Space of modular forms of level 6720, weight 2, and trivial character

• Label: 6720.2.a
• Level: $6720$
• Weight: $2$
• Character orbit: 6720.a
• Rep. character: $\chi_{6720}(1,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $80$
• Sturm bound: $3072$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 6720 = 2^{6} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6720.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 80 \)
Sturm bound:			\(3072\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(11\), \(13\), \(17\), \(19\), \(23\), \(29\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6720))\).

	Total	New	Old
Modular forms	1584	96	1488
Cusp forms	1489	96	1393
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.

\(2\)	\(3\)	\(5\)	\(7\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(5\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(8\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(6\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(5\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(5\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(5\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(8\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(7\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(4\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(6\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(7\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(6\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(7\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(7\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(4\)
Plus space				\(+\)	\(40\)
Minus space				\(-\)	\(56\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6720))\) 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
6720.2.a.a	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
6720.2.a.b	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6720.2.a.c	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
6720.2.a.d	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots\)
6720.2.a.e	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots\)
6720.2.a.f	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}-2q^{11}+4q^{13}+\cdots\)
6720.2.a.g	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}-2q^{13}+q^{15}+\cdots\)
6720.2.a.h	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6720.2.a.i	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6720.2.a.j	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6720.2.a.k	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6720.2.a.l	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}+q^{9}+6q^{11}-4q^{13}+\cdots\)
6720.2.a.m	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6720.2.a.n	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}-2q^{13}+q^{15}+\cdots\)
6720.2.a.o	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}-2q^{13}+q^{15}+\cdots\)
6720.2.a.p	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}+6q^{13}+q^{15}+\cdots\)
6720.2.a.q	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6720.2.a.r	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
6720.2.a.s	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(-1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}-6q^{13}-q^{15}+\cdots\)
6720.2.a.t	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}-2q^{13}-q^{15}+\cdots\)
6720.2.a.u	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}+2q^{13}-q^{15}+\cdots\)
6720.2.a.v	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
6720.2.a.w	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(-1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
6720.2.a.x	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}-6q^{11}+4q^{13}+\cdots\)
6720.2.a.y	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
6720.2.a.z	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6720.2.a.ba	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}-2q^{11}-q^{15}+\cdots\)
6720.2.a.bb	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}-2q^{13}-q^{15}+\cdots\)
6720.2.a.bc	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}-2q^{13}-q^{15}+\cdots\)
6720.2.a.bd	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots\)
6720.2.a.be	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6720.2.a.bf	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6720.2.a.bg	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
6720.2.a.bh	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6720.2.a.bi	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}-2q^{13}-q^{15}+\cdots\)
6720.2.a.bj	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}-2q^{13}-q^{15}+\cdots\)
6720.2.a.bk	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}+6q^{13}-q^{15}+\cdots\)
6720.2.a.bl	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6720.2.a.bm	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}-6q^{11}-4q^{13}+\cdots\)
6720.2.a.bn	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6720.2.a.bo	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6720.2.a.bp	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6720.2.a.bq	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6720.2.a.br	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}-2q^{13}-q^{15}+\cdots\)
6720.2.a.bs	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots\)
6720.2.a.bt	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots\)
6720.2.a.bu	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}+2q^{11}+4q^{13}+\cdots\)
6720.2.a.bv	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
6720.2.a.bw	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6720.2.a.bx	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
6720.2.a.by	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6720.2.a.bz	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6720.2.a.ca	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(-1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
6720.2.a.cb	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots\)
6720.2.a.cc	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(-1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}-2q^{13}+q^{15}+\cdots\)
6720.2.a.cd	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(-1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}-2q^{13}+q^{15}+\cdots\)
6720.2.a.ce	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(-1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}+2q^{11}+q^{15}+\cdots\)
6720.2.a.cf	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
6720.2.a.cg	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6720.2.a.ch	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(-1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}+6q^{11}+4q^{13}+\cdots\)
6720.2.a.ci	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
6720.2.a.cj	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
6720.2.a.ck	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}-6q^{13}+q^{15}+\cdots\)
6720.2.a.cl	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}-2q^{13}+q^{15}+\cdots\)
6720.2.a.cm	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}+2q^{13}+q^{15}+\cdots\)
6720.2.a.cn	$6720$	$2$	6720.a	1.a	$1$	$1$	$1$	$53.659$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
6720.2.a.co	$6720$	$2$	6720.a	1.a	$1$	$2$	$2$	$53.659$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(2\)		$+$	$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}+\beta q^{11}-2q^{13}+\cdots\)
6720.2.a.cp	$6720$	$2$	6720.a	1.a	$1$	$2$	$2$	$53.659$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(2\)		$-$	$+$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}+\beta q^{13}+q^{15}+\cdots\)
6720.2.a.cq	$6720$	$2$	6720.a	1.a	$1$	$2$	$2$	$53.659$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(-2\)		$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
6720.2.a.cr	$6720$	$2$	6720.a	1.a	$1$	$2$	$2$	$53.659$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(-2\)		$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}+\beta q^{11}+(2+\cdots)q^{13}+\cdots\)
6720.2.a.cs	$6720$	$2$	6720.a	1.a	$1$	$2$	$2$	$53.659$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(-2\)		$-$	$+$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
6720.2.a.ct	$6720$	$2$	6720.a	1.a	$1$	$2$	$2$	$53.659$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}+(-1-\beta )q^{11}+\cdots\)
6720.2.a.cu	$6720$	$2$	6720.a	1.a	$1$	$2$	$2$	$53.659$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}+\beta q^{11}-2q^{13}+\cdots\)
6720.2.a.cv	$6720$	$2$	6720.a	1.a	$1$	$2$	$2$	$53.659$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}-\beta q^{13}-q^{15}+\cdots\)
6720.2.a.cw	$6720$	$2$	6720.a	1.a	$1$	$2$	$2$	$53.659$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(-2\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}+(1+\beta )q^{11}+\cdots\)
6720.2.a.cx	$6720$	$2$	6720.a	1.a	$1$	$2$	$2$	$53.659$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(2\)		$+$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
6720.2.a.cy	$6720$	$2$	6720.a	1.a	$1$	$2$	$2$	$53.659$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(2\)		$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}+\beta q^{11}+(2+\cdots)q^{13}+\cdots\)
6720.2.a.cz	$6720$	$2$	6720.a	1.a	$1$	$2$	$2$	$53.659$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(2\)		$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
6720.2.a.da	$6720$	$2$	6720.a	1.a	$1$	$3$	$3$	$53.659$	3.3.148.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(-3\)	\(3\)		$+$	$+$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}+q^{9}+(-1+\beta _{2})q^{11}+\cdots\)
6720.2.a.db	$6720$	$2$	6720.a	1.a	$1$	$3$	$3$	$53.659$	3.3.148.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(-3\)	\(-3\)		$+$	$-$	$+$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-q^{7}+q^{9}+(1-\beta _{2})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6720))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6720)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(420))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(448))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(480))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(560))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(672))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(840))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(960))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1344))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1680))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3360))\)\(^{\oplus 2}\)