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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					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	13
845.2.a.b	$845$	$2$	845.a	1.a	$1$	$2$	$2$	$6.747$	\(\Q(\sqrt{5}) \)	None	✓				65.2.e.a	$1$	$1$	\(-1\)	\(0\)	\(-2\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(1-2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
845.2.a.c	$845$	$2$	845.a	1.a	$1$	$2$	$2$	$6.747$	\(\Q(\sqrt{13}) \)	None	✓				65.2.e.b	$1$	$1$	\(-1\)	\(2\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+q^{3}+(1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots\)
845.2.a.g	$845$	$2$	845.a	1.a	$1$	$2$	$2$	$6.747$	\(\Q(\sqrt{2}) \)	None	✓				65.2.a.b	$1$	$1$	\(2\)	\(0\)	\(-2\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}-\beta q^{3}+(1+2\beta )q^{4}-q^{5}+\cdots\)
845.2.a.j	$845$	$2$	845.a	1.a	$1$	$3$	$3$	$6.747$	\(\Q(\zeta_{14})^+\)	None	✓	✓	✓		845.2.a.h	$1$	$1$	\(1\)	\(-5\)	\(-3\)	\(5\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1-\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots\)

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