Space of modular forms of level 3520, weight 2, and trivial character

• Label: 3520.2.a
• Level: $3520$
• Weight: $2$
• Character orbit: 3520.a
• Rep. character: $\chi_{3520}(1,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $52$
• Sturm bound: $1152$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 3520 = 2^{6} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3520.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 52 \)
Sturm bound:			\(1152\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(3\), \(7\), \(13\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3520))\).

	Total	New	Old
Modular forms	600	80	520
Cusp forms	553	80	473
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.

\(2\)	\(5\)	\(11\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(10\)
\(+\)	\(+\)	\(-\)	\(-\)	\(12\)
\(+\)	\(-\)	\(+\)	\(-\)	\(10\)
\(+\)	\(-\)	\(-\)	\(+\)	\(8\)
\(-\)	\(+\)	\(+\)	\(-\)	\(10\)
\(-\)	\(+\)	\(-\)	\(+\)	\(8\)
\(-\)	\(-\)	\(+\)	\(+\)	\(10\)
\(-\)	\(-\)	\(-\)	\(-\)	\(12\)
Plus space			\(+\)	\(36\)
Minus space			\(-\)	\(44\)

Trace form

\( 80 q + 80 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3520))\) 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	11
3520.2.a.a	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(-1\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-q^{5}+q^{7}+6q^{9}+q^{11}+6q^{13}+\cdots\)
3520.2.a.b	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+q^{9}-q^{11}-4q^{13}+\cdots\)
3520.2.a.c	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+q^{9}-q^{11}+2q^{15}+\cdots\)
3520.2.a.d	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+4q^{7}+q^{9}-q^{11}+4q^{13}+\cdots\)
3520.2.a.e	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+4q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
3520.2.a.f	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}-2q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
3520.2.a.g	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-3q^{7}-2q^{9}+q^{11}+2q^{13}+\cdots\)
3520.2.a.h	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-3q^{7}-2q^{9}+q^{11}+6q^{13}+\cdots\)
3520.2.a.i	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}-2q^{9}-q^{11}+2q^{13}+\cdots\)
3520.2.a.j	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-3q^{7}-2q^{9}-q^{11}+2q^{13}+\cdots\)
3520.2.a.k	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}-2q^{9}+q^{11}-2q^{13}+\cdots\)
3520.2.a.l	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(5\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+5q^{7}-2q^{9}-q^{11}-2q^{13}+\cdots\)
3520.2.a.m	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-4q^{7}-3q^{9}-q^{11}-6q^{13}+\cdots\)
3520.2.a.n	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{9}-q^{11}-2q^{13}+6q^{17}+\cdots\)
3520.2.a.o	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{9}-q^{11}+2q^{13}-2q^{17}+\cdots\)
3520.2.a.p	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{9}+q^{11}-2q^{13}+6q^{17}+\cdots\)
3520.2.a.q	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{9}+q^{11}+2q^{13}-2q^{17}+\cdots\)
3520.2.a.r	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{7}-3q^{9}+q^{11}-6q^{13}+\cdots\)
3520.2.a.s	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-3q^{9}-q^{11}+4q^{13}+\cdots\)
3520.2.a.t	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-3q^{9}+q^{11}+8q^{19}+\cdots\)
3520.2.a.u	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-3q^{9}-q^{11}-8q^{19}+\cdots\)
3520.2.a.v	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-3q^{9}+q^{11}+4q^{13}+\cdots\)
3520.2.a.w	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}-2q^{9}+q^{11}+2q^{13}+\cdots\)
3520.2.a.x	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+3q^{7}-2q^{9}-q^{11}+2q^{13}+\cdots\)
3520.2.a.y	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+3q^{7}-2q^{9}-q^{11}+6q^{13}+\cdots\)
3520.2.a.z	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(-5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-5q^{7}-2q^{9}+q^{11}-2q^{13}+\cdots\)
3520.2.a.ba	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}-2q^{9}-q^{11}-2q^{13}+\cdots\)
3520.2.a.bb	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+3q^{7}-2q^{9}+q^{11}+2q^{13}+\cdots\)
3520.2.a.bc	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}-4q^{7}+q^{9}-q^{11}-4q^{13}+\cdots\)
3520.2.a.bd	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}-4q^{7}+q^{9}+q^{11}+4q^{13}+\cdots\)
3520.2.a.be	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+q^{9}+q^{11}-4q^{13}+\cdots\)
3520.2.a.bf	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+q^{9}+q^{11}-2q^{15}+\cdots\)
3520.2.a.bg	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(1\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}+2q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
3520.2.a.bh	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-q^{5}-q^{7}+6q^{9}-q^{11}+6q^{13}+\cdots\)
3520.2.a.bi	$3520$	$2$	3520.a	1.a	$1$	$2$	$2$	$28.107$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(4\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+q^{5}+2q^{7}+(3+2\beta )q^{9}+\cdots\)
3520.2.a.bj	$3520$	$2$	3520.a	1.a	$1$	$2$	$2$	$28.107$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-q^{5}-\beta q^{7}+(5+\beta )q^{9}-q^{11}+\cdots\)
3520.2.a.bk	$3520$	$2$	3520.a	1.a	$1$	$2$	$2$	$28.107$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-q^{5}+\beta q^{7}+(1+\beta )q^{9}+q^{11}+\cdots\)
3520.2.a.bl	$3520$	$2$	3520.a	1.a	$1$	$2$	$2$	$28.107$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+q^{5}+(2-\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
3520.2.a.bm	$3520$	$2$	3520.a	1.a	$1$	$2$	$2$	$28.107$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(5\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+q^{5}+(2+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
3520.2.a.bn	$3520$	$2$	3520.a	1.a	$1$	$2$	$2$	$28.107$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-4\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}-2q^{7}+5q^{9}-q^{11}+\cdots\)
3520.2.a.bo	$3520$	$2$	3520.a	1.a	$1$	$2$	$2$	$28.107$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}+2q^{7}+5q^{9}+q^{11}+\cdots\)
3520.2.a.bp	$3520$	$2$	3520.a	1.a	$1$	$2$	$2$	$28.107$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}-\beta q^{7}+(1+\beta )q^{9}-q^{11}+\cdots\)
3520.2.a.bq	$3520$	$2$	3520.a	1.a	$1$	$2$	$2$	$28.107$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}+\beta q^{7}+(5+\beta )q^{9}+q^{11}+\cdots\)
3520.2.a.br	$3520$	$2$	3520.a	1.a	$1$	$2$	$2$	$28.107$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(2\)	\(-5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}+(-2-\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
3520.2.a.bs	$3520$	$2$	3520.a	1.a	$1$	$2$	$2$	$28.107$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}+(-2+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
3520.2.a.bt	$3520$	$2$	3520.a	1.a	$1$	$2$	$2$	$28.107$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(-4\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+q^{5}-2q^{7}+(3+2\beta )q^{9}+\cdots\)
3520.2.a.bu	$3520$	$2$	3520.a	1.a	$1$	$3$	$3$	$28.107$	3.3.229.1	None	✓	$1$	$1$	\(0\)	\(-2\)	\(3\)	\(-4\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+q^{5}+(-1+\beta _{1})q^{7}+\cdots\)
3520.2.a.bv	$3520$	$2$	3520.a	1.a	$1$	$3$	$3$	$28.107$	3.3.229.1	None	✓	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(-7\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+q^{5}+(-2+\beta _{1})q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
3520.2.a.bw	$3520$	$2$	3520.a	1.a	$1$	$3$	$3$	$28.107$	3.3.229.1	None	✓	$1$	$0$	\(0\)	\(1\)	\(3\)	\(7\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+q^{5}+(2-\beta _{1})q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
3520.2.a.bx	$3520$	$2$	3520.a	1.a	$1$	$3$	$3$	$28.107$	3.3.229.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(3\)	\(4\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}+q^{5}+(1-\beta _{1})q^{7}+(2+\cdots)q^{9}+\cdots\)
3520.2.a.by	$3520$	$2$	3520.a	1.a	$1$	$5$	$5$	$28.107$	5.5.792644.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-5\)	\(-2\)		$+$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}-q^{5}-\beta _{4}q^{7}+(2-\beta _{1})q^{9}+\cdots\)
3520.2.a.bz	$3520$	$2$	3520.a	1.a	$1$	$5$	$5$	$28.107$	5.5.792644.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-5\)	\(2\)		$+$	$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}-q^{5}+\beta _{4}q^{7}+(2-\beta _{1})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3520))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3520)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(220))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(352))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(440))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(704))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(880))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1760))\)\(^{\oplus 2}\)