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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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
614.2.a.a	$614$	$2$	614.a	1.a	$1$	$1$	$1$	$4.903$	\(\Q\)	None	✓	✓			614.2.a.a	$1$	$1$	\(1\)	\(-2\)	\(0\)	\(-1\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}+q^{4}-2q^{6}-q^{7}+q^{8}+\cdots\)
614.2.a.b	$614$	$2$	614.a	1.a	$1$	$1$	$1$	$4.903$	\(\Q\)	None	✓	✓			614.2.a.b	$1$	$1$	\(1\)	\(0\)	\(-2\)	\(-3\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{5}-3q^{7}+q^{8}-3q^{9}+\cdots\)
614.2.a.c	$614$	$2$	614.a	1.a	$1$	$3$	$3$	$4.903$	3.3.148.1	None	✓	✓	✓	✓	614.2.a.c	$1$	$1$	\(-3\)	\(0\)	\(-2\)	\(-3\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{2}q^{3}+q^{4}+(-1+\beta _{1})q^{5}+\cdots\)
614.2.a.d	$614$	$2$	614.a	1.a	$1$	$4$	$4$	$4.903$	4.4.8069.1	None	✓	✓			614.2.a.d	$1$	$0$	\(-4\)	\(-1\)	\(3\)	\(4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}+(1-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
614.2.a.e	$614$	$2$	614.a	1.a	$1$	$6$	$6$	$4.903$	6.6.51141537.1	None	✓	✓	✓		614.2.a.e	$1$	$0$	\(-6\)	\(0\)	\(0\)	\(-3\)	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{4}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{4}q^{6}+\cdots\)
614.2.a.f	$614$	$2$	614.a	1.a	$1$	$11$	$11$	$4.903$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	✓	✓	✓	614.2.a.f	$1$	$0$	\(11\)	\(3\)	\(-3\)	\(6\)	$-$	$3$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{2}q^{3}+q^{4}-\beta _{5}q^{5}+\beta _{2}q^{6}+\cdots\)
614.2.c.a	$614$	$2$	614.c	307.c	$3$	$2$	$1$	$4.903$	\(\Q(\sqrt{-3}) \)	None		✓			614.2.c.a	$2$	$1$	\(2\)	\(-6\)	\(-4\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}-3q^{3}+q^{4}+(-4+4\zeta_{6})q^{5}+\cdots\)
614.2.c.b	$614$	$2$	614.c	307.c	$3$	$4$	$2$	$4.903$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		✓			614.2.c.b	$2$	$0$	\(4\)	\(8\)	\(2\)	\(-2\)		$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+q^{2}+2q^{3}+q^{4}+\beta _{1}q^{5}+2q^{6}+\cdots\)
614.2.c.c	$614$	$2$	614.c	307.c	$3$	$22$	$11$	$4.903$		None		✓			614.2.c.c	$2$	$0$	\(22\)	\(-4\)	\(1\)	\(-2\)			$\mathrm{SU}(2)[C_{3}]$
614.2.c.d	$614$	$2$	614.c	307.c	$3$	$26$	$13$	$4.903$		None		✓	✓		614.2.c.d	$2$	$0$	\(-26\)	\(4\)	\(-1\)	\(-4\)			$\mathrm{SU}(2)[C_{3}]$
614.2.e.a	$614$	$2$	614.e	307.e	$9$	$72$	$12$	$4.903$		None		✓			614.2.e.a	$2$	$0$	\(36\)	\(0\)	\(0\)	\(-3\)			$\mathrm{SU}(2)[C_{9}]$
614.2.e.b	$614$	$2$	614.e	307.e	$9$	$78$	$13$	$4.903$		None		✓	✓		614.2.e.b	$2$	$0$	\(-39\)	\(0\)	\(0\)	\(3\)			$\mathrm{SU}(2)[C_{9}]$
614.2.f.a	$614$	$2$	614.f	307.f	$17$	$208$	$13$	$4.903$		None		✓			614.2.f.a	$2$	$0$	\(13\)	\(1\)	\(-1\)	\(19\)			$\mathrm{SU}(2)[C_{17}]$
614.2.f.b	$614$	$2$	614.f	307.f	$17$	$224$	$14$	$4.903$		None		✓	✓		614.2.f.b	$2$	$0$	\(-14\)	\(-5\)	\(-1\)	\(41\)			$\mathrm{SU}(2)[C_{17}]$
614.2.i.a	$614$	$2$	614.i	307.i	$51$	$416$	$13$	$4.903$		None		✓			614.2.i.a	$2$	$0$	\(26\)	\(-4\)	\(1\)	\(-13\)			$\mathrm{SU}(2)[C_{51}]$
614.2.i.b	$614$	$2$	614.i	307.i	$51$	$448$	$14$	$4.903$		None		✓	✓		614.2.i.b	$2$	$0$	\(-28\)	\(2\)	\(1\)	\(-47\)			$\mathrm{SU}(2)[C_{51}]$
614.2.k.a	$614$	$2$	614.k	307.k	$153$	$1152$	$12$	$4.903$		None		✓			614.2.k.a	$2$	$0$	\(-36\)	\(0\)	\(0\)	\(3\)			$\mathrm{SU}(2)[C_{153}]$
614.2.k.b	$614$	$2$	614.k	307.k	$153$	$1248$	$13$	$4.903$		None		✓	✓		614.2.k.b	$2$	$0$	\(39\)	\(0\)	\(0\)	\(-3\)			$\mathrm{SU}(2)[C_{153}]$
614.3.b.a	$614$	$3$	614.b	307.b	$2$	$2$	$2$	$16.730$	\(\Q(\sqrt{-2}) \)	None		✓			614.3.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(10\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+2\beta q^{3}-2q^{4}-3\beta q^{5}-4q^{6}+\cdots\)
614.3.b.b	$614$	$3$	614.b	307.b	$2$	$48$	$48$	$16.730$		None		✓	✓		614.3.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)			$\mathrm{SU}(2)[C_{2}]$
614.3.d.a	$614$	$3$	614.d	307.d	$6$	$100$	$50$	$16.730$		None		✓	✓	✓	614.3.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)			$\mathrm{SU}(2)[C_{6}]$
614.4.a.a	$614$	$4$	614.a	1.a	$1$	$14$	$14$	$36.227$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	✓	✓	✓	614.4.a.a	$1$	$1$	\(28\)	\(-10\)	\(-15\)	\(-63\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+(-1+\cdots)q^{5}+\cdots\)
614.4.a.b	$614$	$4$	614.a	1.a	$1$	$16$	$16$	$36.227$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	✓	✓	✓	614.4.a.b	$1$	$1$	\(-32\)	\(2\)	\(-15\)	\(-12\)	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q-2q^{2}+\beta _{1}q^{3}+4q^{4}+(-1-\beta _{11}+\cdots)q^{5}+\cdots\)
614.4.a.c	$614$	$4$	614.a	1.a	$1$	$23$	$23$	$36.227$		None	✓	✓	✓	✓	614.4.a.c	$1$	$0$	\(-46\)	\(-1\)	\(10\)	\(16\)	$+$		$\mathrm{SU}(2)$
614.4.a.d	$614$	$4$	614.a	1.a	$1$	$24$	$24$	$36.227$		None	✓	✓	✓	✓	614.4.a.d	$1$	$0$	\(48\)	\(17\)	\(10\)	\(63\)	$+$		$\mathrm{SU}(2)$
614.6.a.a	$614$	$6$	614.a	1.a	$1$	$27$	$27$	$98.476$		None	✓	✓	✓	✓	614.6.a.a	$1$	$1$	\(108\)	\(-46\)	\(-50\)	\(-308\)	$+$		$\mathrm{SU}(2)$
614.6.a.b	$614$	$6$	614.a	1.a	$1$	$28$	$28$	$98.476$		None	✓	✓	✓	✓	614.6.a.b	$1$	$1$	\(-112\)	\(8\)	\(-50\)	\(-75\)	$+$		$\mathrm{SU}(2)$
614.6.a.c	$614$	$6$	614.a	1.a	$1$	$35$	$35$	$98.476$		None	✓	✓	✓	✓	614.6.a.c	$1$	$0$	\(-140\)	\(-1\)	\(75\)	\(121\)	$-$		$\mathrm{SU}(2)$
614.6.a.d	$614$	$6$	614.a	1.a	$1$	$37$	$37$	$98.476$		None	✓	✓	✓	✓	614.6.a.d	$1$	$0$	\(148\)	\(35\)	\(75\)	\(574\)	$-$		$\mathrm{SU}(2)$
614.8.a.a	$614$	$8$	614.a	1.a	$1$	$40$	$40$	$191.804$		None	✓	✓	✓	✓	614.8.a.a	$1$	$1$	\(320\)	\(-121\)	\(-375\)	\(-3902\)	$-$		$\mathrm{SU}(2)$
614.8.a.b	$614$	$8$	614.a	1.a	$1$	$41$	$41$	$191.804$		None	✓	✓	✓	✓	614.8.a.b	$1$	$1$	\(-328\)	\(-13\)	\(-165\)	\(-939\)	$-$		$\mathrm{SU}(2)$
614.8.a.c	$614$	$8$	614.a	1.a	$1$	$48$	$48$	$191.804$		None	✓	✓	✓	✓	614.8.a.c	$1$	$0$	\(-384\)	\(-40\)	\(460\)	\(433\)	$+$		$\mathrm{SU}(2)$
614.8.a.d	$614$	$8$	614.a	1.a	$1$	$50$	$50$	$191.804$		None	✓	✓	✓	✓	614.8.a.d	$1$	$0$	\(400\)	\(122\)	\(250\)	\(2272\)	$+$		$\mathrm{SU}(2)$

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