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Results (27 matches)

 

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
7.3.b.a	$7$	$3$	7.b	7.b	$2$	$1$	$1$	$0.191$	\(\Q\)	\(\Q(\sqrt{-7}) \)	✓	$2$	$0$	\(-3\)	\(0\)	\(0\)	\(-7\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3q^{2}+5q^{4}-7q^{7}-3q^{8}+9q^{9}+\cdots\)
7.4.a.a	$7$	$4$	7.a	1.a	$1$	$1$	$1$	$0.413$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(-2\)	\(16\)	\(-7\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}-7q^{4}+2^{4}q^{5}+2q^{6}+\cdots\)
7.4.c.a	$7$	$4$	7.c	7.c	$3$	$2$	$1$	$0.413$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-2\)	\(-7\)	\(-7\)	\(28\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+2\zeta_{6})q^{2}-7\zeta_{6}q^{3}+4\zeta_{6}q^{4}+\cdots\)
7.5.b.a	$7$	$5$	7.b	7.b	$2$	$1$	$1$	$0.724$	\(\Q\)	\(\Q(\sqrt{-7}) \)	✓	$2$	$0$	\(1\)	\(0\)	\(0\)	\(49\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+q^{2}-15q^{4}+7^{2}q^{7}-31q^{8}+3^{4}q^{9}+\cdots\)
7.5.d.a	$7$	$5$	7.d	7.d	$6$	$4$	$2$	$0.724$	\(\Q(\sqrt{-3}, \sqrt{22})\)	None		$2$	$0$	\(-4\)	\(6\)	\(-30\)	\(0\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+\beta _{1}-2\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
7.6.a.a	$7$	$6$	7.a	1.a	$1$	$1$	$1$	$1.123$	\(\Q\)	None	✓	$1$	$1$	\(-10\)	\(-14\)	\(-56\)	\(-49\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-10q^{2}-14q^{3}+68q^{4}-56q^{5}+\cdots\)
7.6.a.b	$7$	$6$	7.a	1.a	$1$	$2$	$2$	$1.123$	\(\Q(\sqrt{57}) \)	None	✓	$1$	$0$	\(9\)	\(-6\)	\(-18\)	\(98\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(5-\beta )q^{2}+(-6+6\beta )q^{3}+(7-9\beta )q^{4}+\cdots\)
7.6.c.a	$7$	$6$	7.c	7.c	$3$	$4$	$2$	$1.123$	\(\Q(\sqrt{-3}, \sqrt{37})\)	None		$2$	$0$	\(-2\)	\(8\)	\(38\)	\(-168\)		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{2})q^{2}+(4-4\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots\)
7.7.b.a	$7$	$7$	7.b	7.b	$2$	$1$	$1$	$1.610$	\(\Q\)	\(\Q(\sqrt{-7}) \)	✓	$2$	$0$	\(9\)	\(0\)	\(0\)	\(-343\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+9q^{2}+17q^{4}-7^{3}q^{7}-423q^{8}+\cdots\)
7.7.b.b	$7$	$7$	7.b	7.b	$2$	$2$	$2$	$1.610$	\(\Q(\sqrt{-510}) \)	None		$2$	$0$	\(-16\)	\(0\)	\(0\)	\(266\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-8q^{2}+\beta q^{3}-\beta q^{5}-8\beta q^{6}+(133+\cdots)q^{7}+\cdots\)
7.7.d.a	$7$	$7$	7.d	7.d	$6$	$2$	$1$	$1.610$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(12\)	\(-21\)	\(315\)	\(-686\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+12\zeta_{6}q^{2}+(-7-7\zeta_{6})q^{3}+(-80+\cdots)q^{4}+\cdots\)
7.7.d.b	$7$	$7$	7.d	7.d	$6$	$4$	$2$	$1.610$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(-8\)	\(18\)	\(-150\)	\(280\)		$3$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-4-4\beta _{1}+\beta _{2}+\beta _{3})q^{2}+(6+3\beta _{1}+\cdots)q^{3}+\cdots\)
7.8.a.a	$7$	$8$	7.a	1.a	$1$	$1$	$1$	$2.187$	\(\Q\)	None	✓	$1$	$1$	\(-6\)	\(-42\)	\(-84\)	\(343\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-6q^{2}-42q^{3}-92q^{4}-84q^{5}+252q^{6}+\cdots\)
7.8.a.b	$7$	$8$	7.a	1.a	$1$	$2$	$2$	$2.187$	\(\Q(\sqrt{865}) \)	None	✓	$1$	$0$	\(-3\)	\(94\)	\(330\)	\(-686\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+(46+2\beta )q^{3}+(89+3\beta )q^{4}+\cdots\)
7.8.c.a	$7$	$8$	7.c	7.c	$3$	$8$	$4$	$2.187$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(6\)	\(-28\)	\(-252\)	\(672\)		$2^{8}\cdot 3\cdot 7^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+2\beta _{2}+\beta _{3}-\beta _{4})q^{2}+(-6+\cdots)q^{3}+\cdots\)
7.9.b.a	$7$	$9$	7.b	7.b	$2$	$1$	$1$	$2.852$	\(\Q\)	\(\Q(\sqrt{-7}) \)	✓	$2$	$0$	\(-31\)	\(0\)	\(0\)	\(2401\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-31q^{2}+705q^{4}+7^{4}q^{7}-13919q^{8}+\cdots\)
7.9.b.b	$7$	$9$	7.b	7.b	$2$	$4$	$4$	$2.852$	\(\mathbb{Q}[x]/(x^{4} + \cdots)\)	None		$2$	$0$	\(32\)	\(0\)	\(0\)	\(1428\)		$2^{4}\cdot 3\cdot 7$	$\mathrm{SU}(2)[C_{2}]$	\(q+(8+\beta _{3})q^{2}-\beta _{1}q^{3}+(-8+2^{4}\beta _{3})q^{4}+\cdots\)
7.9.d.a	$7$	$9$	7.d	7.d	$6$	$8$	$4$	$2.852$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(-4\)	\(-84\)	\(-840\)	\(-140\)		$2^{4}\cdot 3\cdot 7^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}+\beta _{2}+\beta _{3})q^{2}+(-7+7\beta _{2}+\cdots)q^{3}+\cdots\)
7.10.a.a	$7$	$10$	7.a	1.a	$1$	$2$	$2$	$3.605$	\(\Q(\sqrt{193}) \)	None	✓	$1$	$1$	\(-6\)	\(-86\)	\(-2238\)	\(-4802\)	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-3-\beta )q^{2}+(-43+11\beta )q^{3}+(-310+\cdots)q^{4}+\cdots\)
7.10.a.b	$7$	$10$	7.a	1.a	$1$	$3$	$3$	$3.605$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(21\)	\(84\)	\(1554\)	\(7203\)	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(7-\beta _{2})q^{2}+(28-\beta _{1}-\beta _{2})q^{3}+(519+\cdots)q^{4}+\cdots\)
7.10.c.a	$7$	$10$	7.c	7.c	$3$	$10$	$5$	$3.605$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(-18\)	\(161\)	\(1533\)	\(-1036\)		$2^{12}\cdot 3^{3}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{2}-4\beta _{3})q^{2}+(33-\beta _{1}+\cdots)q^{3}+\cdots\)
7.11.b.a	$7$	$11$	7.b	7.b	$2$	$1$	$1$	$4.448$	\(\Q\)	\(\Q(\sqrt{-7}) \)	✓	$2$	$0$	\(57\)	\(0\)	\(0\)	\(-16807\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+57q^{2}+2225q^{4}-7^{5}q^{7}+68457q^{8}+\cdots\)
7.11.b.b	$7$	$11$	7.b	7.b	$2$	$4$	$4$	$4.448$	4.0.373770240.2	None		$2$	$0$	\(-48\)	\(0\)	\(0\)	\(4900\)		$2^{7}\cdot 3\cdot 5\cdot 7$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-12+\beta _{2})q^{2}-\beta _{1}q^{3}+(-12^{2}+\cdots)q^{4}+\cdots\)
7.11.d.a	$7$	$11$	7.d	7.d	$6$	$12$	$6$	$4.448$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(-12\)	\(-246\)	\(3330\)	\(-12572\)		$2^{10}\cdot 3^{4}\cdot 7^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2-\beta _{1}-2\beta _{2})q^{2}+(-3^{3}+2\beta _{1}+\cdots)q^{3}+\cdots\)
7.12.a.a	$7$	$12$	7.a	1.a	$1$	$2$	$2$	$5.378$	\(\Q(\sqrt{3369}) \)	None	✓	$1$	$1$	\(-54\)	\(120\)	\(-13500\)	\(33614\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-3^{3}-\beta )q^{2}+(60+6\beta )q^{3}+(2050+\cdots)q^{4}+\cdots\)
7.12.a.b	$7$	$12$	7.a	1.a	$1$	$3$	$3$	$5.378$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(77\)	\(-140\)	\(5026\)	\(-50421\)	$+$	$2$	$\mathrm{SU}(2)$	\(q+(26+\beta _{2})q^{2}+(-47-11\beta _{1}+10\beta _{2})q^{3}+\cdots\)
7.12.c.a	$7$	$12$	7.c	7.c	$3$	$12$	$6$	$5.378$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(22\)	\(-244\)	\(-8782\)	\(-504\)		$2^{20}\cdot 3^{3}\cdot 7^{6}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(4-\beta _{1}-4\beta _{2})q^{2}+(\beta _{1}-40\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots\)