Newform search results

Results (1-50 of 273 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
5.4.a.a	$5$	$4$	5.a	1.a	$1$	$1$	$1$	$0.295$	\(\Q\)	None	✓	$1$	$0$	\(-4\)	\(2\)	\(-5\)	\(6\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+2q^{3}+8q^{4}-5q^{5}-8q^{6}+\cdots\)
5.5.c.a	$5$	$5$	5.c	5.c	$4$	$2$	$1$	$0.517$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(-2\)	\(-12\)	\(40\)	\(-52\)		$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-i)q^{2}+(-6+6i)q^{3}-14iq^{4}+\cdots\)
5.6.a.a	$5$	$6$	5.a	1.a	$1$	$1$	$1$	$0.802$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(-4\)	\(25\)	\(192\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-4q^{3}-28q^{4}+5^{2}q^{5}-8q^{6}+\cdots\)
5.6.b.a	$5$	$6$	5.b	5.b	$2$	$2$	$2$	$0.802$	\(\Q(\sqrt{-11}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-90\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{2}+3\beta q^{3}-12q^{4}+(-45-5\beta )q^{5}+\cdots\)
5.7.c.a	$5$	$7$	5.c	5.c	$4$	$4$	$2$	$1.150$	\(\Q(i, \sqrt{201})\)	None		$2$	$0$	\(-10\)	\(30\)	\(-70\)	\(550\)		$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2+2\beta _{1}+\beta _{3})q^{2}+(7+8\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
5.8.a.a	$5$	$8$	5.a	1.a	$1$	$1$	$1$	$1.562$	\(\Q\)	None	✓	$1$	$1$	\(-14\)	\(-48\)	\(125\)	\(-1644\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-14q^{2}-48q^{3}+68q^{4}+5^{3}q^{5}+\cdots\)
5.8.a.b	$5$	$8$	5.a	1.a	$1$	$2$	$2$	$1.562$	\(\Q(\sqrt{19}) \)	None	✓	$1$	$0$	\(20\)	\(20\)	\(-250\)	\(-100\)	$+$	$2$	$\mathrm{SU}(2)$	\(q+(10+\beta )q^{2}+(10-8\beta )q^{3}+(48+20\beta )q^{4}+\cdots\)
5.8.b.a	$5$	$8$	5.b	5.b	$2$	$2$	$2$	$1.562$	\(\Q(\sqrt{-29}) \)	None		$2$	$0$	\(0\)	\(0\)	\(150\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+3\beta q^{3}+12q^{4}+(75-5^{2}\beta )q^{5}+\cdots\)
5.9.c.a	$5$	$9$	5.c	5.c	$4$	$6$	$3$	$2.037$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		$2$	$0$	\(-2\)	\(-72\)	\(220\)	\(-2352\)		$2^{6}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{3}q^{2}+(-12-12\beta _{1}-\beta _{2}-\beta _{5})q^{3}+\cdots\)
5.10.a.a	$5$	$10$	5.a	1.a	$1$	$1$	$1$	$2.575$	\(\Q\)	None	✓	$1$	$1$	\(-8\)	\(-114\)	\(-625\)	\(4242\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-8q^{2}-114q^{3}-448q^{4}-5^{4}q^{5}+\cdots\)
5.10.a.b	$5$	$10$	5.a	1.a	$1$	$2$	$2$	$2.575$	\(\Q(\sqrt{1009}) \)	None	✓	$1$	$0$	\(-10\)	\(260\)	\(1250\)	\(1700\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-5-\beta )q^{2}+(130+2\beta )q^{3}+(522+\cdots)q^{4}+\cdots\)
5.10.b.a	$5$	$10$	5.b	5.b	$2$	$4$	$4$	$2.575$	4.0.49740556.1	None		$2$	$0$	\(0\)	\(0\)	\(1140\)	\(0\)		$2^{5}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-342+\cdots)q^{4}+\cdots\)
5.11.c.a	$5$	$11$	5.c	5.c	$4$	$8$	$4$	$3.177$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(30\)	\(60\)	\(-5340\)	\(-14500\)		$2^{8}\cdot 3^{2}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(4+4\beta _{1}-\beta _{3})q^{2}+(8-8\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
5.12.a.a	$5$	$12$	5.a	1.a	$1$	$1$	$1$	$3.842$	\(\Q\)	None	✓	$1$	$1$	\(34\)	\(-792\)	\(3125\)	\(-17556\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+34q^{2}-792q^{3}-892q^{4}+5^{5}q^{5}+\cdots\)
5.12.a.b	$5$	$12$	5.a	1.a	$1$	$2$	$2$	$3.842$	\(\Q(\sqrt{151}) \)	None	✓	$1$	$0$	\(-20\)	\(-220\)	\(-6250\)	\(57900\)	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-10+3\beta )q^{2}+(-110+2^{4}\beta )q^{3}+\cdots\)
5.12.b.a	$5$	$12$	5.b	5.b	$2$	$4$	$4$	$3.842$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-300\)	\(0\)		$2^{5}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-18-\beta _{2})q^{4}+\cdots\)
5.13.c.a	$5$	$13$	5.c	5.c	$4$	$10$	$5$	$4.570$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(-2\)	\(318\)	\(-4250\)	\(279598\)		$2^{13}\cdot 3^{2}\cdot 5^{9}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{5}q^{2}+(31-31\beta _{1}-\beta _{3}+3\beta _{6}+\cdots)q^{3}+\cdots\)
5.14.a.a	$5$	$14$	5.a	1.a	$1$	$2$	$2$	$5.362$	\(\Q(\sqrt{499}) \)	None	✓	$1$	$1$	\(-80\)	\(780\)	\(-31250\)	\(-616300\)	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-40+\beta )q^{2}+(390-12\beta )q^{3}+(1392+\cdots)q^{4}+\cdots\)
5.14.a.b	$5$	$14$	5.a	1.a	$1$	$3$	$3$	$5.362$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(142\)	\(416\)	\(46875\)	\(448292\)	$-$	$2^{3}\cdot 5$	$\mathrm{SU}(2)$	\(q+(47-\beta _{1})q^{2}+(138-3\beta _{1}-\beta _{2})q^{3}+\cdots\)
5.14.b.a	$5$	$14$	5.b	5.b	$2$	$6$	$6$	$5.362$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(24570\)	\(0\)		$2^{11}\cdot 3^{4}\cdot 5^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-5492-\beta _{3}+\cdots)q^{4}+\cdots\)
5.15.c.a	$5$	$15$	5.c	5.c	$4$	$12$	$6$	$6.216$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(-130\)	\(-2160\)	\(17240\)	\(-1646400\)		$2^{24}\cdot 3^{8}\cdot 5^{13}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-11+11\beta _{2}-\beta _{3})q^{2}+(-180+\cdots)q^{3}+\cdots\)
5.16.a.a	$5$	$16$	5.a	1.a	$1$	$2$	$2$	$7.135$	\(\Q(\sqrt{3169}) \)	None	✓	$1$	$1$	\(-310\)	\(1740\)	\(156250\)	\(-3420900\)	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(-155-\beta )q^{2}+(870-2\beta )q^{3}+(19778+\cdots)q^{4}+\cdots\)
5.16.a.b	$5$	$16$	5.a	1.a	$1$	$3$	$3$	$7.135$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(4\)	\(3518\)	\(-234375\)	\(-905206\)	$+$	$2^{4}\cdot 5$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1170-2^{4}\beta _{1}+8\beta _{2})q^{3}+\cdots\)
5.16.b.a	$5$	$16$	5.b	5.b	$2$	$6$	$6$	$7.135$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-238350\)	\(0\)		$2^{13}\cdot 3^{4}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(2\beta _{1}-\beta _{2})q^{3}+(-6428+\cdots)q^{4}+\cdots\)
5.17.c.a	$5$	$17$	5.c	5.c	$4$	$14$	$7$	$8.116$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(-2\)	\(7908\)	\(192880\)	\(-386452\)		$2^{34}\cdot 3^{10}\cdot 5^{18}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{2}q^{2}+(565-3\beta _{1}-565\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)
5.18.a.a	$5$	$18$	5.a	1.a	$1$	$2$	$2$	$9.161$	\(\Q(\sqrt{39}) \)	None	✓	$1$	$1$	\(680\)	\(-10980\)	\(-781250\)	\(-22820700\)	$+$	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(340+\beta )q^{2}+(-5490-52\beta )q^{3}+\cdots\)
5.18.a.b	$5$	$18$	5.a	1.a	$1$	$3$	$3$	$9.161$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(118\)	\(15944\)	\(1171875\)	\(2139308\)	$-$	$2^{3}\cdot 5$	$\mathrm{SU}(2)$	\(q+(39-\beta _{1})q^{2}+(5317+8\beta _{1}+\beta _{2})q^{3}+\cdots\)
5.18.b.a	$5$	$18$	5.b	5.b	$2$	$8$	$8$	$9.161$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(379200\)	\(0\)		$2^{21}\cdot 3^{8}\cdot 5^{12}\cdot 11$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-72387+\beta _{3}+\cdots)q^{4}+\cdots\)
5.19.c.a	$5$	$19$	5.c	5.c	$4$	$16$	$8$	$10.269$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(510\)	\(-20130\)	\(3145170\)	\(78767350\)		$2^{39}\cdot 3^{12}\cdot 5^{25}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2^{5}+\beta _{2}+2^{5}\beta _{4})q^{2}+(-1259-5\beta _{1}+\cdots)q^{3}+\cdots\)
5.20.a.a	$5$	$20$	5.a	1.a	$1$	$3$	$3$	$11.441$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(-1006\)	\(-73452\)	\(5859375\)	\(-54910456\)	$-$	$2^{3}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q+(-335+\beta _{1})q^{2}+(-24478+18\beta _{1}+\cdots)q^{3}+\cdots\)
5.20.a.b	$5$	$20$	5.a	1.a	$1$	$4$	$4$	$11.441$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(-420\)	\(3080\)	\(-7812500\)	\(214021400\)	$+$	$2^{8}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q+(-105-\beta _{1})q^{2}+(770+14\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
5.20.b.a	$5$	$20$	5.b	5.b	$2$	$8$	$8$	$11.441$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(147000\)	\(0\)		$2^{20}\cdot 3^{8}\cdot 5^{13}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-202593+\cdots)q^{4}+\cdots\)
5.21.c.a	$5$	$21$	5.c	5.c	$4$	$18$	$9$	$12.676$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(-2\)	\(29448\)	\(-7302140\)	\(-585532752\)		$2^{48}\cdot 3^{16}\cdot 5^{32}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{1}q^{2}+(1636-\beta _{2}-1636\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)
5.22.a.a	$5$	$22$	5.a	1.a	$1$	$3$	$3$	$13.974$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(-1312\)	\(52194\)	\(-29296875\)	\(684416558\)	$+$	$2^{7}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q+(-437+\beta _{1})q^{2}+(17400+8\beta _{1}+\cdots)q^{3}+\cdots\)
5.22.a.b	$5$	$22$	5.a	1.a	$1$	$4$	$4$	$13.974$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(2910\)	\(83240\)	\(39062500\)	\(512613800\)	$-$	$2^{6}\cdot 3\cdot 5^{2}\cdot 7$	$\mathrm{SU}(2)$	\(q+(728-\beta _{1})q^{2}+(20803+14\beta _{1}+\beta _{3})q^{3}+\cdots\)
5.22.b.a	$5$	$22$	5.b	5.b	$2$	$10$	$10$	$13.974$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-25175970\)	\(0\)		$2^{30}\cdot 3^{10}\cdot 5^{19}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-6\beta _{1}-\beta _{4})q^{3}+(-927372+\cdots)q^{4}+\cdots\)
5.23.c.a	$5$	$23$	5.c	5.c	$4$	$20$	$10$	$15.335$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(-2050\)	\(33900\)	\(9244700\)	\(1362465500\)		$2^{61}\cdot 3^{18}\cdot 5^{41}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-102-\beta _{1}-103\beta _{4})q^{2}+(1697+\cdots)q^{3}+\cdots\)
5.24.a.a	$5$	$24$	5.a	1.a	$1$	$3$	$3$	$16.760$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(666\)	\(-139428\)	\(146484375\)	\(-2432683344\)	$-$	$2^{3}\cdot 3^{3}\cdot 5$	$\mathrm{SU}(2)$	\(q+(222+\beta _{1})q^{2}+(-46476+2^{6}\beta _{1}+\cdots)q^{3}+\cdots\)
5.24.a.b	$5$	$24$	5.a	1.a	$1$	$4$	$4$	$16.760$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(-780\)	\(-206680\)	\(-195312500\)	\(-1010710600\)	$+$	$2^{8}\cdot 3\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q+(-195-\beta _{1})q^{2}+(-51670-39\beta _{1}+\cdots)q^{3}+\cdots\)
5.24.b.a	$5$	$24$	5.b	5.b	$2$	$10$	$10$	$16.760$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(124761750\)	\(0\)		$2^{32}\cdot 3^{12}\cdot 5^{22}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(18\beta _{1}-\beta _{3})q^{3}+(-4127268+\cdots)q^{4}+\cdots\)
5.25.c.a	$5$	$25$	5.c	5.c	$4$	$22$	$11$	$18.248$		None		$2$	$0$	\(-2\)	\(-434562\)	\(-413381810\)	\(9255727198\)			$\mathrm{SU}(2)[C_{4}]$
5.26.a.a	$5$	$26$	5.a	1.a	$1$	$4$	$4$	$19.800$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$1$	\(600\)	\(-798600\)	\(-976562500\)	\(-48938107000\)	$+$	$2^{14}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q+(150-\beta _{1})q^{2}+(-199650+17\beta _{1}+\cdots)q^{3}+\cdots\)
5.26.a.b	$5$	$26$	5.a	1.a	$1$	$5$	$5$	$19.800$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$0$	\(-4602\)	\(626204\)	\(1220703125\)	\(55481235808\)	$-$	$2^{12}\cdot 3^{3}\cdot 5^{4}$	$\mathrm{SU}(2)$	\(q+(-920-\beta _{1})q^{2}+(125251-5^{2}\beta _{1}+\cdots)q^{3}+\cdots\)
5.26.b.a	$5$	$26$	5.b	5.b	$2$	$12$	$12$	$19.800$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(549543060\)	\(0\)		$2^{44}\cdot 3^{20}\cdot 5^{29}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-19\beta _{1}-\beta _{3})q^{3}+(-13890962+\cdots)q^{4}+\cdots\)
5.27.c.a	$5$	$27$	5.c	5.c	$4$	$24$	$12$	$21.415$		None		$2$	$0$	\(8190\)	\(1867680\)	\(-140947920\)	\(-99234643200\)			$\mathrm{SU}(2)[C_{4}]$
5.28.a.a	$5$	$28$	5.a	1.a	$1$	$4$	$4$	$23.093$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$1$	\(-11550\)	\(-2473800\)	\(4882812500\)	\(-215015185000\)	$-$	$2^{9}\cdot 3^{4}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q+(-2887+\beta _{1})q^{2}+(-618547-195\beta _{1}+\cdots)q^{3}+\cdots\)
5.28.a.b	$5$	$28$	5.a	1.a	$1$	$5$	$5$	$23.093$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$0$	\(19916\)	\(4870682\)	\(-6103515625\)	\(155646348206\)	$+$	$2^{16}\cdot 3^{5}\cdot 5^{4}\cdot 7$	$\mathrm{SU}(2)$	\(q+(3983-\beta _{1})q^{2}+(974132-24\beta _{1}+\cdots)q^{3}+\cdots\)
5.28.b.a	$5$	$28$	5.b	5.b	$2$	$12$	$12$	$23.093$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-1634543100\)	\(0\)		$2^{50}\cdot 3^{18}\cdot 5^{31}\cdot 7^{4}\cdot 11$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(-65836838+\beta _{2}+\cdots)q^{4}+\cdots\)
5.29.c.a	$5$	$29$	5.c	5.c	$4$	$26$	$13$	$24.834$		None		$2$	$0$	\(-2\)	\(-5427372\)	\(2639800120\)	\(523124011148\)			$\mathrm{SU}(2)[C_{4}]$
5.30.a.a	$5$	$30$	5.a	1.a	$1$	$4$	$4$	$26.639$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$1$	\(-15600\)	\(2712600\)	\(-24414062500\)	\(11\!\cdots\!00\)	$+$	$2^{11}\cdot 3^{3}\cdot 5^{2}\cdot 7$	$\mathrm{SU}(2)$	\(q+(-3900+\beta _{1})q^{2}+(678150+50\beta _{1}+\cdots)q^{3}+\cdots\)