Newform search results

Results (1-50 of 293 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3.6.a.a	$3$	$6$	3.a	1.a	$1$	$1$	$1$	$0.481$	\(\Q\)	None	✓	$1$	$0$	\(-6\)	\(9\)	\(6\)	\(-40\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-6q^{2}+9q^{3}+4q^{4}+6q^{5}-54q^{6}+\cdots\)
3.7.b.a	$3$	$7$	3.b	3.b	$2$	$1$	$1$	$0.690$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(-27\)	\(0\)	\(-286\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3^{3}q^{3}+2^{6}q^{4}-286q^{7}+3^{6}q^{9}+\cdots\)
3.8.a.a	$3$	$8$	3.a	1.a	$1$	$1$	$1$	$0.937$	\(\Q\)	None	✓	$1$	$0$	\(6\)	\(-27\)	\(390\)	\(-64\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+6q^{2}-3^{3}q^{3}-92q^{4}+390q^{5}+\cdots\)
3.9.b.a	$3$	$9$	3.b	3.b	$2$	$2$	$2$	$1.222$	\(\Q(\sqrt{-14}) \)	None		$2$	$0$	\(0\)	\(90\)	\(0\)	\(-3500\)		$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+(45-3\beta )q^{3}-248q^{4}-10\beta q^{5}+\cdots\)
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	✓	$1$	$0$	\(18\)	\(81\)	\(-1530\)	\(9128\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+18q^{2}+3^{4}q^{3}-188q^{4}-1530q^{5}+\cdots\)
3.11.b.a	$3$	$11$	3.b	3.b	$2$	$2$	$2$	$1.906$	\(\Q(\sqrt{-5}) \)	None		$2$	$0$	\(0\)	\(-54\)	\(0\)	\(34468\)		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+(-3^{3}+9\beta )q^{3}+304q^{4}+\cdots\)
3.12.a.a	$3$	$12$	3.a	1.a	$1$	$1$	$1$	$2.305$	\(\Q\)	None	✓	$1$	$0$	\(78\)	\(-243\)	\(-5370\)	\(-27760\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+78q^{2}-3^{5}q^{3}+4036q^{4}-5370q^{5}+\cdots\)
3.13.b.a	$3$	$13$	3.b	3.b	$2$	$1$	$1$	$2.742$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(729\)	\(0\)	\(-153502\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3^{6}q^{3}+2^{12}q^{4}-153502q^{7}+3^{12}q^{9}+\cdots\)
3.13.b.b	$3$	$13$	3.b	3.b	$2$	$2$	$2$	$2.742$	\(\Q(\sqrt{-26}) \)	None		$2$	$0$	\(0\)	\(-1350\)	\(0\)	\(80500\)		$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+(-675-3\beta )q^{3}-4328q^{4}+\cdots\)
3.14.a.a	$3$	$14$	3.a	1.a	$1$	$1$	$1$	$3.217$	\(\Q\)	None	✓	$1$	$1$	\(-12\)	\(-729\)	\(-30210\)	\(235088\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-12q^{2}-3^{6}q^{3}-8048q^{4}-30210q^{5}+\cdots\)
3.14.a.b	$3$	$14$	3.a	1.a	$1$	$2$	$2$	$3.217$	\(\Q(\sqrt{1969}) \)	None	✓	$1$	$0$	\(-54\)	\(1458\)	\(40716\)	\(-21008\)	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(-3^{3}-\beta )q^{2}+3^{6}q^{3}+(10258+54\beta )q^{4}+\cdots\)
3.15.b.a	$3$	$15$	3.b	3.b	$2$	$4$	$4$	$3.730$	4.0.1929141760.2	None		$2$	$0$	\(0\)	\(2196\)	\(0\)	\(825608\)		$2^{10}\cdot 3^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(549+3\beta _{1}-\beta _{2})q^{3}+(-9824+\cdots)q^{4}+\cdots\)
3.16.a.a	$3$	$16$	3.a	1.a	$1$	$1$	$1$	$4.281$	\(\Q\)	None	✓	$1$	$0$	\(-234\)	\(-2187\)	\(280710\)	\(-1373344\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-234q^{2}-3^{7}q^{3}+21988q^{4}+280710q^{5}+\cdots\)
3.16.a.b	$3$	$16$	3.a	1.a	$1$	$1$	$1$	$4.281$	\(\Q\)	None	✓	$1$	$1$	\(-72\)	\(2187\)	\(-221490\)	\(-2149000\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-72q^{2}+3^{7}q^{3}-27584q^{4}-221490q^{5}+\cdots\)
3.17.b.a	$3$	$17$	3.b	3.b	$2$	$4$	$4$	$4.870$	\(\mathbb{Q}[x]/(x^{4} + \cdots)\)	None		$2$	$0$	\(0\)	\(-2052\)	\(0\)	\(-3141544\)		$2^{6}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-513+\beta _{1}+\beta _{2})q^{3}+(-3116+\cdots)q^{4}+\cdots\)
3.18.a.a	$3$	$18$	3.a	1.a	$1$	$1$	$1$	$5.497$	\(\Q\)	None	✓	$1$	$1$	\(204\)	\(-6561\)	\(-163554\)	\(-20846560\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+204q^{2}-3^{8}q^{3}-89456q^{4}-163554q^{5}+\cdots\)
3.18.a.b	$3$	$18$	3.a	1.a	$1$	$2$	$2$	$5.497$	\(\Q(\sqrt{14569}) \)	None	✓	$1$	$0$	\(594\)	\(13122\)	\(382860\)	\(24471568\)	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(297-\beta )q^{2}+3^{8}q^{3}+(88258-594\beta )q^{4}+\cdots\)
3.19.b.a	$3$	$19$	3.b	3.b	$2$	$1$	$1$	$6.162$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(-19683\)	\(0\)	\(77549186\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3^{9}q^{3}+2^{18}q^{4}+77549186q^{7}+\cdots\)
3.19.b.b	$3$	$19$	3.b	3.b	$2$	$4$	$4$	$6.162$	4.0.601940665.1	None		$2$	$0$	\(0\)	\(15876\)	\(0\)	\(-95744152\)		$2^{11}\cdot 3^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(63^{2}+11\beta _{1}+\beta _{2})q^{3}+(-263384+\cdots)q^{4}+\cdots\)
3.20.a.a	$3$	$20$	3.a	1.a	$1$	$1$	$1$	$6.865$	\(\Q\)	None	✓	$1$	$1$	\(-1104\)	\(19683\)	\(3516270\)	\(-195590584\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-1104q^{2}+3^{9}q^{3}+694528q^{4}+\cdots\)
3.20.a.b	$3$	$20$	3.a	1.a	$1$	$2$	$2$	$6.865$	\(\Q(\sqrt{87481}) \)	None	✓	$1$	$0$	\(702\)	\(-39366\)	\(6016140\)	\(113892064\)	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(351-\beta )q^{2}-3^{9}q^{3}+(386242-702\beta )q^{4}+\cdots\)
3.21.b.a	$3$	$21$	3.b	3.b	$2$	$6$	$6$	$7.605$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(-4122\)	\(0\)	\(559607916\)		$2^{14}\cdot 3^{19}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-687+11\beta _{1}+\beta _{2})q^{3}+\cdots\)
3.22.a.a	$3$	$22$	3.a	1.a	$1$	$1$	$1$	$8.384$	\(\Q\)	None	✓	$1$	$1$	\(-2844\)	\(-59049\)	\(3109950\)	\(363303920\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2844q^{2}-3^{10}q^{3}+5991184q^{4}+\cdots\)
3.22.a.b	$3$	$22$	3.a	1.a	$1$	$1$	$1$	$8.384$	\(\Q\)	None	✓	$1$	$1$	\(1728\)	\(-59049\)	\(-41512770\)	\(538429808\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+12^{3}q^{2}-3^{10}q^{3}+888832q^{4}+\cdots\)
3.22.a.c	$3$	$22$	3.a	1.a	$1$	$2$	$2$	$8.384$	\(\Q(\sqrt{649}) \)	None	✓	$1$	$0$	\(666\)	\(118098\)	\(996876\)	\(679896112\)	$-$	$2\cdot 3^{2}\cdot 7$	$\mathrm{SU}(2)$	\(q+(333-\beta )q^{2}+3^{10}q^{3}+(589618+\cdots)q^{4}+\cdots\)
3.23.b.a	$3$	$23$	3.b	3.b	$2$	$6$	$6$	$9.201$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(86670\)	\(0\)	\(-3447063060\)		$2^{21}\cdot 3^{22}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(14445-8\beta _{1}+\beta _{2})q^{3}+\cdots\)
3.24.a.a	$3$	$24$	3.a	1.a	$1$	$1$	$1$	$10.056$	\(\Q\)	None	✓	$1$	$1$	\(1128\)	\(177147\)	\(-48863730\)	\(-1723688680\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+1128q^{2}+3^{11}q^{3}-7116224q^{4}+\cdots\)
3.24.a.b	$3$	$24$	3.a	1.a	$1$	$2$	$2$	$10.056$	\(\Q(\sqrt{530401}) \)	None	✓	$1$	$0$	\(-1242\)	\(-354294\)	\(-46808820\)	\(-211963904\)	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(-621-\beta )q^{2}-3^{11}q^{3}+(-3229358+\cdots)q^{4}+\cdots\)
3.25.b.a	$3$	$25$	3.b	3.b	$2$	$1$	$1$	$10.949$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(531441\)	\(0\)	\(-4119710398\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3^{12}q^{3}+2^{24}q^{4}-4119710398q^{7}+\cdots\)
3.25.b.b	$3$	$25$	3.b	3.b	$2$	$6$	$6$	$10.949$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(-616842\)	\(0\)	\(1988064876\)		$2^{13}\cdot 3^{24}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-102807+2^{4}\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
3.26.a.a	$3$	$26$	3.a	1.a	$1$	$2$	$2$	$11.880$	\(\Q(\sqrt{1287001}) \)	None	✓	$1$	$1$	\(-324\)	\(-1062882\)	\(570861756\)	\(-29687385728\)	$+$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	\(q+(-162-\beta )q^{2}-3^{12}q^{3}+(12803848+\cdots)q^{4}+\cdots\)
3.26.a.b	$3$	$26$	3.a	1.a	$1$	$3$	$3$	$11.880$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(-3678\)	\(1594323\)	\(-163152750\)	\(-9622572744\)	$-$	$2^{6}\cdot 3^{5}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q+(-1226+\beta _{1})q^{2}+3^{12}q^{3}+(30249196+\cdots)q^{4}+\cdots\)
3.27.b.a	$3$	$27$	3.b	3.b	$2$	$8$	$8$	$12.849$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(-1261080\)	\(0\)	\(-83723264240\)		$2^{33}\cdot 3^{38}\cdot 5^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-157635-5\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
3.28.a.a	$3$	$28$	3.a	1.a	$1$	$2$	$2$	$13.856$	\(\Q(\sqrt{6469}) \)	None	✓	$1$	$1$	\(3168\)	\(3188646\)	\(-4906065060\)	\(-151657089584\)	$-$	$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(1584-\beta )q^{2}+3^{13}q^{3}+(2432512+\cdots)q^{4}+\cdots\)
3.28.a.b	$3$	$28$	3.a	1.a	$1$	$2$	$2$	$13.856$	\(\Q(\sqrt{30001}) \)	None	✓	$1$	$0$	\(21582\)	\(-3188646\)	\(-1771946100\)	\(369665199904\)	$+$	$2\cdot 3^{2}\cdot 7$	$\mathrm{SU}(2)$	\(q+(10791-\beta )q^{2}-3^{13}q^{3}+(101301922+\cdots)q^{4}+\cdots\)
3.29.b.a	$3$	$29$	3.b	3.b	$2$	$8$	$8$	$14.901$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(6092280\)	\(0\)	\(401156726320\)		$2^{31}\cdot 3^{40}\cdot 5^{2}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(761535-18\beta _{1}-\beta _{2})q^{3}+\cdots\)
3.30.a.a	$3$	$30$	3.a	1.a	$1$	$2$	$2$	$15.983$	\(\Q(\sqrt{77089}) \)	None	✓	$1$	$1$	\(-45036\)	\(-9565938\)	\(187613820\)	\(26\!\cdots\!48\)	$+$	$2^{2}\cdot 3\cdot 7$	$\mathrm{SU}(2)$	\(q+(-22518-\beta )q^{2}-3^{14}q^{3}+(106174408+\cdots)q^{4}+\cdots\)
3.30.a.b	$3$	$30$	3.a	1.a	$1$	$3$	$3$	$15.983$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(11370\)	\(14348907\)	\(35492909586\)	\(723913582632\)	$-$	$2^{6}\cdot 3^{5}$	$\mathrm{SU}(2)$	\(q+(3790-\beta _{1})q^{2}+3^{14}q^{3}+(701653900+\cdots)q^{4}+\cdots\)
3.31.b.a	$3$	$31$	3.b	3.b	$2$	$1$	$1$	$17.104$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(-14348907\)	\(0\)	\(-79\!\cdots\!86\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3^{15}q^{3}+2^{30}q^{4}-7945347009886q^{7}+\cdots\)
3.31.b.b	$3$	$31$	3.b	3.b	$2$	$8$	$8$	$17.104$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(5373000\)	\(0\)	\(11\!\cdots\!80\)		$2^{36}\cdot 3^{45}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(671625-17\beta _{1}-\beta _{2})q^{3}+\cdots\)
3.32.a.a	$3$	$32$	3.a	1.a	$1$	$2$	$2$	$18.263$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	$1$	$1$	\(-39528\)	\(28697814\)	\(-7930517220\)	\(-10\!\cdots\!76\)	$-$	$2^{3}\cdot 3$	$\mathrm{SU}(2)$	\(q+(-19764-\beta )q^{2}+3^{15}q^{3}+(-100683488+\cdots)q^{4}+\cdots\)
3.32.a.b	$3$	$32$	3.a	1.a	$1$	$3$	$3$	$18.263$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(-7626\)	\(-43046721\)	\(50622172050\)	\(-25\!\cdots\!08\)	$+$	$2^{9}\cdot 3^{5}\cdot 5$	$\mathrm{SU}(2)$	\(q+(-2542+\beta _{1})q^{2}-3^{15}q^{3}+(1406276044+\cdots)q^{4}+\cdots\)
3.33.b.a	$3$	$33$	3.b	3.b	$2$	$10$	$10$	$19.460$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(-21387150\)	\(0\)	\(-55\!\cdots\!40\)		$2^{45}\cdot 3^{61}\cdot 5^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-2138715+35\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
3.34.a.a	$3$	$34$	3.a	1.a	$1$	$3$	$3$	$20.695$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(41202\)	\(129140163\)	\(51261823890\)	\(76\!\cdots\!56\)	$-$	$2^{6}\cdot 3^{6}\cdot 5\cdot 7\cdot 11$	$\mathrm{SU}(2)$	\(q+(13734-\beta _{1})q^{2}+3^{16}q^{3}+(-369155924+\cdots)q^{4}+\cdots\)
3.34.a.b	$3$	$34$	3.a	1.a	$1$	$3$	$3$	$20.695$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(136620\)	\(-129140163\)	\(-260488036134\)	\(10\!\cdots\!32\)	$+$	$2^{11}\cdot 3^{6}\cdot 11$	$\mathrm{SU}(2)$	\(q+(45540-\beta _{1})q^{2}-3^{16}q^{3}+(4863185200+\cdots)q^{4}+\cdots\)
3.35.b.a	$3$	$35$	3.b	3.b	$2$	$10$	$10$	$21.968$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(119369106\)	\(0\)	\(-12\!\cdots\!72\)		$2^{54}\cdot 3^{65}\cdot 5^{4}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(11936911+41\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
3.36.a.a	$3$	$36$	3.a	1.a	$1$	$2$	$2$	$23.279$	\(\Q(\sqrt{2196841}) \)	None	✓	$1$	$1$	\(-60912\)	\(258280326\)	\(-13\!\cdots\!40\)	\(-12\!\cdots\!44\)	$-$	$2^{4}\cdot 3\cdot 7$	$\mathrm{SU}(2)$	\(q+(-30456-\beta )q^{2}+3^{17}q^{3}+(28571469952+\cdots)q^{4}+\cdots\)
3.36.a.b	$3$	$36$	3.a	1.a	$1$	$3$	$3$	$23.279$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(-87330\)	\(-387420489\)	\(27\!\cdots\!10\)	\(48\!\cdots\!64\)	$+$	$2^{7}\cdot 3^{5}\cdot 5$	$\mathrm{SU}(2)$	\(q+(-29110+\beta _{1})q^{2}-3^{17}q^{3}+(10829584300+\cdots)q^{4}+\cdots\)
3.37.b.a	$3$	$37$	3.b	3.b	$2$	$1$	$1$	$24.627$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(387420489\)	\(0\)	\(27\!\cdots\!98\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3^{18}q^{3}+2^{36}q^{4}+2757049053441698q^{7}+\cdots\)