Space of modular forms of level 8880, weight 2, and trivial character

• Label: 8880.2.a
• Level: $8880$
• Weight: $2$
• Character orbit: 8880.a
• Rep. character: $\chi_{8880}(1,\cdot)$
• Character field: $\Q$
• Dimension: $144$
• Newform subspaces: $67$
• Sturm bound: $3648$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 8880 = 2^{4} \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8880.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 67 \)
Sturm bound:			\(3648\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8880))\).

	Total	New	Old
Modular forms	1848	144	1704
Cusp forms	1801	144	1657
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.

\(2\)	\(3\)	\(5\)	\(37\)	Fricke		Total				Cusp				Eisenstein
						All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)		\(104\)	\(7\)	\(97\)		\(102\)	\(7\)	\(95\)		\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)		\(127\)	\(11\)	\(116\)		\(124\)	\(11\)	\(113\)		\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)		\(115\)	\(10\)	\(105\)		\(112\)	\(10\)	\(102\)		\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)		\(116\)	\(8\)	\(108\)		\(113\)	\(8\)	\(105\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)		\(119\)	\(10\)	\(109\)		\(116\)	\(10\)	\(106\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)		\(112\)	\(8\)	\(104\)		\(109\)	\(8\)	\(101\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)		\(124\)	\(7\)	\(117\)		\(121\)	\(7\)	\(114\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)		\(107\)	\(11\)	\(96\)		\(104\)	\(11\)	\(93\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)		\(119\)	\(9\)	\(110\)		\(116\)	\(9\)	\(107\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)		\(112\)	\(8\)	\(104\)		\(109\)	\(8\)	\(101\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)		\(108\)	\(10\)	\(98\)		\(105\)	\(10\)	\(95\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)		\(123\)	\(9\)	\(114\)		\(120\)	\(9\)	\(111\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)		\(120\)	\(10\)	\(110\)		\(117\)	\(10\)	\(107\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)		\(111\)	\(9\)	\(102\)		\(108\)	\(9\)	\(99\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)		\(115\)	\(9\)	\(106\)		\(112\)	\(9\)	\(103\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)		\(116\)	\(8\)	\(108\)		\(113\)	\(8\)	\(105\)		\(3\)	\(0\)	\(3\)
Plus space				\(+\)		\(912\)	\(66\)	\(846\)		\(889\)	\(66\)	\(823\)		\(23\)	\(0\)	\(23\)
Minus space				\(-\)		\(936\)	\(78\)	\(858\)		\(912\)	\(78\)	\(834\)		\(24\)	\(0\)	\(24\)

Trace form

144 * q + 144 * q^9 - 4 * q^15 - 8 * q^19 + 144 * q^25 - 8 * q^31 + 24 * q^43 + 48 * q^47 + 144 * q^49 - 8 * q^51 - 32 * q^53 - 16 * q^55 + 16 * q^59 - 16 * q^61 + 16 * q^69 - 32 * q^71 - 32 * q^77 + 40 * q^79 + 144 * q^81 + 16 * q^85 - 24 * q^87 - 32 * q^89 - 80 * q^91 - 32 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8880))\) 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	37
8880.2.a.a	$8880$	$2$	8880.a	1.a	$1$	$1$	$1$	$70.907$	\(\Q\)	None	✓				1110.2.a.g	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-4\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-4q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
8880.2.a.b	$8880$	$2$	8880.a	1.a	$1$	$1$	$1$	$70.907$	\(\Q\)	None	✓				1110.2.a.o	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-4\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-4q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
8880.2.a.c	$8880$	$2$	8880.a	1.a	$1$	$1$	$1$	$70.907$	\(\Q\)	None	✓				2220.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{7}+q^{9}-q^{13}+q^{15}+\cdots\)
8880.2.a.d	$8880$	$2$	8880.a	1.a	$1$	$1$	$1$	$70.907$	\(\Q\)	None	✓				1110.2.a.f	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}+5q^{11}+2q^{13}+\cdots\)
8880.2.a.e	$8880$	$2$	8880.a	1.a	$1$	$1$	$1$	$70.907$	\(\Q\)	None	✓				4440.2.a.f	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}-4q^{11}+6q^{13}+\cdots\)
8880.2.a.f	$8880$	$2$	8880.a	1.a	$1$	$1$	$1$	$70.907$	\(\Q\)	None	✓				1110.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}-3q^{11}-7q^{13}+\cdots\)
8880.2.a.g	$8880$	$2$	8880.a	1.a	$1$	$1$	$1$	$70.907$	\(\Q\)	None	✓				1110.2.a.n	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}-3q^{11}+2q^{13}+\cdots\)
8880.2.a.h	$8880$	$2$	8880.a	1.a	$1$	$1$	$1$	$70.907$	\(\Q\)	None	✓				555.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+2q^{7}+q^{9}-4q^{11}+5q^{13}+\cdots\)
8880.2.a.i	$8880$	$2$	8880.a	1.a	$1$	$1$	$1$	$70.907$	\(\Q\)	None	✓				1110.2.a.m	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(5\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+5q^{7}+q^{9}+5q^{11}-q^{13}+\cdots\)
8880.2.a.j	$8880$	$2$	8880.a	1.a	$1$	$1$	$1$	$70.907$	\(\Q\)	None	✓				4440.2.a.i	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(-3\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-3q^{7}+q^{9}+q^{11}+3q^{13}+\cdots\)
8880.2.a.k	$8880$	$2$	8880.a	1.a	$1$	$1$	$1$	$70.907$	\(\Q\)	None	✓				555.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(-2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{7}+q^{9}-q^{13}-q^{15}+\cdots\)
8880.2.a.l	$8880$	$2$	8880.a	1.a	$1$	$1$	$1$	$70.907$	\(\Q\)	None	✓				4440.2.a.h	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}-3q^{11}+6q^{13}+\cdots\)
8880.2.a.m	$8880$	$2$	8880.a	1.a	$1$	$1$	$1$	$70.907$	\(\Q\)	None	✓				4440.2.a.g	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(2\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+2q^{7}+q^{9}-3q^{13}-q^{15}+\cdots\)
8880.2.a.n	$8880$	$2$	8880.a	1.a	$1$	$1$	$1$	$70.907$	\(\Q\)	None	✓				1110.2.a.h	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(4\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+4q^{7}+q^{9}-6q^{11}+2q^{13}+\cdots\)
8880.2.a.o	$8880$	$2$	8880.a	1.a	$1$	$1$	$1$	$70.907$	\(\Q\)	None	✓				2220.2.a.b	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-4\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-4q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
8880.2.a.p	$8880$	$2$	8880.a	1.a	$1$	$1$	$1$	$70.907$	\(\Q\)	None	✓				1110.2.a.c	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-3\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-3q^{7}+q^{9}+3q^{11}-5q^{13}+\cdots\)
8880.2.a.q	$8880$	$2$	8880.a	1.a	$1$	$1$	$1$	$70.907$	\(\Q\)	None	✓				4440.2.a.d	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-3\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-3q^{7}+q^{9}+3q^{11}-3q^{13}+\cdots\)
8880.2.a.r	$8880$	$2$	8880.a	1.a	$1$	$1$	$1$	$70.907$	\(\Q\)	None	✓				2220.2.a.a	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{7}+q^{9}-4q^{11}+5q^{13}+\cdots\)
8880.2.a.s	$8880$	$2$	8880.a	1.a	$1$	$1$	$1$	$70.907$	\(\Q\)	None	✓				1110.2.a.b	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
8880.2.a.t	$8880$	$2$	8880.a	1.a	$1$	$1$	$1$	$70.907$	\(\Q\)	None	✓				4440.2.a.c	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}-2q^{11}+6q^{13}+\cdots\)
8880.2.a.u	$8880$	$2$	8880.a	1.a	$1$	$1$	$1$	$70.907$	\(\Q\)	None	✓				4440.2.a.b	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}-2q^{13}-q^{15}-2q^{17}+\cdots\)
8880.2.a.v	$8880$	$2$	8880.a	1.a	$1$	$1$	$1$	$70.907$	\(\Q\)	None	✓				1110.2.a.i	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}+2q^{11}-2q^{13}+\cdots\)
8880.2.a.w	$8880$	$2$	8880.a	1.a	$1$	$1$	$1$	$70.907$	\(\Q\)	None	✓				1110.2.a.a	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(4\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+4q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
8880.2.a.x	$8880$	$2$	8880.a	1.a	$1$	$1$	$1$	$70.907$	\(\Q\)	None	✓				4440.2.a.a	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(4\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+4q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
8880.2.a.y	$8880$	$2$	8880.a	1.a	$1$	$1$	$1$	$70.907$	\(\Q\)	None	✓				1110.2.a.l	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-3\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-3q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
8880.2.a.z	$8880$	$2$	8880.a	1.a	$1$	$1$	$1$	$70.907$	\(\Q\)	None	✓				1110.2.a.d	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-3\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-3q^{7}+q^{9}+5q^{11}-2q^{13}+\cdots\)
8880.2.a.ba	$8880$	$2$	8880.a	1.a	$1$	$1$	$1$	$70.907$	\(\Q\)	None	✓				1110.2.a.k	$1$	$1$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
8880.2.a.bb	$8880$	$2$	8880.a	1.a	$1$	$1$	$1$	$70.907$	\(\Q\)	None	✓				4440.2.a.e	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}+6q^{13}+q^{15}+2q^{17}+\cdots\)
8880.2.a.bc	$8880$	$2$	8880.a	1.a	$1$	$1$	$1$	$70.907$	\(\Q\)	None	✓				1110.2.a.j	$1$	$0$	\(0\)	\(1\)	\(1\)	\(3\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+3q^{7}+q^{9}+5q^{11}-2q^{13}+\cdots\)
8880.2.a.bd	$8880$	$2$	8880.a	1.a	$1$	$2$	$2$	$70.907$	\(\Q(\sqrt{13}) \)	None	✓				555.2.a.g	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}-\beta q^{11}+(1+\cdots)q^{13}+\cdots\)
8880.2.a.be	$8880$	$2$	8880.a	1.a	$1$	$2$	$2$	$70.907$	\(\Q(\sqrt{13}) \)	None	✓				2220.2.a.f	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+(1-2\beta )q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
8880.2.a.bf	$8880$	$2$	8880.a	1.a	$1$	$2$	$2$	$70.907$	\(\Q(\sqrt{5}) \)	None	✓				555.2.a.e	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}+(5-\beta )q^{11}+\cdots\)
8880.2.a.bg	$8880$	$2$	8880.a	1.a	$1$	$2$	$2$	$70.907$	\(\Q(\sqrt{17}) \)	None	✓				4440.2.a.l	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(3\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+(1+\beta )q^{7}+q^{9}+(1-\beta )q^{11}+\cdots\)
8880.2.a.bh	$8880$	$2$	8880.a	1.a	$1$	$2$	$2$	$70.907$	\(\Q(\sqrt{113}) \)	None	✓				1110.2.a.q	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(-6\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-3q^{7}+q^{9}+q^{11}+(1+\cdots)q^{13}+\cdots\)
8880.2.a.bi	$8880$	$2$	8880.a	1.a	$1$	$2$	$2$	$70.907$	\(\Q(\sqrt{5}) \)	None	✓				4440.2.a.n	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(1-2\beta )q^{7}+q^{9}+(1+\beta )q^{11}+\cdots\)
8880.2.a.bj	$8880$	$2$	8880.a	1.a	$1$	$2$	$2$	$70.907$	\(\Q(\sqrt{5}) \)	None	✓				555.2.a.c	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(4\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(1+2\beta )q^{7}+q^{9}+(3-3\beta )q^{11}+\cdots\)
8880.2.a.bk	$8880$	$2$	8880.a	1.a	$1$	$2$	$2$	$70.907$	\(\Q(\sqrt{5}) \)	None	✓				4440.2.a.m	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(4\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(1+2\beta )q^{7}+q^{9}+(4-3\beta )q^{11}+\cdots\)
8880.2.a.bl	$8880$	$2$	8880.a	1.a	$1$	$2$	$2$	$70.907$	\(\Q(\sqrt{5}) \)	None	✓				2220.2.a.g	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(6\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+3q^{7}+q^{9}+(4-3\beta )q^{11}+\cdots\)
8880.2.a.bm	$8880$	$2$	8880.a	1.a	$1$	$2$	$2$	$70.907$	\(\Q(\sqrt{5}) \)	None	✓				4440.2.a.j	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+(1-2\beta )q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
8880.2.a.bn	$8880$	$2$	8880.a	1.a	$1$	$2$	$2$	$70.907$	\(\Q(\sqrt{5}) \)	None	✓				555.2.a.f	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+(1-2\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
8880.2.a.bo	$8880$	$2$	8880.a	1.a	$1$	$2$	$2$	$70.907$	\(\Q(\sqrt{5}) \)	None	✓				2220.2.a.e	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}+\beta q^{11}+q^{13}+\cdots\)
8880.2.a.bp	$8880$	$2$	8880.a	1.a	$1$	$2$	$2$	$70.907$	\(\Q(\sqrt{17}) \)	None	✓				1110.2.a.r	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}+(1+2\beta )q^{11}+\cdots\)
8880.2.a.bq	$8880$	$2$	8880.a	1.a	$1$	$2$	$2$	$70.907$	\(\Q(\sqrt{109}) \)	None	✓				2220.2.a.d	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(6\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+3q^{7}+q^{9}+(-1+\beta )q^{11}+\cdots\)
8880.2.a.br	$8880$	$2$	8880.a	1.a	$1$	$2$	$2$	$70.907$	\(\Q(\sqrt{33}) \)	None	✓				1110.2.a.p	$1$	$0$	\(0\)	\(2\)	\(2\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+\beta q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
8880.2.a.bs	$8880$	$2$	8880.a	1.a	$1$	$2$	$2$	$70.907$	\(\Q(\sqrt{17}) \)	None	✓				4440.2.a.k	$1$	$0$	\(0\)	\(2\)	\(2\)	\(2\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+2\beta q^{7}+q^{9}+4q^{11}+\cdots\)
8880.2.a.bt	$8880$	$2$	8880.a	1.a	$1$	$2$	$2$	$70.907$	\(\Q(\sqrt{13}) \)	None	✓				555.2.a.d	$1$	$1$	\(0\)	\(2\)	\(2\)	\(6\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+3q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
8880.2.a.bu	$8880$	$2$	8880.a	1.a	$1$	$3$	$3$	$70.907$	3.3.621.1	None	✓		✓		2220.2.a.j	$1$	$0$	\(0\)	\(-3\)	\(-3\)	\(0\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+\beta _{2}q^{7}+q^{9}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
8880.2.a.bv	$8880$	$2$	8880.a	1.a	$1$	$3$	$3$	$70.907$	3.3.469.1	None	✓				4440.2.a.s	$1$	$0$	\(0\)	\(-3\)	\(-3\)	\(2\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+(\beta _{1}-\beta _{2})q^{7}+q^{9}+(-2\beta _{1}+\cdots)q^{11}+\cdots\)
8880.2.a.bw	$8880$	$2$	8880.a	1.a	$1$	$3$	$3$	$70.907$	3.3.229.1	None	✓				4440.2.a.r	$1$	$1$	\(0\)	\(-3\)	\(-3\)	\(3\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}+(1-2\beta _{1}+\beta _{2})q^{11}+\cdots\)
8880.2.a.bx	$8880$	$2$	8880.a	1.a	$1$	$3$	$3$	$70.907$	3.3.229.1	None	✓		✓		555.2.a.i	$1$	$0$	\(0\)	\(-3\)	\(3\)	\(4\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(1+\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)
8880.2.a.by	$8880$	$2$	8880.a	1.a	$1$	$3$	$3$	$70.907$	3.3.2429.1	None	✓				4440.2.a.o	$1$	$0$	\(0\)	\(3\)	\(-3\)	\(-2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+(-1+\beta _{1})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
8880.2.a.bz	$8880$	$2$	8880.a	1.a	$1$	$3$	$3$	$70.907$	3.3.621.1	None	✓		✓		2220.2.a.i	$1$	$1$	\(0\)	\(3\)	\(3\)	\(-6\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+(-2+\beta _{2})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
8880.2.a.ca	$8880$	$2$	8880.a	1.a	$1$	$3$	$3$	$70.907$	3.3.469.1	None	✓				555.2.a.h	$1$	$0$	\(0\)	\(3\)	\(3\)	\(-4\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+(-2+\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)
8880.2.a.cb	$8880$	$2$	8880.a	1.a	$1$	$3$	$3$	$70.907$	3.3.229.1	None	✓				4440.2.a.q	$1$	$1$	\(0\)	\(3\)	\(3\)	\(-3\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}+(\beta _{1}-2\beta _{2})q^{11}+\cdots\)
8880.2.a.cc	$8880$	$2$	8880.a	1.a	$1$	$3$	$3$	$70.907$	3.3.2677.1	None	✓				4440.2.a.p	$1$	$0$	\(0\)	\(3\)	\(3\)	\(3\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}+\beta _{1}q^{11}+(-1+\cdots)q^{13}+\cdots\)
8880.2.a.cd	$8880$	$2$	8880.a	1.a	$1$	$3$	$3$	$70.907$	3.3.1101.1	None	✓				2220.2.a.h	$1$	$0$	\(0\)	\(3\)	\(3\)	\(4\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+(1-\beta _{2})q^{7}+q^{9}-\beta _{1}q^{11}+\cdots\)
8880.2.a.ce	$8880$	$2$	8880.a	1.a	$1$	$4$	$4$	$70.907$	\(\Q(\sqrt{50 +2 \sqrt{33}})\)	None	✓		✓		4440.2.a.v	$1$	$1$	\(0\)	\(-4\)	\(-4\)	\(-3\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+(-1-\beta _{2})q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
8880.2.a.cf	$8880$	$2$	8880.a	1.a	$1$	$4$	$4$	$70.907$	\(\Q(\sqrt{19 +2 \sqrt{89}})\)	None	✓				2220.2.a.k	$1$	$1$	\(0\)	\(-4\)	\(4\)	\(-4\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(-1+\beta _{3})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
8880.2.a.cg	$8880$	$2$	8880.a	1.a	$1$	$4$	$4$	$70.907$	4.4.54764.1	None	✓				1110.2.a.s	$1$	$1$	\(0\)	\(-4\)	\(4\)	\(-4\)		$-$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(-1-\beta _{2})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
8880.2.a.ch	$8880$	$2$	8880.a	1.a	$1$	$4$	$4$	$70.907$	4.4.119893.1	None	✓		✓		4440.2.a.t	$1$	$1$	\(0\)	\(4\)	\(-4\)	\(1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+\beta _{3}q^{7}+q^{9}+(-2-\beta _{1}+\cdots)q^{11}+\cdots\)
8880.2.a.ci	$8880$	$2$	8880.a	1.a	$1$	$4$	$4$	$70.907$	4.4.48389.1	None	✓		✓		4440.2.a.u	$1$	$1$	\(0\)	\(4\)	\(4\)	\(-1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+(-\beta _{1}-\beta _{3})q^{7}+q^{9}+\cdots\)
8880.2.a.cj	$8880$	$2$	8880.a	1.a	$1$	$5$	$5$	$70.907$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓		✓		4440.2.a.y	$1$	$0$	\(0\)	\(-5\)	\(-5\)	\(-3\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+(-1+\beta _{1})q^{7}+q^{9}-\beta _{3}q^{11}+\cdots\)
8880.2.a.ck	$8880$	$2$	8880.a	1.a	$1$	$5$	$5$	$70.907$	5.5.13350941.1	None	✓		✓		4440.2.a.z	$1$	$1$	\(0\)	\(-5\)	\(5\)	\(-7\)		$+$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(-1+\beta _{2})q^{7}+q^{9}+\beta _{4}q^{11}+\cdots\)
8880.2.a.cl	$8880$	$2$	8880.a	1.a	$1$	$5$	$5$	$70.907$	5.5.20193189.1	None	✓		✓		4440.2.a.w	$1$	$0$	\(0\)	\(5\)	\(-5\)	\(-2\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+\beta _{4}q^{7}+q^{9}+(-\beta _{1}-\beta _{4})q^{11}+\cdots\)
8880.2.a.cm	$8880$	$2$	8880.a	1.a	$1$	$5$	$5$	$70.907$	5.5.600268.1	None	✓		✓		555.2.a.j	$1$	$0$	\(0\)	\(5\)	\(-5\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+(-\beta _{3}+\beta _{4})q^{7}+q^{9}+\cdots\)
8880.2.a.cn	$8880$	$2$	8880.a	1.a	$1$	$5$	$5$	$70.907$	5.5.15147037.1	None	✓		✓		4440.2.a.x	$1$	$0$	\(0\)	\(5\)	\(5\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-\beta _{2}q^{7}+q^{9}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
8880.2.a.co	$8880$	$2$	8880.a	1.a	$1$	$6$	$6$	$70.907$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓		✓		4440.2.a.ba	$1$	$0$	\(0\)	\(-6\)	\(6\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+\beta _{1}q^{7}+q^{9}+(-2+\beta _{4}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8880))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8880)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(111))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(148))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(185))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(222))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(296))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(370))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(444))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(555))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(592))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(740))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(888))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1480))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1776))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2220))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2960))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4440))\)\(^{\oplus 2}\)