Newform search results

Results (1-50 of 4315 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
11.17.b.a	$11$	$17$	11.b	11.b	$2$	$1$	$1$	$17.856$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	$2$	$0$	\(0\)	\(-353\)	\(543551\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-353q^{3}+2^{16}q^{4}+543551q^{5}+\cdots\)
11.17.b.b	$11$	$17$	11.b	11.b	$2$	$14$	$14$	$17.856$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(498\)	\(-535618\)	\(0\)		$2^{34}\cdot 3^{10}\cdot 5\cdot 11^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(6^{2}+\beta _{2})q^{3}+(-43414+\cdots)q^{4}+\cdots\)
11.17.d.a	$11$	$17$	11.d	11.d	$10$	$60$	$15$	$17.856$		None		$2$	$0$	\(-5\)	\(-150\)	\(-7938\)	\(2885320\)			$\mathrm{SU}(2)[C_{10}]$
12.17.c.a	$12$	$17$	12.c	3.b	$2$	$1$	$1$	$19.479$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(6561\)	\(0\)	\(4743554\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3^{8}q^{3}+4743554q^{7}+3^{16}q^{9}+\cdots\)
12.17.c.b	$12$	$17$	12.c	3.b	$2$	$4$	$4$	$19.479$	\(\mathbb{Q}[x]/(x^{4} + \cdots)\)	None		$2$	$0$	\(0\)	\(-12420\)	\(0\)	\(-1050280\)		$2^{9}\cdot 3^{11}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-3105-\beta _{1})q^{3}+(-8\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
12.17.d.a	$12$	$17$	12.d	4.b	$2$	$16$	$16$	$19.479$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(-186\)	\(0\)	\(354144\)	\(0\)		$2^{106}\cdot 3^{51}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-12-\beta _{1})q^{2}+(\beta _{1}-\beta _{3})q^{3}+(8542+\cdots)q^{4}+\cdots\)
11.18.a.a	$11$	$18$	11.a	1.a	$1$	$6$	$6$	$20.154$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(11865\)	\(347991\)	\(-31314630\)	$+$	$2^{12}\cdot 3^{6}\cdot 11$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1977+14\beta _{1}-\beta _{2})q^{3}+\cdots\)
11.18.a.b	$11$	$18$	11.a	1.a	$1$	$8$	$8$	$20.154$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(256\)	\(3058\)	\(1795234\)	\(-896364\)	$-$	$2^{11}\cdot 3^{5}\cdot 11$	$\mathrm{SU}(2)$	\(q+(2^{5}-\beta _{1})q^{2}+(382-9\beta _{1}+\beta _{2})q^{3}+\cdots\)
11.18.c.a	$11$	$18$	11.c	11.c	$5$	$64$	$16$	$20.154$		None		$2$	$0$	\(795\)	\(-6360\)	\(-91530\)	\(49560700\)			$\mathrm{SU}(2)[C_{5}]$
13.17.d.a	$13$	$17$	13.d	13.d	$4$	$34$	$17$	$21.102$		None		$2$	$0$	\(-2\)	\(-4\)	\(-177074\)	\(5074208\)			$\mathrm{SU}(2)[C_{4}]$
13.17.f.a	$13$	$17$	13.f	13.f	$12$	$72$	$18$	$21.102$		None		$2$	$0$	\(-4\)	\(-2\)	\(177068\)	\(-15884904\)			$\mathrm{SU}(2)[C_{12}]$
12.18.a.a	$12$	$18$	12.a	1.a	$1$	$1$	$1$	$21.987$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-6561\)	\(-1608930\)	\(-9417184\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-3^{8}q^{3}-1608930q^{5}-9417184q^{7}+\cdots\)
12.18.a.b	$12$	$18$	12.a	1.a	$1$	$1$	$1$	$21.987$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(6561\)	\(130950\)	\(-14846776\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+3^{8}q^{3}+130950q^{5}-14846776q^{7}+\cdots\)
12.18.b.a	$12$	$18$	12.b	12.b	$2$	$32$	$32$	$21.987$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
11.19.b.a	$11$	$19$	11.b	11.b	$2$	$1$	$1$	$22.592$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	$2$	$0$	\(0\)	\(-20870\)	\(-3063526\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-20870q^{3}+2^{18}q^{4}-3063526q^{5}+\cdots\)
11.19.b.b	$11$	$19$	11.b	11.b	$2$	$16$	$16$	$22.592$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(38544\)	\(5217660\)	\(0\)		$2^{41}\cdot 3^{13}\cdot 11^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(2409-\beta _{2})q^{3}+(-136842+\cdots)q^{4}+\cdots\)
11.19.d.a	$11$	$19$	11.d	11.d	$10$	$68$	$17$	$22.592$		None		$2$	$0$	\(-5\)	\(-17679\)	\(-2154139\)	\(-91602365\)			$\mathrm{SU}(2)[C_{10}]$
14.17.b.a	$14$	$17$	14.b	7.b	$2$	$12$	$12$	$22.725$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(222636\)		$2^{63}\cdot 3^{6}\cdot 7^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+\beta _{1}q^{3}+2^{15}q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots\)
14.17.d.a	$14$	$17$	14.d	7.d	$6$	$20$	$10$	$22.725$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(0\)	\(-13122\)	\(-483786\)	\(-1987412\)		$2^{86}\cdot 3^{16}\cdot 7^{17}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{2}+\beta _{3})q^{2}+(-438+437\beta _{1}+2\beta _{2}+\cdots)q^{3}+\cdots\)
13.18.a.a	$13$	$18$	13.a	1.a	$1$	$8$	$8$	$23.819$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(15\)	\(-15400\)	\(468726\)	\(-14154372\)	$+$	$2^{12}\cdot 3^{4}\cdot 13$	$\mathrm{SU}(2)$	\(q+(2-\beta _{1})q^{2}+(-1925+\beta _{2})q^{3}+(10318+\cdots)q^{4}+\cdots\)
13.18.a.b	$13$	$18$	13.a	1.a	$1$	$9$	$9$	$23.819$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(783\)	\(10844\)	\(746568\)	\(39913380\)	$-$	$2^{13}\cdot 3^{5}\cdot 13$	$\mathrm{SU}(2)$	\(q+(87-\beta _{1})q^{2}+(1205-2\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
13.18.b.a	$13$	$18$	13.b	13.b	$2$	$20$	$20$	$23.819$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(13120\)	\(0\)	\(0\)		$2^{43}\cdot 3^{22}\cdot 13^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(656-\beta _{3})q^{3}+(-72090+\cdots)q^{4}+\cdots\)
13.18.c.a	$13$	$18$	13.c	13.c	$3$	$36$	$18$	$23.819$		None		$2$	$0$	\(255\)	\(6560\)	\(836400\)	\(-7280660\)			$\mathrm{SU}(2)[C_{3}]$
13.18.e.a	$13$	$18$	13.e	13.e	$6$	$38$	$19$	$23.819$		None		$2$	$0$	\(-3\)	\(-6562\)	\(0\)	\(-4632540\)			$\mathrm{SU}(2)[C_{6}]$
15.17.c.a	$15$	$17$	15.c	3.b	$2$	$22$	$22$	$24.349$		None		$2$	$0$	\(0\)	\(-3808\)	\(0\)	\(5515404\)			$\mathrm{SU}(2)[C_{2}]$
15.17.d.a	$15$	$17$	15.d	15.d	$2$	$1$	$1$	$24.349$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	$2$	$0$	\(-223\)	\(6561\)	\(390625\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-223q^{2}+3^{8}q^{3}-15807q^{4}+5^{8}q^{5}+\cdots\)
15.17.d.b	$15$	$17$	15.d	15.d	$2$	$1$	$1$	$24.349$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	$2$	$0$	\(223\)	\(-6561\)	\(-390625\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+223q^{2}-3^{8}q^{3}-15807q^{4}-5^{8}q^{5}+\cdots\)
15.17.d.c	$15$	$17$	15.d	15.d	$2$	$28$	$28$	$24.349$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
15.17.f.a	$15$	$17$	15.f	5.c	$4$	$32$	$16$	$24.349$		None		$2$	$0$	\(0\)	\(0\)	\(-385764\)	\(1540580\)			$\mathrm{SU}(2)[C_{4}]$
12.19.c.a	$12$	$19$	12.c	3.b	$2$	$6$	$6$	$24.646$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(23934\)	\(0\)	\(11024364\)		$2^{32}\cdot 3^{19}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(3989-\beta _{1})q^{3}+(-4\beta _{1}+\beta _{2})q^{5}+\cdots\)
12.19.d.a	$12$	$19$	12.d	4.b	$2$	$18$	$18$	$24.646$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(-170\)	\(0\)	\(-1721764\)	\(0\)		$2^{139}\cdot 3^{67}\cdot 13^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-9-\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-24281+\cdots)q^{4}+\cdots\)
11.20.a.a	$11$	$20$	11.a	1.a	$1$	$7$	$7$	$25.170$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-69558\)	\(2165100\)	\(-10203532\)	$-$	$2^{15}\cdot 3^{6}\cdot 5\cdot 11^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-9937+5\beta _{1}-\beta _{2})q^{3}+\cdots\)
11.20.a.b	$11$	$20$	11.a	1.a	$1$	$9$	$9$	$25.170$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(512\)	\(14725\)	\(1363307\)	\(250021690\)	$+$	$2^{18}\cdot 3^{7}\cdot 5^{2}\cdot 11^{2}$	$\mathrm{SU}(2)$	\(q+(57-\beta _{1})q^{2}+(1636-2\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots\)
11.20.c.a	$11$	$20$	11.c	11.c	$5$	$72$	$18$	$25.170$		None		$2$	$0$	\(-1429\)	\(-46476\)	\(1226408\)	\(-97787860\)			$\mathrm{SU}(2)[C_{5}]$
14.18.a.a	$14$	$18$	14.a	1.a	$1$	$1$	$1$	$25.651$	\(\Q\)	None	✓	$1$	$1$	\(256\)	\(4626\)	\(-851700\)	\(5764801\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+2^{8}q^{2}+4626q^{3}+2^{16}q^{4}-851700q^{5}+\cdots\)
14.18.a.b	$14$	$18$	14.a	1.a	$1$	$2$	$2$	$25.651$	\(\Q(\sqrt{229889}) \)	None	✓	$1$	$1$	\(-512\)	\(-10710\)	\(-427070\)	\(-11529602\)	$+$	$2\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q-2^{8}q^{2}+(-5355-\beta )q^{3}+2^{16}q^{4}+\cdots\)
14.18.a.c	$14$	$18$	14.a	1.a	$1$	$2$	$2$	$25.651$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	$1$	$0$	\(512\)	\(5642\)	\(-888286\)	\(-11529602\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+2^{8}q^{2}+(2821-\beta )q^{3}+2^{16}q^{4}+\cdots\)
14.18.a.d	$14$	$18$	14.a	1.a	$1$	$3$	$3$	$25.651$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(-768\)	\(1396\)	\(-796110\)	\(17294403\)	$-$	$2^{4}\cdot 3^{2}\cdot 7$	$\mathrm{SU}(2)$	\(q-2^{8}q^{2}+(465+\beta _{1})q^{3}+2^{16}q^{4}+\cdots\)
14.18.c.a	$14$	$18$	14.c	7.c	$3$	$12$	$6$	$25.651$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(-1536\)	\(-1904\)	\(-786758\)	\(-15349712\)		$2^{28}\cdot 3^{8}\cdot 7^{10}$	$\mathrm{SU}(2)[C_{3}]$	\(q+2^{8}\beta _{1}q^{2}+(-317-317\beta _{1}-\beta _{4}+\cdots)q^{3}+\cdots\)
14.18.c.b	$14$	$18$	14.c	7.c	$3$	$12$	$6$	$25.651$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(1536\)	\(1904\)	\(-611590\)	\(-8956688\)		$2^{28}\cdot 3^{9}\cdot 7^{9}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2^{8}+2^{8}\beta _{1})q^{2}+(-317\beta _{1}-\beta _{4}+\cdots)q^{3}+\cdots\)
16.17.c.a	$16$	$17$	16.c	4.b	$2$	$2$	$2$	$25.972$	\(\Q(\sqrt{-3003}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-60\)	\(0\)		$2^{4}\cdot 3\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{3}-30q^{5}-462\beta q^{7}-196479q^{9}+\cdots\)
16.17.c.b	$16$	$17$	16.c	4.b	$2$	$6$	$6$	$25.972$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(531276\)	\(0\)		$2^{60}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(88546+\beta _{2})q^{5}+(-139\beta _{1}+\cdots)q^{7}+\cdots\)
16.17.f.a	$16$	$17$	16.f	16.f	$4$	$62$	$31$	$25.972$		None		$2$	$0$	\(-2\)	\(-2\)	\(-2\)	\(-4\)			$\mathrm{SU}(2)[C_{4}]$
13.19.d.a	$13$	$19$	13.d	13.d	$4$	$40$	$20$	$26.700$		None		$2$	$0$	\(-514\)	\(-4\)	\(4304408\)	\(-14341202\)			$\mathrm{SU}(2)[C_{4}]$
13.19.f.a	$13$	$19$	13.f	13.f	$12$	$80$	$20$	$26.700$		None		$2$	$0$	\(508\)	\(-2\)	\(-4304414\)	\(-11472964\)			$\mathrm{SU}(2)[C_{12}]$
12.20.a.a	$12$	$20$	12.a	1.a	$1$	$2$	$2$	$27.458$	\(\Q(\sqrt{193153}) \)	None	✓	$1$	$1$	\(0\)	\(-39366\)	\(624780\)	\(4667104\)	$-$	$2^{7}\cdot 3^{3}\cdot 5$	$\mathrm{SU}(2)$	\(q-3^{9}q^{3}+(312390-\beta )q^{5}+(2333552+\cdots)q^{7}+\cdots\)
12.20.a.b	$12$	$20$	12.a	1.a	$1$	$2$	$2$	$27.458$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(39366\)	\(-3267108\)	\(-27023984\)	$+$	$2^{8}\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q+3^{9}q^{3}+(-1633554-\beta )q^{5}+(-13511992+\cdots)q^{7}+\cdots\)
12.20.b.a	$12$	$20$	12.b	12.b	$2$	$36$	$36$	$27.458$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
15.18.a.a	$15$	$18$	15.a	1.a	$1$	$2$	$2$	$27.483$	\(\Q(\sqrt{849}) \)	None	✓	$1$	$1$	\(-356\)	\(13122\)	\(781250\)	\(-20754552\)	$+$	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(-178-\beta )q^{2}+3^{8}q^{3}+(175688+\cdots)q^{4}+\cdots\)
15.18.a.b	$15$	$18$	15.a	1.a	$1$	$3$	$3$	$27.483$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(-442\)	\(-19683\)	\(-1171875\)	\(4962644\)	$+$	$2^{6}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q+(-147+\beta _{1})q^{2}-3^{8}q^{3}+(99318+\cdots)q^{4}+\cdots\)