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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1547.1.e.a	$1547$	$1$	1547.e	1547.e	$2$	$1$	$1$	$0.772$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-1547}) \)	None	✓	✓			1547.1.e.a	$2$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)		$1$		\(q-q^{3}+q^{4}-q^{7}+q^{11}-q^{12}-q^{13}+\cdots\)
1547.1.e.b	$1547$	$1$	1547.e	1547.e	$2$	$1$	$1$	$0.772$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-1547}) \)	None	✓	✓			1547.1.e.a	$2$	$0$	\(0\)	\(-1\)	\(0\)	\(1\)		$1$		\(q-q^{3}+q^{4}+q^{7}-q^{11}-q^{12}+q^{13}+\cdots\)
1547.1.e.c	$1547$	$1$	1547.e	1547.e	$2$	$1$	$1$	$0.772$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-1547}) \)	None	✓	✓			1547.1.e.a	$2$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)		$1$		\(q+q^{3}+q^{4}-q^{7}+q^{11}+q^{12}+q^{13}+\cdots\)
1547.1.e.d	$1547$	$1$	1547.e	1547.e	$2$	$1$	$1$	$0.772$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-1547}) \)	None	✓	✓			1547.1.e.a	$2$	$0$	\(0\)	\(1\)	\(0\)	\(1\)		$1$		\(q+q^{3}+q^{4}+q^{7}-q^{11}+q^{12}-q^{13}+\cdots\)
1547.2.a.a	$1547$	$2$	1547.a	1.a	$1$	$1$	$1$	$12.353$	\(\Q\)	$_{}$	None	None	✓	✓			1547.2.a.a	$1$	$1$	\(-1\)	\(-2\)	\(0\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}-q^{4}+2q^{6}-q^{7}+3q^{8}+\cdots\)
1547.2.a.b	$1547$	$2$	1547.a	1.a	$1$	$2$	$2$	$12.353$	\(\Q(\sqrt{5}) \)	$_{}$	None	None	✓	✓			1547.2.a.b	$1$	$0$	\(-2\)	\(-2\)	\(2\)	\(2\)	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+(-1+\beta )q^{3}-q^{4}+(1+\beta )q^{5}+\cdots\)
1547.2.a.c	$1547$	$2$	1547.a	1.a	$1$	$4$	$4$	$12.353$	4.4.17417.1	$_{}$	None	None	✓	✓			1547.2.a.c	$1$	$0$	\(0\)	\(2\)	\(1\)	\(-4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}-2q^{4}+(-\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots\)
1547.2.a.d	$1547$	$2$	1547.a	1.a	$1$	$6$	$6$	$12.353$	6.6.5611169.1	$_{}$	None	None	✓	✓	✓		1547.2.a.d	$1$	$1$	\(-1\)	\(0\)	\(-2\)	\(-6\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}-\beta _{1}q^{3}+(\beta _{2}-\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1547.2.a.e	$1547$	$2$	1547.a	1.a	$1$	$6$	$6$	$12.353$	6.6.3319769.1	$_{}$	None	None	✓	✓	✓	✓	1547.2.a.e	$1$	$1$	\(0\)	\(-2\)	\(-3\)	\(6\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}+(-1+\beta _{5})q^{5}+\cdots\)
1547.2.a.f	$1547$	$2$	1547.a	1.a	$1$	$7$	$7$	$12.353$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	$_{}$	None	None	✓	✓	✓		1547.2.a.f	$1$	$0$	\(2\)	\(0\)	\(4\)	\(-7\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{5}q^{2}+\beta _{1}q^{3}+(2+\beta _{1})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
1547.2.a.g	$1547$	$2$	1547.a	1.a	$1$	$9$	$9$	$12.353$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	$_{}$	None	None	✓	✓	✓	✓	1547.2.a.g	$1$	$1$	\(-3\)	\(-4\)	\(-6\)	\(9\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{5}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1547.2.a.h	$1547$	$2$	1547.a	1.a	$1$	$14$	$14$	$12.353$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	$_{}$	None	None	✓	✓	✓	✓	1547.2.a.h	$1$	$0$	\(-1\)	\(8\)	\(8\)	\(-14\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1-\beta _{5})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
1547.2.a.i	$1547$	$2$	1547.a	1.a	$1$	$14$	$14$	$12.353$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	$_{}$	None	None	✓	✓	✓	✓	1547.2.a.i	$1$	$1$	\(1\)	\(-4\)	\(-9\)	\(-14\)	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{10}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1547.2.a.j	$1547$	$2$	1547.a	1.a	$1$	$14$	$14$	$12.353$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	$_{}$	None	None	✓	✓	✓	✓	1547.2.a.j	$1$	$0$	\(2\)	\(2\)	\(4\)	\(14\)	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{2})q^{4}+\beta _{6}q^{5}+\cdots\)
1547.2.a.k	$1547$	$2$	1547.a	1.a	$1$	$18$	$18$	$12.353$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	$_{}$	None	None	✓	✓	✓		1547.2.a.k	$1$	$0$	\(4\)	\(6\)	\(3\)	\(18\)	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{8}q^{3}+(2+\beta _{2})q^{4}-\beta _{16}q^{5}+\cdots\)
1547.4.a.a	$1547$	$4$	1547.a	1.a	$1$	$1$	$1$	$91.276$	\(\Q\)	$_{}$	None	None	✓	✓			1547.4.a.a	$1$	$2$	\(1\)	\(-8\)	\(-6\)	\(-7\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-8q^{3}-7q^{4}-6q^{5}-8q^{6}+\cdots\)
1547.4.a.b	$1547$	$4$	1547.a	1.a	$1$	$27$	$27$	$91.276$		$_{}$	None	None	✓	✓	✓	✓	1547.4.a.b	$1$	$1$	\(-6\)	\(-23\)	\(-36\)	\(189\)	$-$		$\mathrm{SU}(2)$
1547.4.a.c	$1547$	$4$	1547.a	1.a	$1$	$34$	$34$	$91.276$		$_{}$	None	None	✓	✓	✓	✓	1547.4.a.c	$1$	$0$	\(-5\)	\(13\)	\(44\)	\(-238\)	$+$		$\mathrm{SU}(2)$
1547.4.a.d	$1547$	$4$	1547.a	1.a	$1$	$34$	$34$	$91.276$		$_{}$	None	None	✓	✓	✓	✓	1547.4.a.d	$1$	$1$	\(-1\)	\(-23\)	\(-28\)	\(-238\)	$-$		$\mathrm{SU}(2)$
1547.4.a.e	$1547$	$4$	1547.a	1.a	$1$	$34$	$34$	$91.276$		$_{}$	None	None	✓	✓	✓	✓	1547.4.a.e	$1$	$1$	\(0\)	\(-5\)	\(-14\)	\(238\)	$-$		$\mathrm{SU}(2)$
1547.4.a.f	$1547$	$4$	1547.a	1.a	$1$	$37$	$37$	$91.276$		$_{}$	None	None	✓	✓	✓	✓	1547.4.a.f	$1$	$1$	\(-7\)	\(-5\)	\(-26\)	\(-259\)	$-$		$\mathrm{SU}(2)$
1547.4.a.g	$1547$	$4$	1547.a	1.a	$1$	$39$	$39$	$91.276$		$_{}$	None	None	✓	✓	✓	✓	1547.4.a.g	$1$	$0$	\(10\)	\(13\)	\(36\)	\(273\)	$+$		$\mathrm{SU}(2)$
1547.4.a.h	$1547$	$4$	1547.a	1.a	$1$	$40$	$40$	$91.276$		$_{}$	None	None	✓	✓	✓		1547.4.a.h	$1$	$0$	\(0\)	\(15\)	\(28\)	\(-280\)	$+$		$\mathrm{SU}(2)$
1547.4.a.i	$1547$	$4$	1547.a	1.a	$1$	$42$	$42$	$91.276$		$_{}$	None	None	✓	✓	✓	✓	1547.4.a.i	$1$	$0$	\(4\)	\(7\)	\(34\)	\(294\)	$+$		$\mathrm{SU}(2)$

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