Space of modular forms of level 6080, weight 2, and trivial character

• Label: 6080.2.a
• Level: $6080$
• Weight: $2$
• Character orbit: 6080.a
• Rep. character: $\chi_{6080}(1,\cdot)$
• Character field: $\Q$
• Dimension: $144$
• Newform subspaces: $64$
• Sturm bound: $1920$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 6080 = 2^{6} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6080.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 64 \)
Sturm bound:			\(1920\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6080))\).

	Total	New	Old
Modular forms	984	144	840
Cusp forms	937	144	793
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.

\(2\)	\(5\)	\(19\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(112\)	\(17\)	\(95\)		\(107\)	\(17\)	\(90\)		\(5\)	\(0\)	\(5\)
\(+\)	\(+\)	\(-\)	\(-\)		\(134\)	\(21\)	\(113\)		\(128\)	\(21\)	\(107\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)		\(128\)	\(19\)	\(109\)		\(122\)	\(19\)	\(103\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)		\(118\)	\(15\)	\(103\)		\(112\)	\(15\)	\(97\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)		\(126\)	\(19\)	\(107\)		\(120\)	\(19\)	\(101\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)		\(120\)	\(15\)	\(105\)		\(114\)	\(15\)	\(99\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)		\(126\)	\(17\)	\(109\)		\(120\)	\(17\)	\(103\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)		\(120\)	\(21\)	\(99\)		\(114\)	\(21\)	\(93\)		\(6\)	\(0\)	\(6\)
Plus space			\(+\)		\(476\)	\(64\)	\(412\)		\(453\)	\(64\)	\(389\)		\(23\)	\(0\)	\(23\)
Minus space			\(-\)		\(508\)	\(80\)	\(428\)		\(484\)	\(80\)	\(404\)		\(24\)	\(0\)	\(24\)

Trace form

\( 144 q + 144 q^{9} + 144 q^{25} + 32 q^{29} + 32 q^{37} + 144 q^{49} + 32 q^{53} + 32 q^{77} + 176 q^{81} + 32 q^{89} + 96 q^{93}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6080))\) 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	19
6080.2.a.a	$6080$	$2$	6080.a	1.a	$1$	$1$	$1$	$48.549$	\(\Q\)	None	✓				760.2.a.e	$1$	$2$	\(0\)	\(-3\)	\(-1\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-q^{5}-q^{7}+6q^{9}-4q^{11}+\cdots\)
6080.2.a.b	$6080$	$2$	6080.a	1.a	$1$	$1$	$1$	$48.549$	\(\Q\)	None	✓				190.2.a.b	$1$	$0$	\(0\)	\(-3\)	\(1\)	\(5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+q^{5}+5q^{7}+6q^{9}-4q^{11}+\cdots\)
6080.2.a.c	$6080$	$2$	6080.a	1.a	$1$	$1$	$1$	$48.549$	\(\Q\)	None	✓				760.2.a.b	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots\)
6080.2.a.d	$6080$	$2$	6080.a	1.a	$1$	$1$	$1$	$48.549$	\(\Q\)	None	✓				760.2.a.a	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+q^{9}-4q^{11}-4q^{13}+\cdots\)
6080.2.a.e	$6080$	$2$	6080.a	1.a	$1$	$1$	$1$	$48.549$	\(\Q\)	None	✓				760.2.a.d	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots\)
6080.2.a.f	$6080$	$2$	6080.a	1.a	$1$	$1$	$1$	$48.549$	\(\Q\)	None	✓				380.2.a.b	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}+2q^{7}+q^{9}-6q^{13}+\cdots\)
6080.2.a.g	$6080$	$2$	6080.a	1.a	$1$	$1$	$1$	$48.549$	\(\Q\)	None	✓				3040.2.a.a	$1$	$2$	\(0\)	\(-1\)	\(-1\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-3q^{7}-2q^{9}-5q^{13}+\cdots\)
6080.2.a.h	$6080$	$2$	6080.a	1.a	$1$	$1$	$1$	$48.549$	\(\Q\)	None	✓				190.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-q^{7}-2q^{9}+q^{13}+q^{15}+\cdots\)
6080.2.a.i	$6080$	$2$	6080.a	1.a	$1$	$1$	$1$	$48.549$	\(\Q\)	None	✓				190.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}-2q^{9}+3q^{13}-q^{15}+\cdots\)
6080.2.a.j	$6080$	$2$	6080.a	1.a	$1$	$1$	$1$	$48.549$	\(\Q\)	None	✓				760.2.a.c	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{9}-4q^{11}+6q^{13}-6q^{17}+\cdots\)
6080.2.a.k	$6080$	$2$	6080.a	1.a	$1$	$1$	$1$	$48.549$	\(\Q\)	None	✓				760.2.a.c	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{9}+4q^{11}+6q^{13}-6q^{17}+\cdots\)
6080.2.a.l	$6080$	$2$	6080.a	1.a	$1$	$1$	$1$	$48.549$	\(\Q\)	None	✓				3040.2.a.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-3q^{9}-4q^{11}+4q^{13}+\cdots\)
6080.2.a.m	$6080$	$2$	6080.a	1.a	$1$	$1$	$1$	$48.549$	\(\Q\)	None	✓				380.2.a.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-3q^{9}+4q^{11}+4q^{13}+\cdots\)
6080.2.a.n	$6080$	$2$	6080.a	1.a	$1$	$1$	$1$	$48.549$	\(\Q\)	None	✓				380.2.a.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-3q^{9}-4q^{11}+4q^{13}+\cdots\)
6080.2.a.o	$6080$	$2$	6080.a	1.a	$1$	$1$	$1$	$48.549$	\(\Q\)	None	✓				3040.2.a.b	$1$	$0$	\(0\)	\(0\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-3q^{9}+4q^{11}+4q^{13}+\cdots\)
6080.2.a.p	$6080$	$2$	6080.a	1.a	$1$	$1$	$1$	$48.549$	\(\Q\)	None	✓				190.2.a.c	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{7}-2q^{9}+q^{13}-q^{15}+\cdots\)
6080.2.a.q	$6080$	$2$	6080.a	1.a	$1$	$1$	$1$	$48.549$	\(\Q\)	None	✓				3040.2.a.a	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+3q^{7}-2q^{9}-5q^{13}+\cdots\)
6080.2.a.r	$6080$	$2$	6080.a	1.a	$1$	$1$	$1$	$48.549$	\(\Q\)	None	✓				190.2.a.a	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}-2q^{9}+3q^{13}+q^{15}+\cdots\)
6080.2.a.s	$6080$	$2$	6080.a	1.a	$1$	$1$	$1$	$48.549$	\(\Q\)	None	✓				760.2.a.d	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
6080.2.a.t	$6080$	$2$	6080.a	1.a	$1$	$1$	$1$	$48.549$	\(\Q\)	None	✓				760.2.a.a	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+q^{9}+4q^{11}-4q^{13}+\cdots\)
6080.2.a.u	$6080$	$2$	6080.a	1.a	$1$	$1$	$1$	$48.549$	\(\Q\)	None	✓				760.2.a.b	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots\)
6080.2.a.v	$6080$	$2$	6080.a	1.a	$1$	$1$	$1$	$48.549$	\(\Q\)	None	✓				380.2.a.b	$1$	$1$	\(0\)	\(2\)	\(1\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}-2q^{7}+q^{9}-6q^{13}+\cdots\)
6080.2.a.w	$6080$	$2$	6080.a	1.a	$1$	$1$	$1$	$48.549$	\(\Q\)	None	✓				760.2.a.e	$1$	$0$	\(0\)	\(3\)	\(-1\)	\(1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-q^{5}+q^{7}+6q^{9}+4q^{11}+\cdots\)
6080.2.a.x	$6080$	$2$	6080.a	1.a	$1$	$1$	$1$	$48.549$	\(\Q\)	None	✓				190.2.a.b	$1$	$0$	\(0\)	\(3\)	\(1\)	\(-5\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+q^{5}-5q^{7}+6q^{9}+4q^{11}+\cdots\)
6080.2.a.y	$6080$	$2$	6080.a	1.a	$1$	$2$	$2$	$48.549$	\(\Q(\sqrt{2}) \)	None	✓				380.2.a.c	$1$	$0$	\(0\)	\(-4\)	\(-2\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-2+\beta )q^{3}-q^{5}+(2+2\beta )q^{7}+(3+\cdots)q^{9}+\cdots\)
6080.2.a.z	$6080$	$2$	6080.a	1.a	$1$	$2$	$2$	$48.549$	\(\Q(\sqrt{3}) \)	None	✓				380.2.a.d	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}-q^{5}+2q^{7}+(1-2\beta )q^{9}+\cdots\)
6080.2.a.ba	$6080$	$2$	6080.a	1.a	$1$	$2$	$2$	$48.549$	\(\Q(\sqrt{3}) \)	None	✓				760.2.a.g	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+q^{5}+(1-2\beta )q^{9}-2q^{11}+\cdots\)
6080.2.a.bb	$6080$	$2$	6080.a	1.a	$1$	$2$	$2$	$48.549$	\(\Q(\sqrt{17}) \)	None	✓				190.2.a.d	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-q^{5}+\beta q^{7}+(1+\beta )q^{9}+4q^{11}+\cdots\)
6080.2.a.bc	$6080$	$2$	6080.a	1.a	$1$	$2$	$2$	$48.549$	\(\Q(\sqrt{17}) \)	None	✓				3040.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(-5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+q^{5}+(-2-\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
6080.2.a.bd	$6080$	$2$	6080.a	1.a	$1$	$2$	$2$	$48.549$	\(\Q(\sqrt{2}) \)	None	✓				3040.2.a.f	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}-\beta q^{7}-3q^{9}-4q^{11}+(-2+\cdots)q^{13}+\cdots\)
6080.2.a.be	$6080$	$2$	6080.a	1.a	$1$	$2$	$2$	$48.549$	\(\Q(\sqrt{2}) \)	None	✓				3040.2.a.f	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}+\beta q^{7}-3q^{9}+4q^{11}+(-2+\cdots)q^{13}+\cdots\)
6080.2.a.bf	$6080$	$2$	6080.a	1.a	$1$	$2$	$2$	$48.549$	\(\Q(\sqrt{2}) \)	None	✓				760.2.a.f	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}-2\beta q^{7}-q^{9}+(-2+2\beta )q^{11}+\cdots\)
6080.2.a.bg	$6080$	$2$	6080.a	1.a	$1$	$2$	$2$	$48.549$	\(\Q(\sqrt{2}) \)	None	✓				760.2.a.f	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}-2\beta q^{7}-q^{9}+(2+2\beta )q^{11}+\cdots\)
6080.2.a.bh	$6080$	$2$	6080.a	1.a	$1$	$2$	$2$	$48.549$	\(\Q(\sqrt{17}) \)	None	✓				190.2.a.d	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}-\beta q^{7}+(1+\beta )q^{9}-4q^{11}+\cdots\)
6080.2.a.bi	$6080$	$2$	6080.a	1.a	$1$	$2$	$2$	$48.549$	\(\Q(\sqrt{17}) \)	None	✓				3040.2.a.e	$1$	$0$	\(0\)	\(1\)	\(2\)	\(5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}+(2+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
6080.2.a.bj	$6080$	$2$	6080.a	1.a	$1$	$2$	$2$	$48.549$	\(\Q(\sqrt{3}) \)	None	✓				380.2.a.d	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-q^{5}-2q^{7}+(1+2\beta )q^{9}+\cdots\)
6080.2.a.bk	$6080$	$2$	6080.a	1.a	$1$	$2$	$2$	$48.549$	\(\Q(\sqrt{3}) \)	None	✓				760.2.a.g	$1$	$0$	\(0\)	\(2\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+q^{5}+(1+2\beta )q^{9}+2q^{11}+\cdots\)
6080.2.a.bl	$6080$	$2$	6080.a	1.a	$1$	$2$	$2$	$48.549$	\(\Q(\sqrt{2}) \)	None	✓				380.2.a.c	$1$	$0$	\(0\)	\(4\)	\(-2\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(2+\beta )q^{3}-q^{5}+(-2+2\beta )q^{7}+(3+\cdots)q^{9}+\cdots\)
6080.2.a.bm	$6080$	$2$	6080.a	1.a	$1$	$3$	$3$	$48.549$	3.3.148.1	None	✓				3040.2.a.j	$1$	$1$	\(0\)	\(-4\)	\(-3\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}-q^{5}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots\)
6080.2.a.bn	$6080$	$2$	6080.a	1.a	$1$	$3$	$3$	$48.549$	3.3.148.1	None	✓				3040.2.a.i	$1$	$1$	\(0\)	\(-4\)	\(3\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}+q^{5}+(1+\beta _{1}-\beta _{2})q^{7}+\cdots\)
6080.2.a.bo	$6080$	$2$	6080.a	1.a	$1$	$3$	$3$	$48.549$	3.3.148.1	None	✓				95.2.a.a	$1$	$0$	\(0\)	\(-2\)	\(-3\)	\(0\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}-q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots\)
6080.2.a.bp	$6080$	$2$	6080.a	1.a	$1$	$3$	$3$	$48.549$	3.3.564.1	None	✓				3040.2.a.k	$1$	$1$	\(0\)	\(-2\)	\(3\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
6080.2.a.bq	$6080$	$2$	6080.a	1.a	$1$	$3$	$3$	$48.549$	3.3.229.1	None	✓				760.2.a.j	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(1\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}-q^{5}-\beta _{1}q^{7}+(1-\beta _{1})q^{9}+\cdots\)
6080.2.a.br	$6080$	$2$	6080.a	1.a	$1$	$3$	$3$	$48.549$	3.3.316.1	None	✓				760.2.a.i	$1$	$0$	\(0\)	\(-1\)	\(3\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+(1-2\beta _{1}+\beta _{2})q^{7}+\cdots\)
6080.2.a.bs	$6080$	$2$	6080.a	1.a	$1$	$3$	$3$	$48.549$	3.3.568.1	None	✓				760.2.a.h	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+(2+\beta _{2})q^{7}+(1+2\beta _{1}+\cdots)q^{9}+\cdots\)
6080.2.a.bt	$6080$	$2$	6080.a	1.a	$1$	$3$	$3$	$48.549$	3.3.148.1	None	✓				3040.2.a.l	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}-q^{5}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots\)
6080.2.a.bu	$6080$	$2$	6080.a	1.a	$1$	$3$	$3$	$48.549$	3.3.148.1	None	✓				3040.2.a.l	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}-q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
6080.2.a.bv	$6080$	$2$	6080.a	1.a	$1$	$3$	$3$	$48.549$	3.3.229.1	None	✓				760.2.a.j	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(-1\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}-q^{5}+\beta _{1}q^{7}+(1-\beta _{1})q^{9}+\cdots\)
6080.2.a.bw	$6080$	$2$	6080.a	1.a	$1$	$3$	$3$	$48.549$	3.3.568.1	None	✓				760.2.a.h	$1$	$1$	\(0\)	\(1\)	\(3\)	\(-5\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+(-2-\beta _{2})q^{7}+(1+2\beta _{1}+\cdots)q^{9}+\cdots\)
6080.2.a.bx	$6080$	$2$	6080.a	1.a	$1$	$3$	$3$	$48.549$	3.3.316.1	None	✓				760.2.a.i	$1$	$0$	\(0\)	\(1\)	\(3\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+(-1+2\beta _{1}-\beta _{2})q^{7}+\cdots\)
6080.2.a.by	$6080$	$2$	6080.a	1.a	$1$	$3$	$3$	$48.549$	3.3.148.1	None	✓				95.2.a.a	$1$	$0$	\(0\)	\(2\)	\(-3\)	\(0\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}-q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
6080.2.a.bz	$6080$	$2$	6080.a	1.a	$1$	$3$	$3$	$48.549$	3.3.564.1	None	✓				3040.2.a.k	$1$	$0$	\(0\)	\(2\)	\(3\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+q^{5}+(1-\beta _{2})q^{7}+(2+\cdots)q^{9}+\cdots\)
6080.2.a.ca	$6080$	$2$	6080.a	1.a	$1$	$3$	$3$	$48.549$	3.3.148.1	None	✓				3040.2.a.j	$1$	$0$	\(0\)	\(4\)	\(-3\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}-q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+\cdots\)
6080.2.a.cb	$6080$	$2$	6080.a	1.a	$1$	$3$	$3$	$48.549$	3.3.148.1	None	✓				3040.2.a.i	$1$	$0$	\(0\)	\(4\)	\(3\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+q^{5}+(-1-\beta _{1}+\beta _{2})q^{7}+\cdots\)
6080.2.a.cc	$6080$	$2$	6080.a	1.a	$1$	$4$	$4$	$48.549$	4.4.11344.1	None	✓				95.2.a.b	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(4\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+q^{5}+(1-\beta _{1})q^{7}+(2-\beta _{3})q^{9}+\cdots\)
6080.2.a.cd	$6080$	$2$	6080.a	1.a	$1$	$4$	$4$	$48.549$	4.4.17428.1	None	✓		✓		3040.2.a.r	$1$	$0$	\(0\)	\(-1\)	\(-4\)	\(5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+(1+\beta _{2})q^{7}+\beta _{2}q^{9}+\cdots\)
6080.2.a.ce	$6080$	$2$	6080.a	1.a	$1$	$4$	$4$	$48.549$	4.4.78292.1	None	✓		✓		3040.2.a.q	$1$	$1$	\(0\)	\(-1\)	\(4\)	\(-5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+(-1-\beta _{2})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
6080.2.a.cf	$6080$	$2$	6080.a	1.a	$1$	$4$	$4$	$48.549$	4.4.17428.1	None	✓		✓		3040.2.a.r	$1$	$1$	\(0\)	\(1\)	\(-4\)	\(-5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+(-1-\beta _{2})q^{7}+\beta _{2}q^{9}+\cdots\)
6080.2.a.cg	$6080$	$2$	6080.a	1.a	$1$	$4$	$4$	$48.549$	4.4.78292.1	None	✓				3040.2.a.q	$1$	$0$	\(0\)	\(1\)	\(4\)	\(5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+(1+\beta _{2})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
6080.2.a.ch	$6080$	$2$	6080.a	1.a	$1$	$4$	$4$	$48.549$	4.4.11344.1	None	✓				95.2.a.b	$1$	$0$	\(0\)	\(2\)	\(4\)	\(-4\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+q^{5}+(-1+\beta _{1})q^{7}+(2-\beta _{3})q^{9}+\cdots\)
6080.2.a.ci	$6080$	$2$	6080.a	1.a	$1$	$5$	$5$	$48.549$	5.5.387268.1	None	✓		✓		3040.2.a.u	$1$	$1$	\(0\)	\(-4\)	\(5\)	\(-4\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}+q^{5}+(-1-\beta _{4})q^{7}+\cdots\)
6080.2.a.cj	$6080$	$2$	6080.a	1.a	$1$	$5$	$5$	$48.549$	5.5.2363492.1	None	✓		✓		3040.2.a.v	$1$	$1$	\(0\)	\(-2\)	\(-5\)	\(-2\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}-\beta _{2}q^{7}+(4-\beta _{3})q^{9}+\cdots\)
6080.2.a.ck	$6080$	$2$	6080.a	1.a	$1$	$5$	$5$	$48.549$	5.5.2363492.1	None	✓		✓		3040.2.a.v	$1$	$0$	\(0\)	\(2\)	\(-5\)	\(2\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+\beta _{2}q^{7}+(4-\beta _{3})q^{9}+\cdots\)
6080.2.a.cl	$6080$	$2$	6080.a	1.a	$1$	$5$	$5$	$48.549$	5.5.387268.1	None	✓		✓		3040.2.a.u	$1$	$0$	\(0\)	\(4\)	\(5\)	\(4\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+q^{5}+(1+\beta _{4})q^{7}+(2+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6080))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6080)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(190))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(380))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(608))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(760))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1216))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1520))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3040))\)\(^{\oplus 2}\)