Newform search results

Results (1-50 of 349 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	$2$	$1$	$1$	$0.191$	\(\Q\)	\(\Q(\sqrt{-7}) \)	✓	$2$	$0$	\(-3\)	\(0\)	\(0\)	\(-7\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3q^{2}+5q^{4}-7q^{7}-3q^{8}+9q^{9}+\cdots\)
8.3.d.a	$8$	$3$	8.d	8.d	$2$	$1$	$1$	$0.218$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓	$2$	$0$	\(-2\)	\(-2\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2q^{2}-2q^{3}+4q^{4}+4q^{6}-8q^{8}+\cdots\)
5.4.a.a	$5$	$4$	5.a	1.a	$1$	$1$	$1$	$0.295$	\(\Q\)	None	✓	$1$	$0$	\(-4\)	\(2\)	\(-5\)	\(6\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+2q^{3}+8q^{4}-5q^{5}-8q^{6}+\cdots\)
6.4.a.a	$6$	$4$	6.a	1.a	$1$	$1$	$1$	$0.354$	\(\Q\)	None	✓	$1$	$0$	\(-2\)	\(-3\)	\(6\)	\(-16\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-3q^{3}+4q^{4}+6q^{5}+6q^{6}+\cdots\)
7.4.a.a	$7$	$4$	7.a	1.a	$1$	$1$	$1$	$0.413$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(-2\)	\(16\)	\(-7\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}-7q^{4}+2^{4}q^{5}+2q^{6}+\cdots\)
4.5.b.a	$4$	$5$	4.b	4.b	$2$	$1$	$1$	$0.413$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(-4\)	\(0\)	\(-14\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-4q^{2}+2^{4}q^{4}-14q^{5}-2^{6}q^{8}+3^{4}q^{9}+\cdots\)
8.4.a.a	$8$	$4$	8.a	1.a	$1$	$1$	$1$	$0.472$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-4\)	\(-2\)	\(24\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{3}-2q^{5}+24q^{7}-11q^{9}-44q^{11}+\cdots\)
3.6.a.a	$3$	$6$	3.a	1.a	$1$	$1$	$1$	$0.481$	\(\Q\)	None	✓	$1$	$0$	\(-6\)	\(9\)	\(6\)	\(-40\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-6q^{2}+9q^{3}+4q^{4}+6q^{5}-54q^{6}+\cdots\)
9.4.a.a	$9$	$4$	9.a	1.a	$1$	$1$	$1$	$0.531$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(20\)	$+$	$1$	$N(\mathrm{U}(1))$	\(q-8q^{4}+20q^{7}-70q^{13}+2^{6}q^{16}+\cdots\)
10.4.a.a	$10$	$4$	10.a	1.a	$1$	$1$	$1$	$0.590$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(-8\)	\(5\)	\(-4\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-8q^{3}+4q^{4}+5q^{5}-2^{4}q^{6}+\cdots\)
2.8.a.a	$2$	$8$	2.a	1.a	$1$	$1$	$1$	$0.625$	\(\Q\)	None	✓	$1$	$0$	\(-8\)	\(12\)	\(-210\)	\(1016\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-8q^{2}+12q^{3}+2^{6}q^{4}-210q^{5}+\cdots\)
4.6.a.a	$4$	$6$	4.a	1.a	$1$	$1$	$1$	$0.642$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-12\)	\(54\)	\(-88\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-12q^{3}+54q^{5}-88q^{7}-99q^{9}+\cdots\)
3.7.b.a	$3$	$7$	3.b	3.b	$2$	$1$	$1$	$0.690$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(-27\)	\(0\)	\(-286\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3^{3}q^{3}+2^{6}q^{4}-286q^{7}+3^{6}q^{9}+\cdots\)
7.5.b.a	$7$	$5$	7.b	7.b	$2$	$1$	$1$	$0.724$	\(\Q\)	\(\Q(\sqrt{-7}) \)	✓	$2$	$0$	\(1\)	\(0\)	\(0\)	\(49\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+q^{2}-15q^{4}+7^{2}q^{7}-31q^{8}+3^{4}q^{9}+\cdots\)
5.6.a.a	$5$	$6$	5.a	1.a	$1$	$1$	$1$	$0.802$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(-4\)	\(25\)	\(192\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-4q^{3}-28q^{4}+5^{2}q^{5}-8q^{6}+\cdots\)
8.5.d.a	$8$	$5$	8.d	8.d	$2$	$1$	$1$	$0.827$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓	$2$	$0$	\(4\)	\(-14\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4q^{2}-14q^{3}+2^{4}q^{4}-56q^{6}+2^{6}q^{8}+\cdots\)
3.8.a.a	$3$	$8$	3.a	1.a	$1$	$1$	$1$	$0.937$	\(\Q\)	None	✓	$1$	$0$	\(6\)	\(-27\)	\(390\)	\(-64\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+6q^{2}-3^{3}q^{3}-92q^{4}+390q^{5}+\cdots\)
6.6.a.a	$6$	$6$	6.a	1.a	$1$	$1$	$1$	$0.962$	\(\Q\)	None	✓	$1$	$0$	\(4\)	\(-9\)	\(-66\)	\(176\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}-9q^{3}+2^{4}q^{4}-66q^{5}-6^{2}q^{6}+\cdots\)
2.10.a.a	$2$	$10$	2.a	1.a	$1$	$1$	$1$	$1.030$	\(\Q\)	None	✓	$1$	$0$	\(16\)	\(-156\)	\(870\)	\(-952\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2^{4}q^{2}-156q^{3}+2^{8}q^{4}+870q^{5}+\cdots\)
7.6.a.a	$7$	$6$	7.a	1.a	$1$	$1$	$1$	$1.123$	\(\Q\)	None	✓	$1$	$1$	\(-10\)	\(-14\)	\(-56\)	\(-49\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-10q^{2}-14q^{3}+68q^{4}-56q^{5}+\cdots\)
8.6.a.a	$8$	$6$	8.a	1.a	$1$	$1$	$1$	$1.283$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(20\)	\(-74\)	\(-24\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+20q^{3}-74q^{5}-24q^{7}+157q^{9}+\cdots\)
9.6.a.a	$9$	$6$	9.a	1.a	$1$	$1$	$1$	$1.443$	\(\Q\)	None	✓	$1$	$0$	\(6\)	\(0\)	\(-6\)	\(-40\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+6q^{2}+4q^{4}-6q^{5}-40q^{7}-168q^{8}+\cdots\)
3.10.a.a	$3$	$10$	3.a	1.a	$1$	$1$	$1$	$1.545$	\(\Q\)	None	✓	$1$	$1$	\(-36\)	\(-81\)	\(-1314\)	\(-4480\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-6^{2}q^{2}-3^{4}q^{3}+28^{2}q^{4}-1314q^{5}+\cdots\)
3.10.a.b	$3$	$10$	3.a	1.a	$1$	$1$	$1$	$1.545$	\(\Q\)	None	✓	$1$	$0$	\(18\)	\(81\)	\(-1530\)	\(9128\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+18q^{2}+3^{4}q^{3}-188q^{4}-1530q^{5}+\cdots\)
5.8.a.a	$5$	$8$	5.a	1.a	$1$	$1$	$1$	$1.562$	\(\Q\)	None	✓	$1$	$1$	\(-14\)	\(-48\)	\(125\)	\(-1644\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-14q^{2}-48q^{3}+68q^{4}+5^{3}q^{5}+\cdots\)
10.6.a.a	$10$	$6$	10.a	1.a	$1$	$1$	$1$	$1.604$	\(\Q\)	None	✓	$1$	$1$	\(-4\)	\(-26\)	\(-25\)	\(-22\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}-26q^{3}+2^{4}q^{4}-5^{2}q^{5}+104q^{6}+\cdots\)
10.6.a.b	$10$	$6$	10.a	1.a	$1$	$1$	$1$	$1.604$	\(\Q\)	None	✓	$1$	$0$	\(-4\)	\(24\)	\(25\)	\(-172\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+24q^{3}+2^{4}q^{4}+5^{2}q^{5}-96q^{6}+\cdots\)
10.6.a.c	$10$	$6$	10.a	1.a	$1$	$1$	$1$	$1.604$	\(\Q\)	None	✓	$1$	$0$	\(4\)	\(6\)	\(-25\)	\(-118\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+6q^{3}+2^{4}q^{4}-5^{2}q^{5}+24q^{6}+\cdots\)
7.7.b.a	$7$	$7$	7.b	7.b	$2$	$1$	$1$	$1.610$	\(\Q\)	\(\Q(\sqrt{-7}) \)	✓	$2$	$0$	\(9\)	\(0\)	\(0\)	\(-343\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+9q^{2}+17q^{4}-7^{3}q^{7}-423q^{8}+\cdots\)
4.9.b.a	$4$	$9$	4.b	4.b	$2$	$1$	$1$	$1.630$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(16\)	\(0\)	\(-1054\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{4}q^{2}+2^{8}q^{4}-1054q^{5}+2^{12}q^{8}+\cdots\)
8.7.d.a	$8$	$7$	8.d	8.d	$2$	$1$	$1$	$1.840$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓	$2$	$0$	\(-8\)	\(46\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-8q^{2}+46q^{3}+2^{6}q^{4}-368q^{6}+\cdots\)
6.8.a.a	$6$	$8$	6.a	1.a	$1$	$1$	$1$	$1.874$	\(\Q\)	None	✓	$1$	$0$	\(8\)	\(27\)	\(-114\)	\(-1576\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+8q^{2}+3^{3}q^{3}+2^{6}q^{4}-114q^{5}+\cdots\)
4.10.a.a	$4$	$10$	4.a	1.a	$1$	$1$	$1$	$2.060$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(228\)	\(-666\)	\(-6328\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+228q^{3}-666q^{5}-6328q^{7}+32301q^{9}+\cdots\)
2.14.a.a	$2$	$14$	2.a	1.a	$1$	$1$	$1$	$2.145$	\(\Q\)	None	✓	$1$	$1$	\(-64\)	\(-1836\)	\(3990\)	\(-433432\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2^{6}q^{2}-1836q^{3}+2^{12}q^{4}+3990q^{5}+\cdots\)
2.14.a.b	$2$	$14$	2.a	1.a	$1$	$1$	$1$	$2.145$	\(\Q\)	None	✓	$1$	$0$	\(64\)	\(1236\)	\(-57450\)	\(64232\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2^{6}q^{2}+1236q^{3}+2^{12}q^{4}-57450q^{5}+\cdots\)
7.8.a.a	$7$	$8$	7.a	1.a	$1$	$1$	$1$	$2.187$	\(\Q\)	None	✓	$1$	$1$	\(-6\)	\(-42\)	\(-84\)	\(343\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-6q^{2}-42q^{3}-92q^{4}-84q^{5}+252q^{6}+\cdots\)
3.12.a.a	$3$	$12$	3.a	1.a	$1$	$1$	$1$	$2.305$	\(\Q\)	None	✓	$1$	$0$	\(78\)	\(-243\)	\(-5370\)	\(-27760\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+78q^{2}-3^{5}q^{3}+4036q^{4}-5370q^{5}+\cdots\)
8.8.a.a	$8$	$8$	8.a	1.a	$1$	$1$	$1$	$2.499$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-84\)	\(-82\)	\(-456\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-84q^{3}-82q^{5}-456q^{7}+4869q^{9}+\cdots\)
8.8.a.b	$8$	$8$	8.a	1.a	$1$	$1$	$1$	$2.499$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(44\)	\(430\)	\(-1224\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+44q^{3}+430q^{5}-1224q^{7}-251q^{9}+\cdots\)
5.10.a.a	$5$	$10$	5.a	1.a	$1$	$1$	$1$	$2.575$	\(\Q\)	None	✓	$1$	$1$	\(-8\)	\(-114\)	\(-625\)	\(4242\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-8q^{2}-114q^{3}-448q^{4}-5^{4}q^{5}+\cdots\)
3.13.b.a	$3$	$13$	3.b	3.b	$2$	$1$	$1$	$2.742$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(729\)	\(0\)	\(-153502\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3^{6}q^{3}+2^{12}q^{4}-153502q^{7}+3^{12}q^{9}+\cdots\)
9.8.a.a	$9$	$8$	9.a	1.a	$1$	$1$	$1$	$2.811$	\(\Q\)	None	✓	$1$	$1$	\(-6\)	\(0\)	\(-390\)	\(-64\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-6q^{2}-92q^{4}-390q^{5}-2^{6}q^{7}+\cdots\)
7.9.b.a	$7$	$9$	7.b	7.b	$2$	$1$	$1$	$2.852$	\(\Q\)	\(\Q(\sqrt{-7}) \)	✓	$2$	$0$	\(-31\)	\(0\)	\(0\)	\(2401\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-31q^{2}+705q^{4}+7^{4}q^{7}-13919q^{8}+\cdots\)
2.16.a.a	$2$	$16$	2.a	1.a	$1$	$1$	$1$	$2.854$	\(\Q\)	None	✓	$1$	$0$	\(-128\)	\(6252\)	\(90510\)	\(56\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2^{7}q^{2}+6252q^{3}+2^{14}q^{4}+90510q^{5}+\cdots\)
4.12.a.a	$4$	$12$	4.a	1.a	$1$	$1$	$1$	$3.073$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-516\)	\(-10530\)	\(49304\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-516q^{3}-10530q^{5}+49304q^{7}+\cdots\)
6.10.a.a	$6$	$10$	6.a	1.a	$1$	$1$	$1$	$3.090$	\(\Q\)	None	✓	$1$	$0$	\(-16\)	\(81\)	\(2694\)	\(-3544\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-2^{4}q^{2}+3^{4}q^{3}+2^{8}q^{4}+2694q^{5}+\cdots\)
10.8.a.a	$10$	$8$	10.a	1.a	$1$	$1$	$1$	$3.124$	\(\Q\)	None	✓	$1$	$0$	\(8\)	\(28\)	\(125\)	\(104\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+8q^{2}+28q^{3}+2^{6}q^{4}+5^{3}q^{5}+224q^{6}+\cdots\)
3.14.a.a	$3$	$14$	3.a	1.a	$1$	$1$	$1$	$3.217$	\(\Q\)	None	✓	$1$	$1$	\(-12\)	\(-729\)	\(-30210\)	\(235088\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-12q^{2}-3^{6}q^{3}-8048q^{4}-30210q^{5}+\cdots\)
8.9.d.a	$8$	$9$	8.d	8.d	$2$	$1$	$1$	$3.259$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓	$2$	$0$	\(16\)	\(34\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{4}q^{2}+34q^{3}+2^{8}q^{4}+544q^{6}+\cdots\)
4.13.b.a	$4$	$13$	4.b	4.b	$2$	$1$	$1$	$3.656$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(-64\)	\(0\)	\(23506\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{6}q^{2}+2^{12}q^{4}+23506q^{5}-2^{18}q^{8}+\cdots\)