(1\)	\(4\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots\)
8664.2.a.p	$8664$	$2$	8664.a	1.a	$1$	$2$	$2$	$69.182$	\(\Q(\sqrt{5}) \)	None	✓	✓			8664.2.a.p	$1$	$1$	\(0\)	\(-2\)	\(-3\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
8664.2.a.q	$8664$	$2$	8664.a	1.a	$1$	$2$	$2$	$69.182$	\(\Q(\sqrt{5}) \)	None	✓				456.2.q.d	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(4\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta )q^{5}+(2-\beta )q^{7}+q^{9}+\cdots\)
8664.2.a.r	$8664$	$2$	8664.a	1.a	$1$	$2$	$2$	$69.182$	\(\Q(\sqrt{17}) \)	None	✓				456.2.a.f	$1$	$0$	\(0\)	\(-2\)	\(1\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta q^{5}+\beta q^{7}+q^{9}+(4-\beta )q^{11}+\cdots\)
8664.2.a.s	$8664$	$2$	8664.a	1.a	$1$	$2$	$2$	$69.182$	\(\Q(\sqrt{5}) \)	None	✓				456.2.q.e	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(0\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}-\beta q^{7}+q^{9}+(3+\beta )q^{11}+\cdots\)
8664.2.a.t	$8664$	$2$	8664.a	1.a	$1$	$2$	$2$	$69.182$	\(\Q(\sqrt{5}) \)	None	✓	✓			8664.2.a.p	$1$	$1$	\(0\)	\(2\)	\(-3\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
8664.2.a.u	$8664$	$2$	8664.a	1.a	$1$	$2$	$2$	$69.182$	\(\Q(\sqrt{5}) \)	None	✓				456.2.q.d	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(4\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta )q^{5}+(2-\beta )q^{7}+q^{9}+\cdots\)
8664.2.a.v	$8664$	$2$	8664.a	1.a	$1$	$2$	$2$	$69.182$	\(\Q(\sqrt{41}) \)	None	✓				456.2.a.e	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta q^{5}+(-2+\beta )q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)
8664.2.a.w	$8664$	$2$	8664.a	1.a	$1$	$2$	$2$	$69.182$	\(\Q(\sqrt{5}) \)	None	✓				456.2.q.e	$1$	$0$	\(0\)	\(2\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{5}-\beta q^{7}+q^{9}+(3+\beta )q^{11}+\cdots\)
8664.2.a.x	$8664$	$2$	8664.a	1.a	$1$	$3$	$3$	$69.182$	\(\Q(\zeta_{18})^+\)	None	✓				456.2.q.f	$1$	$0$	\(0\)	\(-3\)	\(0\)	\(3\)		$-$	$+$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{1}q^{5}+(1+\beta _{1})q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
8664.2.a.y	$8664$	$2$	8664.a	1.a	$1$	$3$	$3$	$69.182$	3.3.316.1	None	✓	✓			8664.2.a.y	$1$	$0$	\(0\)	\(-3\)	\(3\)	\(1\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{1})q^{5}-\beta _{2}q^{7}+q^{9}+(-2\beta _{1}+\cdots)q^{11}+\cdots\)
8664.2.a.z	$8664$	$2$	8664.a	1.a	$1$	$3$	$3$	$69.182$	\(\Q(\zeta_{18})^+\)	None	✓				456.2.q.f	$1$	$1$	\(0\)	\(3\)	\(0\)	\(3\)		$+$	$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{1}q^{5}+(1+\beta _{1})q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
8664.2.a.ba	$8664$	$2$	8664.a	1.a	$1$	$3$	$3$	$69.182$	3.3.316.1	None	✓	✓			8664.2.a.y	$1$	$0$	\(0\)	\(3\)	\(3\)	\(1\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-\beta _{1})q^{5}-\beta _{2}q^{7}+q^{9}+(-2\beta _{1}+\cdots)q^{11}+\cdots\)
8664.2.a.bb	$8664$	$2$	8664.a	1.a	$1$	$4$	$4$	$69.182$	4.4.34025.1	None	✓	✓			8664.2.a.bb	$1$	$1$	\(0\)	\(-4\)	\(-2\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{2}q^{5}+(\beta _{2}-\beta _{3})q^{7}+q^{9}+\cdots\)
8664.2.a.bc	$8664$	$2$	8664.a	1.a	$1$	$4$	$4$	$69.182$	4.4.5225.1	None	✓	✓			8664.2.a.bc	$1$	$0$	\(0\)	\(-4\)	\(2\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{3}q^{5}+\beta _{3}q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
8664.2.a.bd	$8664$	$2$	8664.a	1.a	$1$	$4$	$4$	$69.182$	4.4.34025.1	None	✓	✓			8664.2.a.bb	$1$	$1$	\(0\)	\(4\)	\(-2\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{2}q^{5}+(\beta _{2}-\beta _{3})q^{7}+q^{9}+\cdots\)
8664.2.a.be	$8664$	$2$	8664.a	1.a	$1$	$4$	$4$	$69.182$	4.4.5225.1	None	✓	✓			8664.2.a.bc	$1$	$0$	\(0\)	\(4\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{3}q^{5}+\beta _{3}q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
8664.2.a.bf	$8664$	$2$	8664.a	1.a	$1$	$6$	$6$	$69.182$	6.6.1528713.1	None	✓				456.2.bg.a	$1$	$0$	\(0\)	\(-6\)	\(-3\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta _{1}q^{5}+(-1+2\beta _{1}+\beta _{2})q^{7}+\cdots\)
8664.2.a.bg	$8664$	$2$	8664.a	1.a	$1$	$6$	$6$	$69.182$	6.6.142368125.1	None	✓	✓			8664.2.a.bg	$1$	$0$	\(0\)	\(-6\)	\(1\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{5}q^{5}+\beta _{2}q^{7}+q^{9}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
8664.2.a.bh	$8664$	$2$	8664.a	1.a	$1$	$6$	$6$	$69.182$	6.6.65669049.1	None	✓		✓		456.2.bg.b	$1$	$1$	\(0\)	\(-6\)	\(3\)	\(6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{1})q^{5}+(1+\beta _{4})q^{7}+q^{9}+\cdots\)
8664.2.a.bi	$8664$	$2$	8664.a	1.a	$1$	$6$	$6$	$69.182$	6.6.1528713.1	None	✓				456.2.bg.a	$1$	$1$	\(0\)	\(6\)	\(-3\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{1}q^{5}+(-1+2\beta _{1}+\beta _{2})q^{7}+\cdots\)
8664.2.a.bj	$8664$	$2$	8664.a	1.a	$1$	$6$	$6$	$69.182$	6.6.142368125.1	None	✓	✓			8664.2.a.bg	$1$	$0$	\(0\)	\(6\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{5}q^{5}+\beta _{2}q^{7}+q^{9}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
8664.2.a.bk	$8664$	$2$	8664.a	1.a	$1$	$6$	$6$	$69.182$	6.6.65669049.1	None	✓				456.2.bg.b	$1$	$0$	\(0\)	\(6\)	\(3\)	\(6\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1-\beta _{1})q^{5}+(1+\beta _{4})q^{7}+q^{9}+\cdots\)
8664.2.a.bl	$8664$	$2$	8664.a	1.a	$1$	$8$	$8$	$69.182$	8.8.\(\cdots\).1	None	✓	✓			8664.2.a.bl	$1$	$1$	\(0\)	\(-8\)	\(-6\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta _{2})q^{5}-\beta _{1}q^{7}+q^{9}+\cdots\)
8664.2.a.bm	$8664$	$2$	8664.a	1.a	$1$	$8$	$8$	$69.182$	8.8.\(\cdots\).1	None	✓	✓	✓		8664.2.a.bl	$1$	$1$	\(0\)	\(8\)	\(-6\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta _{2})q^{5}-\beta _{1}q^{7}+q^{9}+\cdots\)
8664.2.a.bn	$8664$	$2$	8664.a	1.a	$1$	$9$	$9$	$69.182$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓				456.2.bg.d	$1$	$0$	\(0\)	\(-9\)	\(-3\)	\(-6\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-\beta _{1}-\beta _{3}+\beta _{5})q^{5}+(-1+\cdots)q^{7}+\cdots\)
8664.2.a.bo	$8664$	$2$	8664.a	1.a	$1$	$9$	$9$	$69.182$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓		✓		456.2.bg.c	$1$	$1$	\(0\)	\(-9\)	\(3\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{1}q^{5}+\beta _{7}q^{7}+q^{9}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
8664.2.a.bp	$8664$	$2$	8664.a	1.a	$1$	$9$	$9$	$69.182$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓		✓		456.2.bg.d	$1$	$1$	\(0\)	\(9\)	\(-3\)	\(-6\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-\beta _{1}-\beta _{3}+\beta _{5})q^{5}+(-1+\cdots)q^{7}+\cdots\)
8664.2.a.bq	$8664$	$2$	8664.a	1.a	$1$	$9$	$9$	$69.182$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓		✓		456.2.bg.c	$1$	$0$	\(0\)	\(9\)	\(3\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{5}+\beta _{7}q^{7}+q^{9}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
8664.2.a.br	$8664$	$2$	8664.a	1.a	$1$	$12$	$12$	$69.182$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		8664.2.a.br	$1$	$0$	\(0\)	\(-12\)	\(2\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{1}q^{5}+\beta _{10}q^{7}+q^{9}+(1+\beta _{4}+\cdots)q^{11}+\cdots\)
8664.2.a.bs	$8664$	$2$	8664.a	1.a	$1$	$12$	$12$	$69.182$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		8664.2.a.br	$1$	$0$	\(0\)	\(12\)	\(2\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{5}+\beta _{10}q^{7}+q^{9}+(1+\beta _{4}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8664))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8664)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(228))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(456))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(722))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1083))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1444))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2166))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2888))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4332))\)\(^{\oplus 2}\)