Space of modular forms of level 5600, weight 2, and trivial character

• Label: 5600.2.a
• Level: $5600$
• Weight: $2$
• Character orbit: 5600.a
• Rep. character: $\chi_{5600}(1,\cdot)$
• Character field: $\Q$
• Dimension: $114$
• Newform subspaces: $52$
• Sturm bound: $1920$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 5600 = 2^{5} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5600.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 52 \)
Sturm bound:			\(1920\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(3\), \(11\), \(13\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5600))\).

	Total	New	Old
Modular forms	1008	114	894
Cusp forms	913	114	799
Eisenstein series	95	0	95

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

\(2\)	\(5\)	\(7\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(14\)
\(+\)	\(+\)	\(-\)	$-$	\(16\)
\(+\)	\(-\)	\(+\)	$-$	\(16\)
\(+\)	\(-\)	\(-\)	$+$	\(12\)
\(-\)	\(+\)	\(+\)	$-$	\(13\)
\(-\)	\(+\)	\(-\)	$+$	\(11\)
\(-\)	\(-\)	\(+\)	$+$	\(14\)
\(-\)	\(-\)	\(-\)	$-$	\(18\)
Plus space			\(+\)	\(51\)
Minus space			\(-\)	\(63\)

Trace form

\( 114 q + 122 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5600))\) 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	5	7
5600.2.a.a	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-q^{7}+6q^{9}+q^{11}+q^{13}+\cdots\)
5600.2.a.b	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-q^{7}+6q^{9}+3q^{11}-q^{13}+\cdots\)
5600.2.a.c	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{7}+q^{9}+4q^{11}+4q^{13}+\cdots\)
5600.2.a.d	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}-2q^{9}-3q^{11}+2q^{13}+\cdots\)
5600.2.a.e	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}-2q^{9}-3q^{11}+7q^{13}+\cdots\)
5600.2.a.f	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}-2q^{9}-q^{11}-3q^{13}+\cdots\)
5600.2.a.g	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}-2q^{9}-q^{11}+q^{13}-q^{17}+\cdots\)
5600.2.a.h	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}-2q^{9}+3q^{11}-2q^{13}+\cdots\)
5600.2.a.i	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{7}-2q^{9}+5q^{11}-5q^{13}+\cdots\)
5600.2.a.j	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}-3q^{9}+2q^{13}-2q^{17}+8q^{19}+\cdots\)
5600.2.a.k	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{7}-3q^{9}+4q^{11}-2q^{13}-6q^{17}+\cdots\)
5600.2.a.l	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-3q^{9}-4q^{11}-2q^{13}-6q^{17}+\cdots\)
5600.2.a.m	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-3q^{9}+2q^{13}-2q^{17}-8q^{19}+\cdots\)
5600.2.a.n	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}-2q^{9}-5q^{11}-5q^{13}+\cdots\)
5600.2.a.o	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}-2q^{9}-3q^{11}-2q^{13}+\cdots\)
5600.2.a.p	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}-2q^{9}+q^{11}-3q^{13}+\cdots\)
5600.2.a.q	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}-2q^{9}+q^{11}+q^{13}-q^{17}+\cdots\)
5600.2.a.r	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}-2q^{9}+3q^{11}+2q^{13}+\cdots\)
5600.2.a.s	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}-2q^{9}+3q^{11}+7q^{13}+\cdots\)
5600.2.a.t	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots\)
5600.2.a.u	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+q^{7}+6q^{9}-3q^{11}-q^{13}+\cdots\)
5600.2.a.v	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(0\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+q^{7}+6q^{9}-q^{11}+q^{13}+\cdots\)
5600.2.a.w	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	\(\Q(\sqrt{5}) \)	None	✓	$2$	$1$	\(0\)	\(-2\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{7}-2q^{9}-\beta q^{11}+\beta q^{13}+\cdots\)
5600.2.a.x	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+q^{7}+(1-2\beta )q^{9}+(-2+\cdots)q^{11}+\cdots\)
5600.2.a.y	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+q^{7}+(1-2\beta )q^{9}+(2+\cdots)q^{11}+\cdots\)
5600.2.a.z	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+q^{7}+(3+2\beta )q^{9}+(2+\cdots)q^{11}+\cdots\)
5600.2.a.ba	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+q^{7}+(1+\beta )q^{9}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
5600.2.a.bb	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+q^{7}+(1+\beta )q^{9}+(4-\beta )q^{11}+\cdots\)
5600.2.a.bc	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{7}+3q^{9}+(-1-\beta )q^{11}+\cdots\)
5600.2.a.bd	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{7}+3q^{9}+(1+\beta )q^{11}+(4+\cdots)q^{13}+\cdots\)
5600.2.a.be	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{7}+3q^{9}+(-1+\beta )q^{11}+\cdots\)
5600.2.a.bf	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{7}+3q^{9}+(1-\beta )q^{11}+(-4+\cdots)q^{13}+\cdots\)
5600.2.a.bg	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{7}+(1+\beta )q^{9}+(-4+\beta )q^{11}+\cdots\)
5600.2.a.bh	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{7}+(1+\beta )q^{9}-\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
5600.2.a.bi	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-q^{7}+(1+2\beta )q^{9}+(-2+\cdots)q^{11}+\cdots\)
5600.2.a.bj	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(0\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-q^{7}+(1+2\beta )q^{9}+(2-\beta )q^{11}+\cdots\)
5600.2.a.bk	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-q^{7}+(3+2\beta )q^{9}+(-2+\cdots)q^{11}+\cdots\)
5600.2.a.bl	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	\(\Q(\sqrt{5}) \)	None	✓	$2$	$1$	\(0\)	\(2\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}-2q^{9}+\beta q^{11}+\beta q^{13}+\cdots\)
5600.2.a.bm	$5600$	$2$	5600.a	1.a	$1$	$3$	$3$	$44.716$	3.3.1016.1	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+(-3+\cdots)q^{11}+\cdots\)
5600.2.a.bn	$5600$	$2$	5600.a	1.a	$1$	$3$	$3$	$44.716$	3.3.1016.1	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+(3+\cdots)q^{11}+\cdots\)
5600.2.a.bo	$5600$	$2$	5600.a	1.a	$1$	$3$	$3$	$44.716$	3.3.1016.1	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+(-3+\cdots)q^{11}+\cdots\)
5600.2.a.bp	$5600$	$2$	5600.a	1.a	$1$	$3$	$3$	$44.716$	3.3.1016.1	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+(3+\cdots)q^{11}+\cdots\)
5600.2.a.bq	$5600$	$2$	5600.a	1.a	$1$	$4$	$4$	$44.716$	4.4.48396.1	None	✓	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-4\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots\)
5600.2.a.br	$5600$	$2$	5600.a	1.a	$1$	$4$	$4$	$44.716$	4.4.48396.1	None	✓	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-4\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots\)
5600.2.a.bs	$5600$	$2$	5600.a	1.a	$1$	$4$	$4$	$44.716$	4.4.48396.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots\)
5600.2.a.bt	$5600$	$2$	5600.a	1.a	$1$	$4$	$4$	$44.716$	4.4.48396.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots\)
5600.2.a.bu	$5600$	$2$	5600.a	1.a	$1$	$5$	$5$	$44.716$	5.5.504568.1	None	✓	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(5\)		$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+q^{7}+(1+\beta _{2}+\beta _{3})q^{9}+(-1+\cdots)q^{11}+\cdots\)
5600.2.a.bv	$5600$	$2$	5600.a	1.a	$1$	$5$	$5$	$44.716$	5.5.504568.1	None	✓	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(5\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+q^{7}+(1+\beta _{2}+\beta _{3})q^{9}+(1+\cdots)q^{11}+\cdots\)
5600.2.a.bw	$5600$	$2$	5600.a	1.a	$1$	$5$	$5$	$44.716$	5.5.504568.1	None	✓	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-5\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}-q^{7}+(1+\beta _{2}+\beta _{3})q^{9}+(-1+\cdots)q^{11}+\cdots\)
5600.2.a.bx	$5600$	$2$	5600.a	1.a	$1$	$5$	$5$	$44.716$	5.5.504568.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(0\)	\(-5\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}-q^{7}+(1+\beta _{2}+\beta _{3})q^{9}+(1+\cdots)q^{11}+\cdots\)
5600.2.a.by	$5600$	$2$	5600.a	1.a	$1$	$6$	$6$	$44.716$	6.6.29935424.1	None	✓	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(-6\)		$+$	$-$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{7}+(1+\beta _{1}-\beta _{2})q^{9}+\beta _{4}q^{11}+\cdots\)
5600.2.a.bz	$5600$	$2$	5600.a	1.a	$1$	$6$	$6$	$44.716$	6.6.29935424.1	None	✓	$2$	$0$	\(0\)	\(2\)	\(0\)	\(6\)		$-$	$-$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{7}+(1+\beta _{1}-\beta _{2})q^{9}+\beta _{4}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5600))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5600)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(350))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(400))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(560))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(700))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(800))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1400))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2800))\)\(^{\oplus 2}\)