Newform search results

The results below are complete, since the LMFDB contains all newforms with level $N$ at most 10 and $Nk^2$ at most 100000

Results (1-50 of 675 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2.34.a.a	$2$	$34$	2.a	1.a	$1$	$1$	$1$	$13.797$	\(\Q\)	None	✓	✓	✓	✓	2.34.a.a	$1$	$1$	\(-65536\)	\(-133005564\)	\(538799132550\)	\(-33\!\cdots\!68\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2^{16}q^{2}-133005564q^{3}+2^{32}q^{4}+\cdots\)
2.34.a.b	$2$	$34$	2.a	1.a	$1$	$2$	$2$	$13.797$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	✓	✓	✓	2.34.a.b	$1$	$0$	\(131072\)	\(8356488\)	\(-5332476660\)	\(13\!\cdots\!56\)	$-$	$2^{7}\cdot 3\cdot 5\cdot 11$	$\mathrm{SU}(2)$	\(q+2^{16}q^{2}+(4178244-\beta )q^{3}+2^{32}q^{4}+\cdots\)
2.36.a.a	$2$	$36$	2.a	1.a	$1$	$1$	$1$	$15.519$	\(\Q\)	None	✓	✓	✓	✓	2.36.a.a	$1$	$0$	\(-131072\)	\(36494748\)	\(389070858750\)	\(-12\!\cdots\!56\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2^{17}q^{2}+36494748q^{3}+2^{34}q^{4}+\cdots\)
2.36.a.b	$2$	$36$	2.a	1.a	$1$	$1$	$1$	$15.519$	\(\Q\)	None	✓	✓	✓	✓	2.36.a.b	$1$	$1$	\(131072\)	\(159933852\)	\(-28\!\cdots\!90\)	\(-78\!\cdots\!44\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2^{17}q^{2}+159933852q^{3}+2^{34}q^{4}+\cdots\)
2.38.a.a	$2$	$38$	2.a	1.a	$1$	$2$	$2$	$17.343$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	✓	✓	✓	2.38.a.a	$1$	$1$	\(-524288\)	\(423071208\)	\(-13\!\cdots\!40\)	\(31\!\cdots\!56\)	$+$	$2^{8}\cdot 3^{3}\cdot 5$	$\mathrm{SU}(2)$	\(q-2^{18}q^{2}+(211535604-\beta )q^{3}+2^{36}q^{4}+\cdots\)
2.38.a.b	$2$	$38$	2.a	1.a	$1$	$2$	$2$	$17.343$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	✓	✓	✓	2.38.a.b	$1$	$0$	\(524288\)	\(-501686808\)	\(41\!\cdots\!00\)	\(-35\!\cdots\!56\)	$-$	$2^{8}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q+2^{18}q^{2}+(-250843404-\beta )q^{3}+\cdots\)
2.40.a.a	$2$	$40$	2.a	1.a	$1$	$1$	$1$	$19.268$	\(\Q\)	None	✓	✓	✓	✓	2.40.a.a	$1$	$1$	\(524288\)	\(-735458292\)	\(-16\!\cdots\!50\)	\(16\!\cdots\!64\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2^{19}q^{2}-735458292q^{3}+2^{38}q^{4}+\cdots\)
2.40.a.b	$2$	$40$	2.a	1.a	$1$	$2$	$2$	$19.268$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	✓	✓	✓	2.40.a.b	$1$	$0$	\(-1048576\)	\(287418264\)	\(53\!\cdots\!20\)	\(74\!\cdots\!12\)	$+$	$2^{7}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q-2^{19}q^{2}+(143709132-\beta )q^{3}+2^{38}q^{4}+\cdots\)
3.33.b.a	$3$	$33$	3.b	3.b	$2$	$10$	$10$	$19.460$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓	✓	✓	3.33.b.a	$2$	$0$	\(0\)	\(-21387150\)	\(0\)	\(-55\!\cdots\!40\)		$2^{45}\cdot 3^{61}\cdot 5^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-2138715+35\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
3.34.a.a	$3$	$34$	3.a	1.a	$1$	$3$	$3$	$20.695$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓	✓	✓	3.34.a.a	$1$	$0$	\(41202\)	\(129140163\)	\(51261823890\)	\(76\!\cdots\!56\)	$-$	$2^{6}\cdot 3^{6}\cdot 5\cdot 7\cdot 11$	$\mathrm{SU}(2)$	\(q+(13734-\beta _{1})q^{2}+3^{16}q^{3}+(-369155924+\cdots)q^{4}+\cdots\)
3.34.a.b	$3$	$34$	3.a	1.a	$1$	$3$	$3$	$20.695$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓	✓	✓	3.34.a.b	$1$	$1$	\(136620\)	\(-129140163\)	\(-260488036134\)	\(10\!\cdots\!32\)	$+$	$2^{11}\cdot 3^{6}\cdot 11$	$\mathrm{SU}(2)$	\(q+(45540-\beta _{1})q^{2}-3^{16}q^{3}+(4863185200+\cdots)q^{4}+\cdots\)
2.42.a.a	$2$	$42$	2.a	1.a	$1$	$1$	$1$	$21.294$	\(\Q\)	None	✓	✓	✓	✓	2.42.a.a	$1$	$1$	\(-1048576\)	\(5043516516\)	\(-48\!\cdots\!50\)	\(-11\!\cdots\!68\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-2^{20}q^{2}+5043516516q^{3}+2^{40}q^{4}+\cdots\)
2.42.a.b	$2$	$42$	2.a	1.a	$1$	$2$	$2$	$21.294$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	✓	✓	✓	2.42.a.b	$1$	$0$	\(2097152\)	\(8863347528\)	\(97\!\cdots\!80\)	\(21\!\cdots\!56\)	$-$	$2^{7}\cdot 3^{2}\cdot 5$	$\mathrm{SU}(2)$	\(q+2^{20}q^{2}+(4431673764-\beta )q^{3}+\cdots\)
3.35.b.a	$3$	$35$	3.b	3.b	$2$	$10$	$10$	$21.968$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓	✓	✓	3.35.b.a	$2$	$0$	\(0\)	\(119369106\)	\(0\)	\(-12\!\cdots\!72\)		$2^{54}\cdot 3^{65}\cdot 5^{4}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(11936911+41\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
3.36.a.a	$3$	$36$	3.a	1.a	$1$	$2$	$2$	$23.279$	\(\Q(\sqrt{2196841}) \)	None	✓	✓	✓	✓	3.36.a.a	$1$	$1$	\(-60912\)	\(258280326\)	\(-13\!\cdots\!40\)	\(-12\!\cdots\!44\)	$-$	$2^{4}\cdot 3\cdot 7$	$\mathrm{SU}(2)$	\(q+(-30456-\beta )q^{2}+3^{17}q^{3}+(28571469952+\cdots)q^{4}+\cdots\)
3.36.a.b	$3$	$36$	3.a	1.a	$1$	$3$	$3$	$23.279$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓	✓	✓	3.36.a.b	$1$	$0$	\(-87330\)	\(-387420489\)	\(27\!\cdots\!10\)	\(48\!\cdots\!64\)	$+$	$2^{7}\cdot 3^{5}\cdot 5$	$\mathrm{SU}(2)$	\(q+(-29110+\beta _{1})q^{2}-3^{17}q^{3}+(10829584300+\cdots)q^{4}+\cdots\)
2.44.a.a	$2$	$44$	2.a	1.a	$1$	$2$	$2$	$23.422$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	✓	✓	✓	2.44.a.a	$1$	$0$	\(-4194304\)	\(-12981630984\)	\(-39\!\cdots\!00\)	\(11\!\cdots\!08\)	$+$	$2^{8}\cdot 3\cdot 5\cdot 11$	$\mathrm{SU}(2)$	\(q-2^{21}q^{2}+(-6490815492-\beta )q^{3}+\cdots\)
2.44.a.b	$2$	$44$	2.a	1.a	$1$	$2$	$2$	$23.422$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	✓	✓	✓	2.44.a.b	$1$	$1$	\(4194304\)	\(-22341634056\)	\(-47\!\cdots\!20\)	\(-22\!\cdots\!28\)	$-$	$2^{8}\cdot 3^{3}\cdot 5$	$\mathrm{SU}(2)$	\(q+2^{21}q^{2}+(-11170817028-\beta )q^{3}+\cdots\)
3.37.b.a	$3$	$37$	3.b	3.b	$2$	$1$	$1$	$24.627$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	✓			3.37.b.a	$2$	$0$	\(0\)	\(387420489\)	\(0\)	\(27\!\cdots\!98\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3^{18}q^{3}+2^{36}q^{4}+2757049053441698q^{7}+\cdots\)
3.37.b.b	$3$	$37$	3.b	3.b	$2$	$10$	$10$	$24.627$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓	✓		3.37.b.b	$2$	$0$	\(0\)	\(-552156750\)	\(0\)	\(-12\!\cdots\!00\)		$2^{44}\cdot 3^{71}\cdot 5^{4}\cdot 7^{2}\cdot 13$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-55215675-69\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
2.46.a.a	$2$	$46$	2.a	1.a	$1$	$2$	$2$	$25.651$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	✓	✓	✓	2.46.a.a	$1$	$1$	\(-8388608\)	\(-69766206552\)	\(-45\!\cdots\!00\)	\(-95\!\cdots\!44\)	$+$	$2^{8}\cdot 3^{4}\cdot 5^{2}\cdot 11$	$\mathrm{SU}(2)$	\(q-2^{22}q^{2}+(-34883103276-\beta )q^{3}+\cdots\)
2.46.a.b	$2$	$46$	2.a	1.a	$1$	$2$	$2$	$25.651$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	✓	✓	✓	2.46.a.b	$1$	$0$	\(8388608\)	\(59861217192\)	\(43\!\cdots\!00\)	\(79\!\cdots\!24\)	$-$	$2^{8}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q+2^{22}q^{2}+(29930608596-\beta )q^{3}+\cdots\)
4.33.b.a	$4$	$33$	4.b	4.b	$2$	$1$	$1$	$25.947$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	✓			4.33.b.a	$2$	$0$	\(65536\)	\(0\)	\(-196496109694\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{16}q^{2}+2^{32}q^{4}-196496109694q^{5}+\cdots\)
4.33.b.b	$4$	$33$	4.b	4.b	$2$	$14$	$14$	$25.947$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		✓	✓		4.33.b.b	$2$	$0$	\(-23780\)	\(0\)	\(138121491740\)	\(0\)		$2^{182}\cdot 3^{20}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1699+\beta _{1})q^{2}+(9-21\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
3.38.a.a	$3$	$38$	3.a	1.a	$1$	$3$	$3$	$26.014$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓	✓	✓	3.38.a.a	$1$	$1$	\(-310908\)	\(-1162261467\)	\(-96\!\cdots\!90\)	\(-46\!\cdots\!44\)	$+$	$2^{9}\cdot 3^{5}\cdot 5$	$\mathrm{SU}(2)$	\(q+(-103636-\beta _{1})q^{2}-3^{18}q^{3}+(112825533616+\cdots)q^{4}+\cdots\)
3.38.a.b	$3$	$38$	3.a	1.a	$1$	$4$	$4$	$26.014$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	✓	✓	✓	3.38.a.b	$1$	$0$	\(437562\)	\(1549681956\)	\(-40\!\cdots\!04\)	\(66\!\cdots\!84\)	$-$	$2^{15}\cdot 3^{10}\cdot 5\cdot 7$	$\mathrm{SU}(2)$	\(q+(109391-\beta _{1})q^{2}+3^{18}q^{3}+(86524834843+\cdots)q^{4}+\cdots\)
3.39.b.a	$3$	$39$	3.b	3.b	$2$	$12$	$12$	$27.439$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓	✓	✓	3.39.b.a	$2$	$0$	\(0\)	\(-114742404\)	\(0\)	\(81\!\cdots\!48\)		$2^{75}\cdot 3^{91}\cdot 5^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-9561867+97\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
4.34.a.a	$4$	$34$	4.a	1.a	$1$	$3$	$3$	$27.593$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓	✓	✓	4.34.a.a	$1$	$0$	\(0\)	\(92491788\)	\(-53880683886\)	\(45\!\cdots\!92\)	$-$	$2^{22}\cdot 3^{3}\cdot 7\cdot 11\cdot 29$	$\mathrm{SU}(2)$	\(q+(30830596+\beta _{1})q^{3}+(-17960227962+\cdots)q^{5}+\cdots\)
2.48.a.a	$2$	$48$	2.a	1.a	$1$	$1$	$1$	$27.982$	\(\Q\)	None	✓	✓	✓	✓	2.48.a.a	$1$	$1$	\(8388608\)	\(-196634580372\)	\(20\!\cdots\!50\)	\(-51\!\cdots\!96\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2^{23}q^{2}-196634580372q^{3}+2^{46}q^{4}+\cdots\)
2.48.a.b	$2$	$48$	2.a	1.a	$1$	$2$	$2$	$27.982$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	✓	✓	✓	2.48.a.b	$1$	$0$	\(-16777216\)	\(122289844824\)	\(18\!\cdots\!40\)	\(16\!\cdots\!32\)	$+$	$2^{7}\cdot 3^{3}\cdot 5$	$\mathrm{SU}(2)$	\(q-2^{23}q^{2}+(61144922412-5\beta )q^{3}+\cdots\)
3.40.a.a	$3$	$40$	3.a	1.a	$1$	$3$	$3$	$28.902$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓	✓	✓	3.40.a.a	$1$	$1$	\(-1107000\)	\(3486784401\)	\(93\!\cdots\!90\)	\(13\!\cdots\!04\)	$-$	$2^{10}\cdot 3^{6}\cdot 5$	$\mathrm{SU}(2)$	\(q+(-369000-\beta _{1})q^{2}+3^{19}q^{3}+(335300075200+\cdots)q^{4}+\cdots\)
3.40.a.b	$3$	$40$	3.a	1.a	$1$	$3$	$3$	$28.902$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓	✓	✓	3.40.a.b	$1$	$0$	\(533574\)	\(-3486784401\)	\(-53\!\cdots\!30\)	\(-15\!\cdots\!28\)	$+$	$2^{8}\cdot 3^{6}\cdot 5\cdot 7\cdot 13$	$\mathrm{SU}(2)$	\(q+(177858-\beta _{1})q^{2}-3^{19}q^{3}+(319147551244+\cdots)q^{4}+\cdots\)
4.35.b.a	$4$	$35$	4.b	4.b	$2$	$16$	$16$	$29.290$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓	✓	4.35.b.a	$2$	$0$	\(-27372\)	\(0\)	\(-21372255840\)	\(0\)		$2^{240}\cdot 3^{26}\cdot 5^{6}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1711+\beta _{1})q^{2}+(19-76\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
3.41.b.a	$3$	$41$	3.b	3.b	$2$	$12$	$12$	$30.403$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓	✓	✓	3.41.b.a	$2$	$0$	\(0\)	\(-372082572\)	\(0\)	\(-94\!\cdots\!84\)		$2^{63}\cdot 3^{98}\cdot 5^{6}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-31006881-471\beta _{1}+\cdots)q^{3}+\cdots\)
2.50.a.a	$2$	$50$	2.a	1.a	$1$	$2$	$2$	$30.413$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	✓	✓	✓	2.50.a.a	$1$	$1$	\(-33554432\)	\(281051075592\)	\(83\!\cdots\!00\)	\(-43\!\cdots\!36\)	$+$	$2^{7}\cdot 3^{3}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q-2^{24}q^{2}+(140525537796-\beta )q^{3}+\cdots\)
2.50.a.b	$2$	$50$	2.a	1.a	$1$	$3$	$3$	$30.413$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓	✓	✓	2.50.a.b	$1$	$0$	\(50331648\)	\(-16203614388\)	\(-10\!\cdots\!30\)	\(-12\!\cdots\!96\)	$-$	$2^{22}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2}$	$\mathrm{SU}(2)$	\(q+2^{24}q^{2}+(-5401204796-\beta _{1}+\cdots)q^{3}+\cdots\)
4.36.a.a	$4$	$36$	4.a	1.a	$1$	$3$	$3$	$31.038$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓	✓	✓	4.36.a.a	$1$	$1$	\(0\)	\(50908884\)	\(280720890\)	\(-55\!\cdots\!16\)	$-$	$2^{24}\cdot 3^{4}\cdot 5\cdot 7$	$\mathrm{SU}(2)$	\(q+(16969628+\beta _{1})q^{3}+(93573630+\cdots)q^{5}+\cdots\)
3.42.a.a	$3$	$42$	3.a	1.a	$1$	$3$	$3$	$31.942$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓	✓	✓	3.42.a.a	$1$	$1$	\(-289380\)	\(-10460353203\)	\(38\!\cdots\!26\)	\(-44\!\cdots\!68\)	$+$	$2^{10}\cdot 3^{5}\cdot 7$	$\mathrm{SU}(2)$	\(q+(-96460-\beta _{1})q^{2}-3^{20}q^{3}+(-751422059600+\cdots)q^{4}+\cdots\)
3.42.a.b	$3$	$42$	3.a	1.a	$1$	$4$	$4$	$31.942$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	✓	✓	✓	3.42.a.b	$1$	$0$	\(-69822\)	\(13947137604\)	\(11\!\cdots\!80\)	\(15\!\cdots\!36\)	$-$	$2^{13}\cdot 3^{10}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q+(-17455-\beta _{1})q^{2}+3^{20}q^{3}+(1338237117038+\cdots)q^{4}+\cdots\)
5.33.c.a	$5$	$33$	5.c	5.c	$4$	$30$	$15$	$32.433$		None		✓	✓	✓	5.33.c.a	$2$	$0$	\(-2\)	\(-2792232\)	\(229266409900\)	\(21\!\cdots\!48\)			$\mathrm{SU}(2)[C_{4}]$
4.37.b.a	$4$	$37$	4.b	4.b	$2$	$1$	$1$	$32.837$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	✓			4.37.b.a	$2$	$0$	\(-262144\)	\(0\)	\(-42\!\cdots\!34\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{18}q^{2}+2^{36}q^{4}-4228490555534q^{5}+\cdots\)
4.37.b.b	$4$	$37$	4.b	4.b	$2$	$16$	$16$	$32.837$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓	✓		4.37.b.b	$2$	$0$	\(177228\)	\(0\)	\(58\!\cdots\!60\)	\(0\)		$2^{240}\cdot 3^{24}\cdot 5^{6}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(11077+\beta _{1})q^{2}+(50+198\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
2.52.a.a	$2$	$52$	2.a	1.a	$1$	$2$	$2$	$32.946$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	✓	✓	✓	2.52.a.a	$1$	$0$	\(-67108864\)	\(187290382776\)	\(-12\!\cdots\!00\)	\(-41\!\cdots\!52\)	$+$	$2^{8}\cdot 3\cdot 5^{2}\cdot 17$	$\mathrm{SU}(2)$	\(q-2^{25}q^{2}+(93645191388-17\beta )q^{3}+\cdots\)
2.52.a.b	$2$	$52$	2.a	1.a	$1$	$2$	$2$	$32.946$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	✓	✓	✓	2.52.a.b	$1$	$1$	\(67108864\)	\(889619774904\)	\(-50\!\cdots\!00\)	\(-64\!\cdots\!08\)	$-$	$2^{8}\cdot 3^{5}\cdot 5$	$\mathrm{SU}(2)$	\(q+2^{25}q^{2}+(444809887452-\beta )q^{3}+\cdots\)
3.43.b.a	$3$	$43$	3.b	3.b	$2$	$1$	$1$	$33.518$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	✓			3.43.b.a	$2$	$0$	\(0\)	\(-10460353203\)	\(0\)	\(14\!\cdots\!86\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3^{21}q^{3}+2^{42}q^{4}+146246101081752386q^{7}+\cdots\)
3.43.b.b	$3$	$43$	3.b	3.b	$2$	$12$	$12$	$33.518$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓	✓		3.43.b.b	$2$	$0$	\(0\)	\(16987205196\)	\(0\)	\(-41\!\cdots\!32\)		$2^{73}\cdot 3^{104}\cdot 5^{6}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(1415600433+546\beta _{1}+\cdots)q^{3}+\cdots\)
5.34.a.a	$5$	$34$	5.a	1.a	$1$	$5$	$5$	$34.491$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓	✓	✓	5.34.a.a	$1$	$1$	\(30472\)	\(-14988714\)	\(-762939453125\)	\(-65\!\cdots\!58\)	$+$	$2^{21}\cdot 3^{5}\cdot 5^{4}\cdot 11$	$\mathrm{SU}(2)$	\(q+(6094-\beta _{1})q^{2}+(-2997861-296\beta _{1}+\cdots)q^{3}+\cdots\)
5.34.a.b	$5$	$34$	5.a	1.a	$1$	$6$	$6$	$34.491$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓	✓	✓	5.34.a.b	$1$	$0$	\(147350\)	\(26513900\)	\(915527343750\)	\(19\!\cdots\!00\)	$-$	$2^{21}\cdot 3^{5}\cdot 5^{6}\cdot 7\cdot 11^{2}$	$\mathrm{SU}(2)$	\(q+(24558+\beta _{1})q^{2}+(4418958+77\beta _{1}+\cdots)q^{3}+\cdots\)
5.34.b.a	$5$	$34$	5.b	5.b	$2$	$16$	$16$	$34.491$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓	✓	✓	5.34.b.a	$2$	$0$	\(0\)	\(0\)	\(-232168160280\)	\(0\)		$2^{83}\cdot 3^{26}\cdot 5^{53}\cdot 7^{4}\cdot 11^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-52\beta _{1}+\beta _{3})q^{3}+(-4553207930+\cdots)q^{4}+\cdots\)
4.38.a.a	$4$	$38$	4.a	1.a	$1$	$3$	$3$	$34.686$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓	✓	✓	4.38.a.a	$1$	$0$	\(0\)	\(-272163492\)	\(36\!\cdots\!94\)	\(15\!\cdots\!92\)	$-$	$2^{24}\cdot 3^{5}\cdot 7$	$\mathrm{SU}(2)$	\(q+(-90721164-\beta _{1})q^{3}+(1213681705398+\cdots)q^{5}+\cdots\)

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