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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				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
5001.2.a.a	$5001$	$2$	5001.a	1.a	$1$	$3$	$3$	$39.933$	\(\Q(\zeta_{14})^+\)	None	✓	✓			5001.2.a.a	$1$	$1$	\(-2\)	\(-3\)	\(-3\)	\(-7\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
5001.2.a.b	$5001$	$2$	5001.a	1.a	$1$	$57$	$57$	$39.933$		None	✓	✓	✓		5001.2.a.b	$1$	$1$	\(1\)	\(-57\)	\(14\)	\(-9\)	$+$		$\mathrm{SU}(2)$
5001.2.a.c	$5001$	$2$	5001.a	1.a	$1$	$60$	$60$	$39.933$		None	✓	✓	✓	✓	5001.2.a.c	$1$	$1$	\(-13\)	\(60\)	\(-35\)	\(-14\)	$+$		$\mathrm{SU}(2)$
5001.2.a.d	$5001$	$2$	5001.a	1.a	$1$	$78$	$78$	$39.933$		None	✓	✓	✓	✓	5001.2.a.d	$1$	$0$	\(15\)	\(78\)	\(33\)	\(12\)	$-$		$\mathrm{SU}(2)$
5001.2.a.e	$5001$	$2$	5001.a	1.a	$1$	$79$	$79$	$39.933$		None	✓	✓	✓	✓	5001.2.a.e	$1$	$0$	\(0\)	\(-79\)	\(-15\)	\(18\)	$-$		$\mathrm{SU}(2)$
5002.2.a.a	$5002$	$2$	5002.a	1.a	$1$	$1$	$1$	$39.941$	\(\Q\)	None	✓	✓			5002.2.a.a	$1$	$2$	\(-1\)	\(-2\)	\(-2\)	\(-2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}+q^{4}-2q^{5}+2q^{6}-2q^{7}+\cdots\)
5002.2.a.b	$5002$	$2$	5002.a	1.a	$1$	$1$	$1$	$39.941$	\(\Q\)	None	✓	✓			5002.2.a.b	$1$	$1$	\(-1\)	\(-2\)	\(-2\)	\(4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}+q^{4}-2q^{5}+2q^{6}+4q^{7}+\cdots\)
5002.2.a.c	$5002$	$2$	5002.a	1.a	$1$	$1$	$1$	$39.941$	\(\Q\)	None	✓	✓			5002.2.a.c	$1$	$0$	\(1\)	\(2\)	\(2\)	\(2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+2q^{3}+q^{4}+2q^{5}+2q^{6}+2q^{7}+\cdots\)
5002.2.a.d	$5002$	$2$	5002.a	1.a	$1$	$2$	$2$	$39.941$	\(\Q(\sqrt{13}) \)	None	✓	✓			5002.2.a.d	$1$	$1$	\(-2\)	\(1\)	\(-6\)	\(2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta q^{3}+q^{4}-3q^{5}-\beta q^{6}+2\beta q^{7}+\cdots\)
5002.2.a.e	$5002$	$2$	5002.a	1.a	$1$	$2$	$2$	$39.941$	\(\Q(\sqrt{5}) \)	None	✓	✓			5002.2.a.e	$1$	$2$	\(-2\)	\(1\)	\(-4\)	\(-4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta q^{3}+q^{4}+(-1-2\beta )q^{5}+\cdots\)
5002.2.a.f	$5002$	$2$	5002.a	1.a	$1$	$2$	$2$	$39.941$	\(\Q(\sqrt{5}) \)	None	✓	✓			5002.2.a.f	$1$	$2$	\(2\)	\(-3\)	\(-6\)	\(-6\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1-\beta )q^{3}+q^{4}-3q^{5}+(-1+\cdots)q^{6}+\cdots\)
5002.2.a.g	$5002$	$2$	5002.a	1.a	$1$	$2$	$2$	$39.941$	\(\Q(\sqrt{5}) \)	None	✓	✓			5002.2.a.g	$1$	$1$	\(2\)	\(-1\)	\(-2\)	\(2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta q^{3}+q^{4}-q^{5}-\beta q^{6}+(2+\cdots)q^{7}+\cdots\)
5002.2.a.h	$5002$	$2$	5002.a	1.a	$1$	$3$	$3$	$39.941$	\(\Q(\zeta_{18})^+\)	None	✓	✓			5002.2.a.h	$1$	$0$	\(-3\)	\(3\)	\(3\)	\(-3\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1+\beta _{1})q^{3}+q^{4}+(1-\beta _{1}-\beta _{2})q^{5}+\cdots\)
5002.2.a.i	$5002$	$2$	5002.a	1.a	$1$	$3$	$3$	$39.941$	3.3.257.1	None	✓	✓			5002.2.a.i	$1$	$0$	\(3\)	\(3\)	\(-1\)	\(5\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(1+\beta _{2})q^{3}+q^{4}-\beta _{1}q^{5}+(1+\cdots)q^{6}+\cdots\)
5002.2.a.j	$5002$	$2$	5002.a	1.a	$1$	$17$	$17$	$39.941$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	✓	✓		5002.2.a.j	$1$	$1$	\(17\)	\(-7\)	\(-11\)	\(-6\)	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}+(-1+\beta _{2})q^{5}+\cdots\)
5002.2.a.k	$5002$	$2$	5002.a	1.a	$1$	$20$	$20$	$39.941$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	✓	✓		5002.2.a.k	$1$	$0$	\(-20\)	\(11\)	\(9\)	\(12\)	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+\beta _{2}q^{5}+(-1+\cdots)q^{6}+\cdots\)
5002.2.a.l	$5002$	$2$	5002.a	1.a	$1$	$20$	$20$	$39.941$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	✓	✓	✓	5002.2.a.l	$1$	$1$	\(20\)	\(-8\)	\(-9\)	\(-16\)	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{7}q^{5}-\beta _{1}q^{6}+\cdots\)
5002.2.a.m	$5002$	$2$	5002.a	1.a	$1$	$21$	$21$	$39.941$		None	✓	✓	✓		5002.2.a.m	$1$	$0$	\(-21\)	\(7\)	\(4\)	\(-1\)	$-$		$\mathrm{SU}(2)$
5002.2.a.n	$5002$	$2$	5002.a	1.a	$1$	$24$	$24$	$39.941$		None	✓	✓	✓		5002.2.a.n	$1$	$1$	\(-24\)	\(-13\)	\(-1\)	\(-6\)	$+$		$\mathrm{SU}(2)$
5002.2.a.o	$5002$	$2$	5002.a	1.a	$1$	$24$	$24$	$39.941$		None	✓	✓	✓		5002.2.a.o	$1$	$0$	\(24\)	\(8\)	\(16\)	\(9\)	$-$		$\mathrm{SU}(2)$
5002.2.a.p	$5002$	$2$	5002.a	1.a	$1$	$26$	$26$	$39.941$		None	✓	✓	✓		5002.2.a.p	$1$	$1$	\(-26\)	\(-4\)	\(-1\)	\(2\)	$+$		$\mathrm{SU}(2)$
5002.2.a.q	$5002$	$2$	5002.a	1.a	$1$	$30$	$30$	$39.941$		None	✓	✓	✓	✓	5002.2.a.q	$1$	$0$	\(30\)	\(8\)	\(13\)	\(6\)	$-$		$\mathrm{SU}(2)$
5003.2.a.a	$5003$	$2$	5003.a	1.a	$1$	$3$	$3$	$39.949$	\(\Q(\zeta_{14})^+\)	None	✓	✓			5003.2.a.a	$1$	$2$	\(-1\)	\(-3\)	\(-7\)	\(-8\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots\)
5003.2.a.b	$5003$	$2$	5003.a	1.a	$1$	$194$	$194$	$39.949$		None	✓	✓	✓	✓	5003.2.a.b	$1$	$1$	\(-20\)	\(-18\)	\(-39\)	\(-63\)	$+$		$\mathrm{SU}(2)$
5003.2.a.c	$5003$	$2$	5003.a	1.a	$1$	$220$	$220$	$39.949$		None	✓	✓	✓		5003.2.a.c	$1$	$0$	\(21\)	\(19\)	\(44\)	\(71\)	$-$		$\mathrm{SU}(2)$
5004.2.a.a	$5004$	$2$	5004.a	1.a	$1$	$1$	$1$	$39.957$	\(\Q\)	None	✓				1668.2.a.c	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-q^{7}+3q^{11}+5q^{13}+6q^{17}+\cdots\)
5004.2.a.b	$5004$	$2$	5004.a	1.a	$1$	$1$	$1$	$39.957$	\(\Q\)	None	✓	✓			5004.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-2q^{7}-3q^{11}+q^{13}+7q^{17}+\cdots\)
5004.2.a.c	$5004$	$2$	5004.a	1.a	$1$	$1$	$1$	$39.957$	\(\Q\)	None	✓				1668.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+4q^{7}-6q^{11}-2q^{13}+4q^{17}+\cdots\)
5004.2.a.d	$5004$	$2$	5004.a	1.a	$1$	$1$	$1$	$39.957$	\(\Q\)	None	✓				1668.2.a.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-3\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-3q^{7}-3q^{11}+q^{13}+6q^{17}+\cdots\)
5004.2.a.e	$5004$	$2$	5004.a	1.a	$1$	$1$	$1$	$39.957$	\(\Q\)	None	✓				556.2.a.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}-q^{11}-3q^{13}-2q^{17}+\cdots\)
5004.2.a.f	$5004$	$2$	5004.a	1.a	$1$	$1$	$1$	$39.957$	\(\Q\)	None	✓	✓			5004.2.a.b	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-2q^{7}+3q^{11}+q^{13}-7q^{17}+\cdots\)
5004.2.a.g	$5004$	$2$	5004.a	1.a	$1$	$2$	$2$	$39.957$	\(\Q(\sqrt{13}) \)	None	✓				1668.2.a.d	$1$	$1$	\(0\)	\(0\)	\(2\)	\(1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+(1-\beta )q^{7}+3q^{11}+(-4+2\beta )q^{13}+\cdots\)
5004.2.a.h	$5004$	$2$	5004.a	1.a	$1$	$3$	$3$	$39.957$	3.3.1304.1	None	✓				1668.2.a.f	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-3\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{5}+(-1-\beta _{1})q^{7}+(2+\cdots)q^{11}+\cdots\)
5004.2.a.i	$5004$	$2$	5004.a	1.a	$1$	$3$	$3$	$39.957$	3.3.229.1	None	✓				1668.2.a.e	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1}-\beta _{2})q^{5}+(2\beta _{1}-\beta _{2})q^{7}+\cdots\)
5004.2.a.j	$5004$	$2$	5004.a	1.a	$1$	$3$	$3$	$39.957$	3.3.321.1	None	✓				556.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{2})q^{5}+(-1+\beta _{2})q^{7}+(4+\beta _{1}+\cdots)q^{11}+\cdots\)
5004.2.a.k	$5004$	$2$	5004.a	1.a	$1$	$6$	$6$	$39.957$	6.6.582873408.1	None	✓	✓	✓		5004.2.a.k	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}-\beta _{2}q^{7}-\beta _{1}q^{11}+(-1+\beta _{2}+\cdots)q^{13}+\cdots\)
5004.2.a.l	$5004$	$2$	5004.a	1.a	$1$	$6$	$6$	$39.957$	6.6.62452821.1	None	✓				1668.2.a.g	$1$	$0$	\(0\)	\(0\)	\(3\)	\(4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{5}+(1+\beta _{3})q^{7}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
5004.2.a.m	$5004$	$2$	5004.a	1.a	$1$	$7$	$7$	$39.957$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓		✓		1668.2.a.h	$1$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}+(\beta _{4}+\beta _{5})q^{7}+\beta _{5}q^{11}+(1+\cdots)q^{13}+\cdots\)
5004.2.a.n	$5004$	$2$	5004.a	1.a	$1$	$7$	$7$	$39.957$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓		✓		556.2.a.c	$1$	$1$	\(0\)	\(0\)	\(1\)	\(1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{2}+\beta _{5})q^{5}+(-\beta _{2}+\beta _{4})q^{7}+(-2+\cdots)q^{11}+\cdots\)
5004.2.a.o	$5004$	$2$	5004.a	1.a	$1$	$14$	$14$	$39.957$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	✓	✓	✓	5004.2.a.o	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}+(1+\beta _{5})q^{7}-\beta _{9}q^{11}+(\beta _{5}+\cdots)q^{13}+\cdots\)
5004.2.e.a	$5004$	$2$	5004.e	417.d	$2$	$24$	$24$	$39.957$		\(\Q(\sqrt{-139}) \)		✓			5004.2.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{U}(1)[D_{2}]$
5004.2.e.b	$5004$	$2$	5004.e	417.d	$2$	$24$	$24$	$39.957$		None		✓			5004.2.e.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
5004.2.bc.a	$5004$	$2$	5004.bc	417.f	$6$	$92$	$46$	$39.957$		None		✓	✓	✓	5004.2.bc.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)			$\mathrm{SU}(2)[C_{6}]$
5005.2.a.a	$5005$	$2$	5005.a	1.a	$1$	$1$	$1$	$39.965$	\(\Q\)	None	✓	✓			5005.2.a.a	$1$	$1$	\(-2\)	\(0\)	\(1\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+q^{5}-q^{7}-3q^{9}-2q^{10}+\cdots\)
5005.2.a.b	$5005$	$2$	5005.a	1.a	$1$	$1$	$1$	$39.965$	\(\Q\)	None	✓	✓			5005.2.a.b	$1$	$0$	\(-2\)	\(0\)	\(1\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+q^{5}+q^{7}-3q^{9}-2q^{10}+\cdots\)
5005.2.a.c	$5005$	$2$	5005.a	1.a	$1$	$1$	$1$	$39.965$	\(\Q\)	None	✓	✓			5005.2.a.c	$1$	$0$	\(-1\)	\(0\)	\(1\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+q^{5}-q^{7}+3q^{8}-3q^{9}+\cdots\)
5005.2.a.d	$5005$	$2$	5005.a	1.a	$1$	$1$	$1$	$39.965$	\(\Q\)	None	✓	✓			5005.2.a.d	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-q^{5}+q^{7}-3q^{8}-3q^{9}+\cdots\)
5005.2.a.e	$5005$	$2$	5005.a	1.a	$1$	$1$	$1$	$39.965$	\(\Q\)	None	✓	✓			5005.2.a.e	$1$	$0$	\(1\)	\(0\)	\(1\)	\(-1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}-q^{7}-3q^{8}-3q^{9}+\cdots\)
5005.2.a.f	$5005$	$2$	5005.a	1.a	$1$	$1$	$1$	$39.965$	\(\Q\)	None	✓	✓			5005.2.a.f	$1$	$0$	\(1\)	\(0\)	\(1\)	\(1\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}+q^{7}-3q^{8}-3q^{9}+\cdots\)
5005.2.a.g	$5005$	$2$	5005.a	1.a	$1$	$11$	$11$	$39.965$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	✓	✓	✓	5005.2.a.g	$1$	$1$	\(-5\)	\(-9\)	\(11\)	\(11\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1-\beta _{8})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)

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