Space of modular forms of level 4160, weight 2, and trivial character

• Label: 4160.2.a
• Level: $4160$
• Weight: $2$
• Character orbit: 4160.a
• Rep. character: $\chi_{4160}(1,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $50$
• Sturm bound: $1344$
• Trace bound: $29$

Defining parameters

Level:	\( N \)	\(=\)	\( 4160 = 2^{6} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4160.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 50 \)
Sturm bound:			\(1344\)
Trace bound:			\(29\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4160))\).

	Total	New	Old
Modular forms	696	96	600
Cusp forms	649	96	553
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.

\(2\)	\(5\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(12\)
\(+\)	\(+\)	\(-\)	\(-\)	\(14\)
\(+\)	\(-\)	\(+\)	\(-\)	\(14\)
\(+\)	\(-\)	\(-\)	\(+\)	\(8\)
\(-\)	\(+\)	\(+\)	\(-\)	\(12\)
\(-\)	\(+\)	\(-\)	\(+\)	\(10\)
\(-\)	\(-\)	\(+\)	\(+\)	\(10\)
\(-\)	\(-\)	\(-\)	\(-\)	\(16\)
Plus space			\(+\)	\(40\)
Minus space			\(-\)	\(56\)

Trace form

\( 96 q + 96 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4160))\) 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	5	13
4160.2.a.a	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	\(\Q\)	None	✓				520.2.a.b	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+q^{9}-2q^{11}-q^{13}+\cdots\)
4160.2.a.b	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	\(\Q\)	None	✓				130.2.a.a	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+4q^{7}+q^{9}-6q^{11}+\cdots\)
4160.2.a.c	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	\(\Q\)	None	✓				130.2.a.c	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}-4q^{7}+q^{9}+2q^{11}+\cdots\)
4160.2.a.d	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	\(\Q\)	None	✓				260.2.a.a	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}+2q^{7}+q^{9}-4q^{11}+\cdots\)
4160.2.a.e	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	\(\Q\)	None	✓				2080.2.a.a	$1$	$0$	\(0\)	\(-2\)	\(1\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}+4q^{7}+q^{9}-6q^{11}+\cdots\)
4160.2.a.f	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	\(\Q\)	None	✓				65.2.a.a	$1$	$0$	\(0\)	\(-2\)	\(1\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}+4q^{7}+q^{9}+2q^{11}+\cdots\)
4160.2.a.g	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	\(\Q\)	None	✓				2080.2.a.d	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-4q^{7}-3q^{9}+4q^{11}-q^{13}+\cdots\)
4160.2.a.h	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	\(\Q\)	None	✓				130.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{9}-q^{13}+2q^{17}-8q^{19}+\cdots\)
4160.2.a.i	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	\(\Q\)	None	✓				130.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{9}-q^{13}+2q^{17}+8q^{19}+\cdots\)
4160.2.a.j	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	\(\Q\)	None	✓				2080.2.a.d	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{7}-3q^{9}-4q^{11}-q^{13}+\cdots\)
4160.2.a.k	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	\(\Q\)	None	✓				2080.2.a.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-3q^{9}+2q^{11}+q^{13}+\cdots\)
4160.2.a.l	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	\(\Q\)	None	✓				520.2.a.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-3q^{9}-4q^{11}+q^{13}-6q^{17}+\cdots\)
4160.2.a.m	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	\(\Q\)	None	✓				520.2.a.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-3q^{9}+4q^{11}+q^{13}-6q^{17}+\cdots\)
4160.2.a.n	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	\(\Q\)	None	✓				2080.2.a.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-3q^{9}-2q^{11}+q^{13}+\cdots\)
4160.2.a.o	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	\(\Q\)	None	✓				130.2.a.a	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}-4q^{7}+q^{9}+6q^{11}+\cdots\)
4160.2.a.p	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	\(\Q\)	None	✓				520.2.a.b	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+q^{9}+2q^{11}-q^{13}+\cdots\)
4160.2.a.q	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	\(\Q\)	None	✓				65.2.a.a	$1$	$1$	\(0\)	\(2\)	\(1\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}-4q^{7}+q^{9}-2q^{11}+\cdots\)
4160.2.a.r	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	\(\Q\)	None	✓				2080.2.a.a	$1$	$0$	\(0\)	\(2\)	\(1\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}-4q^{7}+q^{9}+6q^{11}+\cdots\)
4160.2.a.s	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	\(\Q\)	None	✓				260.2.a.a	$1$	$0$	\(0\)	\(2\)	\(1\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}-2q^{7}+q^{9}+4q^{11}+\cdots\)
4160.2.a.t	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	\(\Q\)	None	✓				130.2.a.c	$1$	$0$	\(0\)	\(2\)	\(1\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}+4q^{7}+q^{9}-2q^{11}+\cdots\)
4160.2.a.u	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	\(\Q(\sqrt{2}) \)	None	✓				520.2.a.c	$1$	$1$	\(0\)	\(-4\)	\(-2\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-2+\beta )q^{3}-q^{5}+2q^{7}+(3-4\beta )q^{9}+\cdots\)
4160.2.a.v	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	\(\Q(\sqrt{3}) \)	None	✓				520.2.a.d	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+q^{5}+2\beta q^{7}+(1-2\beta )q^{9}+\cdots\)
4160.2.a.w	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	\(\Q(\sqrt{3}) \)	None	✓				520.2.a.e	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+q^{5}-2\beta q^{7}+(1-2\beta )q^{9}+\cdots\)
4160.2.a.x	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	\(\Q(\sqrt{5}) \)	None	✓		✓		520.2.a.g	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+q^{5}+(3+2\beta )q^{9}+(-3+\cdots)q^{11}+\cdots\)
4160.2.a.y	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	\(\Q(\sqrt{3}) \)	None	✓				65.2.a.c	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+q^{5}+2q^{7}+(1-2\beta )q^{9}+\cdots\)
4160.2.a.z	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	\(\Q(\sqrt{2}) \)	None	✓				65.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}+(-2+2\beta )q^{7}-q^{9}+\cdots\)
4160.2.a.ba	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	\(\Q(\sqrt{6}) \)	None	✓				520.2.a.f	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}-2q^{7}+3q^{9}+(-2+\beta )q^{11}+\cdots\)
4160.2.a.bb	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	\(\Q(\sqrt{2}) \)	None	✓				2080.2.a.i	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}+\beta q^{7}-3q^{9}+\beta q^{11}-q^{13}+\cdots\)
4160.2.a.bc	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	\(\Q(\sqrt{2}) \)	None	✓				2080.2.a.j	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}+2\beta q^{7}-q^{9}+\beta q^{11}+\cdots\)
4160.2.a.bd	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	\(\Q(\sqrt{2}) \)	None	✓				2080.2.a.k	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}-2\beta q^{7}-q^{9}+\beta q^{11}+\cdots\)
4160.2.a.be	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	\(\Q(\sqrt{2}) \)	None	✓				2080.2.a.l	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}+5q^{9}+\beta q^{11}-q^{13}+\cdots\)
4160.2.a.bf	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	\(\Q(\sqrt{2}) \)	None	✓				65.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}+(2+2\beta )q^{7}-q^{9}+(-2+\cdots)q^{11}+\cdots\)
4160.2.a.bg	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	\(\Q(\sqrt{6}) \)	None	✓				520.2.a.f	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}+2q^{7}+3q^{9}+(2+\beta )q^{11}+\cdots\)
4160.2.a.bh	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	\(\Q(\sqrt{2}) \)	None	✓				2080.2.a.h	$2$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}-q^{9}+\beta q^{11}-q^{13}+\cdots\)
4160.2.a.bi	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	\(\Q(\sqrt{2}) \)	None	✓				2080.2.a.g	$2$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}-q^{9}-3\beta q^{11}-q^{13}+\cdots\)
4160.2.a.bj	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	\(\Q(\sqrt{3}) \)	None	✓				65.2.a.c	$1$	$1$	\(0\)	\(2\)	\(2\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+q^{5}-2q^{7}+(1+2\beta )q^{9}+\cdots\)
4160.2.a.bk	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	\(\Q(\sqrt{3}) \)	None	✓				520.2.a.e	$1$	$0$	\(0\)	\(2\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+q^{5}-2\beta q^{7}+(1+2\beta )q^{9}+\cdots\)
4160.2.a.bl	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	\(\Q(\sqrt{3}) \)	None	✓				520.2.a.d	$1$	$0$	\(0\)	\(2\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+q^{5}+2\beta q^{7}+(1+2\beta )q^{9}+\cdots\)
4160.2.a.bm	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	\(\Q(\sqrt{5}) \)	None	✓				520.2.a.g	$1$	$0$	\(0\)	\(2\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+q^{5}+(3+2\beta )q^{9}+(3-\beta )q^{11}+\cdots\)
4160.2.a.bn	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	\(\Q(\sqrt{2}) \)	None	✓				520.2.a.c	$1$	$0$	\(0\)	\(4\)	\(-2\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(2+\beta )q^{3}-q^{5}-2q^{7}+(3+4\beta )q^{9}+\cdots\)
4160.2.a.bo	$4160$	$2$	4160.a	1.a	$1$	$3$	$3$	$33.218$	3.3.564.1	None	✓				260.2.a.b	$1$	$1$	\(0\)	\(-2\)	\(-3\)	\(-2\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}-q^{5}+(-1-\beta _{1})q^{7}+\cdots\)
4160.2.a.bp	$4160$	$2$	4160.a	1.a	$1$	$3$	$3$	$33.218$	3.3.148.1	None	✓				2080.2.a.m	$1$	$1$	\(0\)	\(-2\)	\(-3\)	\(6\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}-q^{5}+2q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
4160.2.a.bq	$4160$	$2$	4160.a	1.a	$1$	$3$	$3$	$33.218$	3.3.148.1	None	✓				2080.2.a.m	$1$	$1$	\(0\)	\(2\)	\(-3\)	\(-6\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}-q^{5}-2q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
4160.2.a.br	$4160$	$2$	4160.a	1.a	$1$	$3$	$3$	$33.218$	3.3.564.1	None	✓		✓		260.2.a.b	$1$	$0$	\(0\)	\(2\)	\(-3\)	\(2\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}-q^{5}+(1+\beta _{1})q^{7}+(4+\cdots)q^{9}+\cdots\)
4160.2.a.bs	$4160$	$2$	4160.a	1.a	$1$	$4$	$4$	$33.218$	4.4.4752.1	None	✓				2080.2.a.o	$1$	$0$	\(0\)	\(-4\)	\(-4\)	\(4\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}-q^{5}+(1+\beta _{1})q^{7}+\cdots\)
4160.2.a.bt	$4160$	$2$	4160.a	1.a	$1$	$4$	$4$	$33.218$	4.4.5744.1	None	✓				2080.2.a.p	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(0\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+q^{5}-\beta _{1}q^{7}+(1-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
4160.2.a.bu	$4160$	$2$	4160.a	1.a	$1$	$4$	$4$	$33.218$	\(\Q(\zeta_{16})^+\)	None	✓				2080.2.a.q	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+(\beta _{1}+\beta _{2})q^{7}+(1+\beta _{3})q^{9}+\cdots\)
4160.2.a.bv	$4160$	$2$	4160.a	1.a	$1$	$4$	$4$	$33.218$	4.4.25088.1	None	✓				2080.2.a.r	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+q^{5}+(-\beta _{1}+\beta _{2})q^{7}+(3+\cdots)q^{9}+\cdots\)
4160.2.a.bw	$4160$	$2$	4160.a	1.a	$1$	$4$	$4$	$33.218$	4.4.5744.1	None	✓				2080.2.a.p	$1$	$0$	\(0\)	\(2\)	\(4\)	\(0\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+q^{5}+\beta _{1}q^{7}+(1-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
4160.2.a.bx	$4160$	$2$	4160.a	1.a	$1$	$4$	$4$	$33.218$	4.4.4752.1	None	✓				2080.2.a.o	$1$	$0$	\(0\)	\(4\)	\(-4\)	\(-4\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}-q^{5}+(-1+\beta _{1})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4160))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4160)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(130))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(260))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(416))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(520))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(832))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1040))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2080))\)\(^{\oplus 2}\)