Space of modular forms of level 6480, weight 2, and trivial character

• Label: 6480.2.a
• Level: $6480$
• Weight: $2$
• Character orbit: 6480.a
• Rep. character: $\chi_{6480}(1,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $54$
• Sturm bound: $2592$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 6480 = 2^{4} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6480.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 54 \)
Sturm bound:			\(2592\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(17\), \(19\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6480))\).

	Total	New	Old
Modular forms	1368	96	1272
Cusp forms	1225	96	1129
Eisenstein series	143	0	143

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

\(2\)	\(3\)	\(5\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(11\)
\(+\)	\(+\)	\(-\)	\(-\)	\(13\)
\(+\)	\(-\)	\(+\)	\(-\)	\(13\)
\(+\)	\(-\)	\(-\)	\(+\)	\(11\)
\(-\)	\(+\)	\(+\)	\(-\)	\(13\)
\(-\)	\(+\)	\(-\)	\(+\)	\(11\)
\(-\)	\(-\)	\(+\)	\(+\)	\(11\)
\(-\)	\(-\)	\(-\)	\(-\)	\(13\)
Plus space			\(+\)	\(44\)
Minus space			\(-\)	\(52\)

Trace form

\( 96 q + 96 q^{25} - 24 q^{31} - 24 q^{43} + 96 q^{49} - 48 q^{67} + 24 q^{73} - 48 q^{79} - 24 q^{91} + 24 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6480))\) 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	3	5
6480.2.a.a	$6480$	$2$	6480.a	1.a	$1$	$1$	$1$	$51.743$	\(\Q\)	None	✓				810.2.a.d	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-5q^{7}-q^{13}-6q^{17}-5q^{19}+\cdots\)
6480.2.a.b	$6480$	$2$	6480.a	1.a	$1$	$1$	$1$	$51.743$	\(\Q\)	None	✓				1620.2.a.c	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}-3q^{11}-4q^{13}+6q^{17}+\cdots\)
6480.2.a.c	$6480$	$2$	6480.a	1.a	$1$	$1$	$1$	$51.743$	\(\Q\)	None	✓				405.2.a.c	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}+3q^{11}-4q^{13}-6q^{17}+\cdots\)
6480.2.a.d	$6480$	$2$	6480.a	1.a	$1$	$1$	$1$	$51.743$	\(\Q\)	None	✓				3240.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{11}+7q^{19}-6q^{23}+q^{25}+\cdots\)
6480.2.a.e	$6480$	$2$	6480.a	1.a	$1$	$1$	$1$	$51.743$	\(\Q\)	None	✓				360.2.q.a	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+5q^{11}+3q^{17}-5q^{19}-6q^{23}+\cdots\)
6480.2.a.f	$6480$	$2$	6480.a	1.a	$1$	$1$	$1$	$51.743$	\(\Q\)	None	✓				405.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+5q^{11}+4q^{13}+4q^{17}+5q^{19}+\cdots\)
6480.2.a.g	$6480$	$2$	6480.a	1.a	$1$	$1$	$1$	$51.743$	\(\Q\)	None	✓				90.2.e.a	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}-6q^{11}+2q^{13}+4q^{19}+\cdots\)
6480.2.a.h	$6480$	$2$	6480.a	1.a	$1$	$1$	$1$	$51.743$	\(\Q\)	None	✓				180.2.i.a	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}-4q^{13}+6q^{17}-2q^{19}+\cdots\)
6480.2.a.i	$6480$	$2$	6480.a	1.a	$1$	$1$	$1$	$51.743$	\(\Q\)	None	✓				810.2.a.c	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+q^{7}+5q^{13}+6q^{17}-5q^{19}+\cdots\)
6480.2.a.j	$6480$	$2$	6480.a	1.a	$1$	$1$	$1$	$51.743$	\(\Q\)	None	✓				3240.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-3q^{11}-2q^{17}-q^{19}+\cdots\)
6480.2.a.k	$6480$	$2$	6480.a	1.a	$1$	$1$	$1$	$51.743$	\(\Q\)	None	✓				45.2.e.a	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+3q^{7}+2q^{11}-2q^{13}+4q^{17}+\cdots\)
6480.2.a.l	$6480$	$2$	6480.a	1.a	$1$	$1$	$1$	$51.743$	\(\Q\)	None	✓				90.2.e.b	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{7}+3q^{11}-4q^{13}-3q^{17}+\cdots\)
6480.2.a.m	$6480$	$2$	6480.a	1.a	$1$	$1$	$1$	$51.743$	\(\Q\)	None	✓				1620.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{7}+3q^{11}-4q^{13}-5q^{19}+\cdots\)
6480.2.a.n	$6480$	$2$	6480.a	1.a	$1$	$1$	$1$	$51.743$	\(\Q\)	None	✓				810.2.a.d	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-5q^{7}-q^{13}+6q^{17}-5q^{19}+\cdots\)
6480.2.a.o	$6480$	$2$	6480.a	1.a	$1$	$1$	$1$	$51.743$	\(\Q\)	None	✓				405.2.a.c	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-3q^{11}-4q^{13}+6q^{17}+\cdots\)
6480.2.a.p	$6480$	$2$	6480.a	1.a	$1$	$1$	$1$	$51.743$	\(\Q\)	None	✓				1620.2.a.c	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}+3q^{11}-4q^{13}-6q^{17}+\cdots\)
6480.2.a.q	$6480$	$2$	6480.a	1.a	$1$	$1$	$1$	$51.743$	\(\Q\)	None	✓				360.2.q.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-5q^{11}-3q^{17}-5q^{19}+6q^{23}+\cdots\)
6480.2.a.r	$6480$	$2$	6480.a	1.a	$1$	$1$	$1$	$51.743$	\(\Q\)	None	✓				405.2.a.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-5q^{11}+4q^{13}-4q^{17}+5q^{19}+\cdots\)
6480.2.a.s	$6480$	$2$	6480.a	1.a	$1$	$1$	$1$	$51.743$	\(\Q\)	None	✓				3240.2.a.c	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{11}+7q^{19}+6q^{23}+q^{25}+\cdots\)
6480.2.a.t	$6480$	$2$	6480.a	1.a	$1$	$1$	$1$	$51.743$	\(\Q\)	None	✓				180.2.i.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}-4q^{13}-6q^{17}-2q^{19}+\cdots\)
6480.2.a.u	$6480$	$2$	6480.a	1.a	$1$	$1$	$1$	$51.743$	\(\Q\)	None	✓				810.2.a.c	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}+5q^{13}-6q^{17}-5q^{19}+\cdots\)
6480.2.a.v	$6480$	$2$	6480.a	1.a	$1$	$1$	$1$	$51.743$	\(\Q\)	None	✓				90.2.e.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+q^{7}+6q^{11}+2q^{13}+4q^{19}+\cdots\)
6480.2.a.w	$6480$	$2$	6480.a	1.a	$1$	$1$	$1$	$51.743$	\(\Q\)	None	✓				3240.2.a.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}+3q^{11}+2q^{17}-q^{19}+\cdots\)
6480.2.a.x	$6480$	$2$	6480.a	1.a	$1$	$1$	$1$	$51.743$	\(\Q\)	None	✓				45.2.e.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+3q^{7}-2q^{11}-2q^{13}-4q^{17}+\cdots\)
6480.2.a.y	$6480$	$2$	6480.a	1.a	$1$	$1$	$1$	$51.743$	\(\Q\)	None	✓				1620.2.a.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{7}-3q^{11}-4q^{13}-5q^{19}+\cdots\)
6480.2.a.z	$6480$	$2$	6480.a	1.a	$1$	$1$	$1$	$51.743$	\(\Q\)	None	✓				90.2.e.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{7}-3q^{11}-4q^{13}+3q^{17}+\cdots\)
6480.2.a.ba	$6480$	$2$	6480.a	1.a	$1$	$2$	$2$	$51.743$	\(\Q(\sqrt{3}) \)	None	✓				360.2.q.b	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(-2+\beta )q^{7}+(-2+2\beta )q^{11}+\cdots\)
6480.2.a.bb	$6480$	$2$	6480.a	1.a	$1$	$2$	$2$	$51.743$	\(\Q(\sqrt{3}) \)	None	✓				810.2.a.j	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(-2+\beta )q^{7}+2\beta q^{11}+(2-\beta )q^{13}+\cdots\)
6480.2.a.bc	$6480$	$2$	6480.a	1.a	$1$	$2$	$2$	$51.743$	\(\Q(\sqrt{6}) \)	None	✓				360.2.q.c	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(-1+\beta )q^{7}-2q^{17}+(2-2\beta )q^{19}+\cdots\)
6480.2.a.bd	$6480$	$2$	6480.a	1.a	$1$	$2$	$2$	$51.743$	\(\Q(\sqrt{33}) \)	None	✓				3240.2.a.i	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-\beta q^{7}+(-1+\beta )q^{11}-\beta q^{13}+\cdots\)
6480.2.a.be	$6480$	$2$	6480.a	1.a	$1$	$2$	$2$	$51.743$	\(\Q(\sqrt{33}) \)	None	✓				90.2.e.c	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-\beta q^{7}+(1+\beta )q^{11}-2\beta q^{13}+\cdots\)
6480.2.a.bf	$6480$	$2$	6480.a	1.a	$1$	$2$	$2$	$51.743$	\(\Q(\sqrt{57}) \)	None	✓				3240.2.a.h	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-\beta q^{7}+(3-\beta )q^{11}+(2+\beta )q^{13}+\cdots\)
6480.2.a.bg	$6480$	$2$	6480.a	1.a	$1$	$2$	$2$	$51.743$	\(\Q(\sqrt{3}) \)	None	✓				3240.2.a.g	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(1+\beta )q^{7}+(-2+\beta )q^{11}+(-2+\cdots)q^{13}+\cdots\)
6480.2.a.bh	$6480$	$2$	6480.a	1.a	$1$	$2$	$2$	$51.743$	\(\Q(\sqrt{3}) \)	None	✓				1620.2.a.g	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(1+\beta )q^{7}-\beta q^{11}+(2+2\beta )q^{13}+\cdots\)
6480.2.a.bi	$6480$	$2$	6480.a	1.a	$1$	$2$	$2$	$51.743$	\(\Q(\sqrt{3}) \)	None	✓				405.2.a.g	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(6\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(3+\beta )q^{7}+(-4-\beta )q^{11}+(-2+\cdots)q^{13}+\cdots\)
6480.2.a.bj	$6480$	$2$	6480.a	1.a	$1$	$2$	$2$	$51.743$	\(\Q(\sqrt{3}) \)	None	✓				810.2.a.j	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(-2+\beta )q^{7}-2\beta q^{11}+(2-\beta )q^{13}+\cdots\)
6480.2.a.bk	$6480$	$2$	6480.a	1.a	$1$	$2$	$2$	$51.743$	\(\Q(\sqrt{3}) \)	None	✓				360.2.q.b	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(-2+\beta )q^{7}+(2-2\beta )q^{11}+\cdots\)
6480.2.a.bl	$6480$	$2$	6480.a	1.a	$1$	$2$	$2$	$51.743$	\(\Q(\sqrt{6}) \)	None	✓				360.2.q.c	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(-1+\beta )q^{7}+2q^{17}+(2-2\beta )q^{19}+\cdots\)
6480.2.a.bm	$6480$	$2$	6480.a	1.a	$1$	$2$	$2$	$51.743$	\(\Q(\sqrt{57}) \)	None	✓				3240.2.a.h	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-\beta q^{7}+(-3+\beta )q^{11}+(2+\beta )q^{13}+\cdots\)
6480.2.a.bn	$6480$	$2$	6480.a	1.a	$1$	$2$	$2$	$51.743$	\(\Q(\sqrt{33}) \)	None	✓				90.2.e.c	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-\beta q^{7}+(-1-\beta )q^{11}-2\beta q^{13}+\cdots\)
6480.2.a.bo	$6480$	$2$	6480.a	1.a	$1$	$2$	$2$	$51.743$	\(\Q(\sqrt{33}) \)	None	✓				3240.2.a.i	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-\beta q^{7}+(1-\beta )q^{11}-\beta q^{13}+\cdots\)
6480.2.a.bp	$6480$	$2$	6480.a	1.a	$1$	$2$	$2$	$51.743$	\(\Q(\sqrt{3}) \)	None	✓				1620.2.a.g	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(1+\beta )q^{7}+\beta q^{11}+(2+2\beta )q^{13}+\cdots\)
6480.2.a.bq	$6480$	$2$	6480.a	1.a	$1$	$2$	$2$	$51.743$	\(\Q(\sqrt{3}) \)	None	✓				3240.2.a.g	$1$	$1$	\(0\)	\(0\)	\(2\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(1+\beta )q^{7}+(2-\beta )q^{11}+(-2+\cdots)q^{13}+\cdots\)
6480.2.a.br	$6480$	$2$	6480.a	1.a	$1$	$2$	$2$	$51.743$	\(\Q(\sqrt{3}) \)	None	✓				405.2.a.g	$1$	$0$	\(0\)	\(0\)	\(2\)	\(6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(3+\beta )q^{7}+(4+\beta )q^{11}+(-2+\cdots)q^{13}+\cdots\)
6480.2.a.bs	$6480$	$2$	6480.a	1.a	$1$	$3$	$3$	$51.743$	3.3.564.1	None	✓		✓		45.2.e.b	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(-2+\beta _{1})q^{7}+(-1-\beta _{2})q^{11}+\cdots\)
6480.2.a.bt	$6480$	$2$	6480.a	1.a	$1$	$3$	$3$	$51.743$	3.3.564.1	None	✓		✓		180.2.i.b	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(-3\)		$-$	$+$	$+$	$-$	$3$	$\mathrm{SU}(2)$	\(q-q^{5}+(-1+\beta _{1})q^{7}+\beta _{2}q^{11}+(2+\cdots)q^{13}+\cdots\)
6480.2.a.bu	$6480$	$2$	6480.a	1.a	$1$	$3$	$3$	$51.743$	3.3.564.1	None	✓				360.2.q.d	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(5\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(1+\beta _{1}-\beta _{2})q^{7}+(-1-\beta _{2})q^{11}+\cdots\)
6480.2.a.bv	$6480$	$2$	6480.a	1.a	$1$	$3$	$3$	$51.743$	3.3.564.1	None	✓		✓		45.2.e.b	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(-2+\beta _{1})q^{7}+(1+\beta _{2})q^{11}+\cdots\)
6480.2.a.bw	$6480$	$2$	6480.a	1.a	$1$	$3$	$3$	$51.743$	3.3.564.1	None	✓		✓		180.2.i.b	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-3\)		$-$	$-$	$-$	$-$	$3$	$\mathrm{SU}(2)$	\(q+q^{5}+(-1+\beta _{1})q^{7}-\beta _{2}q^{11}+(2+\cdots)q^{13}+\cdots\)
6480.2.a.bx	$6480$	$2$	6480.a	1.a	$1$	$3$	$3$	$51.743$	3.3.564.1	None	✓				360.2.q.d	$1$	$0$	\(0\)	\(0\)	\(3\)	\(5\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(1+\beta _{1}-\beta _{2})q^{7}+(1+\beta _{2})q^{11}+\cdots\)
6480.2.a.by	$6480$	$2$	6480.a	1.a	$1$	$4$	$4$	$51.743$	4.4.62352.1	None	✓				3240.2.a.t	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(-\beta _{1}+\beta _{2})q^{7}+(2-\beta _{1}+\beta _{3})q^{11}+\cdots\)
6480.2.a.bz	$6480$	$2$	6480.a	1.a	$1$	$4$	$4$	$51.743$	4.4.29268.1	None	✓				360.2.q.e	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(1\)		$+$	$-$	$+$	$-$	$3$	$\mathrm{SU}(2)$	\(q-q^{5}+\beta _{2}q^{7}+(-\beta _{2}-\beta _{3})q^{11}+(1+\cdots)q^{13}+\cdots\)
6480.2.a.ca	$6480$	$2$	6480.a	1.a	$1$	$4$	$4$	$51.743$	4.4.62352.1	None	✓		✓		3240.2.a.t	$1$	$1$	\(0\)	\(0\)	\(4\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(-\beta _{1}+\beta _{2})q^{7}+(-2+\beta _{1}+\cdots)q^{11}+\cdots\)
6480.2.a.cb	$6480$	$2$	6480.a	1.a	$1$	$4$	$4$	$51.743$	4.4.29268.1	None	✓		✓		360.2.q.e	$1$	$0$	\(0\)	\(0\)	\(4\)	\(1\)		$+$	$+$	$-$	$-$	$3$	$\mathrm{SU}(2)$	\(q+q^{5}+\beta _{2}q^{7}+(\beta _{2}+\beta _{3})q^{11}+(1+\beta _{1}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6480))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6480)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(135))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(162))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(216))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(270))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(324))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(405))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(432))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(540))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(648))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(720))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(810))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1080))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1296))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1620))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2160))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3240))\)\(^{\oplus 2}\)