Space of modular forms of level 5880, weight 2, and trivial character

• Label: 5880.2.a
• Level: $5880$
• Weight: $2$
• Character orbit: 5880.a
• Rep. character: $\chi_{5880}(1,\cdot)$
• Character field: $\Q$
• Dimension: $82$
• Newform subspaces: $53$
• Sturm bound: $2688$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 5880 = 2^{3} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5880.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 53 \)
Sturm bound:			\(2688\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(11\), \(13\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5880))\).

	Total	New	Old
Modular forms	1408	82	1326
Cusp forms	1281	82	1199
Eisenstein series	127	0	127

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

\(2\)	\(3\)	\(5\)	\(7\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	$+$	\(4\)
\(+\)	\(+\)	\(+\)	\(-\)	$-$	\(6\)
\(+\)	\(+\)	\(-\)	\(+\)	$-$	\(5\)
\(+\)	\(+\)	\(-\)	\(-\)	$+$	\(6\)
\(+\)	\(-\)	\(+\)	\(+\)	$-$	\(7\)
\(+\)	\(-\)	\(+\)	\(-\)	$+$	\(3\)
\(+\)	\(-\)	\(-\)	\(+\)	$+$	\(4\)
\(+\)	\(-\)	\(-\)	\(-\)	$-$	\(6\)
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(5\)
\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(4\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(4\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(6\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(7\)
\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(3\)
Plus space				\(+\)	\(34\)
Minus space				\(-\)	\(48\)

Trace form

\( 82 q - 2 q^{3} + 82 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5880))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	7
5880.2.a.a	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}-4q^{11}-6q^{13}+\cdots\)
5880.2.a.b	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}-2q^{11}-6q^{13}+\cdots\)
5880.2.a.c	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}-2q^{11}+q^{13}+q^{15}+\cdots\)
5880.2.a.d	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}+2q^{13}+q^{15}+2q^{17}+\cdots\)
5880.2.a.e	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}+2q^{11}+5q^{13}+\cdots\)
5880.2.a.f	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}+3q^{11}+q^{13}+q^{15}+\cdots\)
5880.2.a.g	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
5880.2.a.h	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots\)
5880.2.a.i	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}-6q^{11}+2q^{13}+\cdots\)
5880.2.a.j	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}-4q^{11}+6q^{13}+\cdots\)
5880.2.a.k	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}-q^{11}-5q^{13}-q^{15}+\cdots\)
5880.2.a.l	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}-6q^{13}-q^{15}+2q^{17}+\cdots\)
5880.2.a.m	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}-2q^{13}-q^{15}-2q^{17}+\cdots\)
5880.2.a.n	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}-2q^{13}-q^{15}-2q^{17}+\cdots\)
5880.2.a.o	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}-q^{13}-q^{15}+2q^{17}+\cdots\)
5880.2.a.p	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}+6q^{13}-q^{15}+2q^{17}+\cdots\)
5880.2.a.q	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}+4q^{11}-5q^{13}+\cdots\)
5880.2.a.r	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
5880.2.a.s	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}-6q^{11}-2q^{13}+\cdots\)
5880.2.a.t	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
5880.2.a.u	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}-q^{11}+5q^{13}-q^{15}+\cdots\)
5880.2.a.v	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}-2q^{13}-q^{15}-2q^{17}+\cdots\)
5880.2.a.w	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}+q^{13}-q^{15}-2q^{17}+\cdots\)
5880.2.a.x	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}+2q^{13}-q^{15}+2q^{17}+\cdots\)
5880.2.a.y	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
5880.2.a.z	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
5880.2.a.ba	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}+4q^{11}+5q^{13}+\cdots\)
5880.2.a.bb	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
5880.2.a.bc	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}-2q^{11}-q^{13}+q^{15}+\cdots\)
5880.2.a.bd	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}-2q^{11}+6q^{13}+\cdots\)
5880.2.a.be	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}-2q^{13}+q^{15}-2q^{17}+\cdots\)
5880.2.a.bf	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}+2q^{13}+q^{15}-6q^{17}+\cdots\)
5880.2.a.bg	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}+2q^{11}-5q^{13}+\cdots\)
5880.2.a.bh	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}+3q^{11}-q^{13}+q^{15}+\cdots\)
5880.2.a.bi	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}+4q^{11}-6q^{13}+\cdots\)
5880.2.a.bj	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
5880.2.a.bk	$5880$	$2$	5880.a	1.a	$1$	$2$	$2$	$46.952$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(0\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}-4q^{11}+(2-2\beta )q^{13}+\cdots\)
5880.2.a.bl	$5880$	$2$	5880.a	1.a	$1$	$2$	$2$	$46.952$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(0\)		$+$	$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}+\beta q^{11}-2q^{13}+\cdots\)
5880.2.a.bm	$5880$	$2$	5880.a	1.a	$1$	$2$	$2$	$46.952$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(0\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}+\beta q^{11}+(1+3\beta )q^{13}+\cdots\)
5880.2.a.bn	$5880$	$2$	5880.a	1.a	$1$	$2$	$2$	$46.952$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}+2\beta q^{11}+2q^{13}+\cdots\)
5880.2.a.bo	$5880$	$2$	5880.a	1.a	$1$	$2$	$2$	$46.952$	\(\Q(\sqrt{7}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}+(1+\beta )q^{11}+(2+\beta )q^{13}+\cdots\)
5880.2.a.bp	$5880$	$2$	5880.a	1.a	$1$	$2$	$2$	$46.952$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}+2\beta q^{11}-2q^{13}+\cdots\)
5880.2.a.bq	$5880$	$2$	5880.a	1.a	$1$	$2$	$2$	$46.952$	\(\Q(\sqrt{7}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}+(1+\beta )q^{11}+(-2+\cdots)q^{13}+\cdots\)
5880.2.a.br	$5880$	$2$	5880.a	1.a	$1$	$2$	$2$	$46.952$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}-4q^{11}+(-2+2\beta )q^{13}+\cdots\)
5880.2.a.bs	$5880$	$2$	5880.a	1.a	$1$	$2$	$2$	$46.952$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}+\beta q^{11}+(-1-3\beta )q^{13}+\cdots\)
5880.2.a.bt	$5880$	$2$	5880.a	1.a	$1$	$3$	$3$	$46.952$	3.3.3576.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-3\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}+\beta _{2}q^{11}-\beta _{1}q^{13}+\cdots\)
5880.2.a.bu	$5880$	$2$	5880.a	1.a	$1$	$3$	$3$	$46.952$	3.3.3132.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(3\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}+(-1-\beta _{1}+\beta _{2})q^{11}+\cdots\)
5880.2.a.bv	$5880$	$2$	5880.a	1.a	$1$	$3$	$3$	$46.952$	3.3.3132.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(-3\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}+(-1-\beta _{1}+\beta _{2})q^{11}+\cdots\)
5880.2.a.bw	$5880$	$2$	5880.a	1.a	$1$	$3$	$3$	$46.952$	3.3.3576.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(3\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}+\beta _{2}q^{11}+\beta _{1}q^{13}+\cdots\)
5880.2.a.bx	$5880$	$2$	5880.a	1.a	$1$	$4$	$4$	$46.952$	4.4.22592.1	None	✓	$1$	$0$	\(0\)	\(-4\)	\(-4\)	\(0\)		$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}+(1+\beta _{1}-\beta _{3})q^{11}+\cdots\)
5880.2.a.by	$5880$	$2$	5880.a	1.a	$1$	$4$	$4$	$46.952$	4.4.10304.1	None	✓	$1$	$0$	\(0\)	\(-4\)	\(4\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}+(1+\beta _{2}-\beta _{3})q^{11}+\cdots\)
5880.2.a.bz	$5880$	$2$	5880.a	1.a	$1$	$4$	$4$	$46.952$	4.4.10304.1	None	✓	$1$	$0$	\(0\)	\(4\)	\(-4\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}+(1+\beta _{2}-\beta _{3})q^{11}+\cdots\)
5880.2.a.ca	$5880$	$2$	5880.a	1.a	$1$	$4$	$4$	$46.952$	4.4.22592.1	None	✓	$1$	$0$	\(0\)	\(4\)	\(4\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}+(1+\beta _{1}-\beta _{3})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5880))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5880)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(60))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(420))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(490))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(588))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(735))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(840))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(980))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1470))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1960))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2940))\)\(^{\oplus 2}\)