LMFDB - Newform search results

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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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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
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1.66.a.a	$1$	$66$	1.a	1.a	$1$	$5$	$5$	$26.757$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	✓	✓	✓	1.66.a.a	$1$	$1$	$-3959709648$	$-22\!\cdots\!04$	$26\!\cdots\!50$	$-69\!\cdots\!08$	$+$	$2^{40}\cdot 3^{12}\cdot 5^{4}\cdot 7^{2}\cdot 11\cdot 13^{2}$	$\mathrm{SU}(2)$	$q+(-791941930-\beta _{1})q^{2}+(-446261486940055+\cdots)q^{3}+\cdots$
1.68.a.a	$1$	$68$	1.a	1.a	$1$	$5$	$5$	$28.429$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	✓	✓	✓	1.68.a.a	$1$	$0$	$5554901256$	$34\!\cdots\!72$	$33\!\cdots\!50$	$33\!\cdots\!56$	$+$	$2^{40}\cdot 3^{15}\cdot 5^{4}\cdot 7^{2}\cdot 11\cdot 13\cdot 17$	$\mathrm{SU}(2)$	$q+(1110980251-\beta _{1})q^{2}+(688672053797479+\cdots)q^{3}+\cdots$
1.70.a.a	$1$	$70$	1.a	1.a	$1$	$5$	$5$	$30.151$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	✓	✓	✓	1.70.a.a	$1$	$1$	$-18005734368$	$-48\!\cdots\!04$	$-18\!\cdots\!50$	$76\!\cdots\!92$	$+$	$2^{43}\cdot 3^{17}\cdot 5^{5}\cdot 7^{2}\cdot 17\cdot 23$	$\mathrm{SU}(2)$	$q+(-3601146874-\beta _{1})q^{2}+(-971616465424800+\cdots)q^{3}+\cdots$
1.72.a.a	$1$	$72$	1.a	1.a	$1$	$6$	$6$	$31.925$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	✓	✓	✓	1.72.a.a	$1$	$0$	$66157336440$	$89\!\cdots\!40$	$-42\!\cdots\!20$	$33\!\cdots\!00$	$+$	$2^{55}\cdot 3^{20}\cdot 5^{6}\cdot 7^{3}$	$\mathrm{SU}(2)$	$q+(11026222740-\beta _{1})q^{2}+(14982825462961740+\cdots)q^{3}+\cdots$
1.74.a.a	$1$	$74$	1.a	1.a	$1$	$5$	$5$	$33.748$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	✓	✓	✓	1.74.a.a	$1$	$1$	$-92089333488$	$-12\!\cdots\!04$	$23\!\cdots\!50$	$-43\!\cdots\!08$	$+$	$2^{39}\cdot 3^{15}\cdot 5^{6}\cdot 7^{2}$	$\mathrm{SU}(2)$	$q+(-18417866698-\beta _{1})q^{2}+\cdots$
1.76.a.a	$1$	$76$	1.a	1.a	$1$	$6$	$6$	$35.623$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	✓	✓	✓	1.76.a.a	$1$	$0$	$-57080822040$	$-78\!\cdots\!40$	$-38\!\cdots\!40$	$19\!\cdots\!00$	$+$	$2^{58}\cdot 3^{26}\cdot 5^{7}\cdot 7^{3}\cdot 11\cdot 13\cdot 19$	$\mathrm{SU}(2)$	$q+(-9513470340+\beta _{1})q^{2}+\cdots$
1.78.a.a	$1$	$78$	1.a	1.a	$1$	$6$	$6$	$37.548$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	✓	✓	✓	1.78.a.a	$1$	$1$	$264721893120$	$14\!\cdots\!80$	$-26\!\cdots\!00$	$27\!\cdots\!00$	$+$	$2^{64}\cdot 3^{20}\cdot 5^{8}\cdot 7^{3}\cdot 11^{2}\cdot 13^{2}\cdot 19$	$\mathrm{SU}(2)$	$q+(44120315520-\beta _{1})q^{2}+(240268562631348180+\cdots)q^{3}+\cdots$
1.80.a.a	$1$	$80$	1.a	1.a	$1$	$6$	$6$	$39.524$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	✓	✓	✓	1.80.a.a	$1$	$0$	$-16086577320$	$19\!\cdots\!80$	$60\!\cdots\!40$	$-20\!\cdots\!00$	$+$	$2^{54}\cdot 3^{24}\cdot 5^{6}\cdot 7^{3}\cdot 11\cdot 13^{2}$	$\mathrm{SU}(2)$	$q+(-2681096220+\beta _{1})q^{2}+\cdots$
1.82.a.a	$1$	$82$	1.a	1.a	$1$	$6$	$6$	$41.550$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	✓	✓	✓	1.82.a.a	$1$	$1$	$-460872026640$	$-15\!\cdots\!60$	$-18\!\cdots\!00$	$-31\!\cdots\!00$	$+$	$2^{58}\cdot 3^{26}\cdot 5^{7}\cdot 7^{3}\cdot 13$	$\mathrm{SU}(2)$	$q+(-76812004440-\beta _{1})q^{2}+\cdots$
1.84.a.a	$1$	$84$	1.a	1.a	$1$	$7$	$7$	$43.627$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓	✓	1.84.a.a	$1$	$0$	$347450761416$	$92\!\cdots\!72$	$95\!\cdots\!70$	$41\!\cdots\!56$	$+$	$2^{82}\cdot 3^{30}\cdot 5^{8}\cdot 7^{4}\cdot 17$	$\mathrm{SU}(2)$	$q+(49635823059+\beta _{1})q^{2}+\cdots$
1.86.a.a	$1$	$86$	1.a	1.a	$1$	$6$	$6$	$45.755$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	✓	✓	✓	1.86.a.a	$1$	$1$	$-35\!\cdots\!00$	$-15\!\cdots\!00$	$-93\!\cdots\!00$	$37\!\cdots\!00$	$+$	$2^{65}\cdot 3^{23}\cdot 5^{6}\cdot 7^{3}\cdot 11\cdot 17^{2}$	$\mathrm{SU}(2)$	$q+(-599485114800+\beta _{1})q^{2}+\cdots$
1.88.a.a	$1$	$88$	1.a	1.a	$1$	$7$	$7$	$47.933$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓	✓	1.88.a.a	$1$	$0$	$18\!\cdots\!36$	$-75\!\cdots\!48$	$33\!\cdots\!50$	$45\!\cdots\!56$	$+$	$2^{76}\cdot 3^{35}\cdot 5^{8}\cdot 7^{4}\cdot 11^{2}\cdot 13\cdot 17\cdot 29^{2}$	$\mathrm{SU}(2)$	$q+(2599574577562+\beta _{1})q^{2}+\cdots$
1.90.a.a	$1$	$90$	1.a	1.a	$1$	$7$	$7$	$50.162$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓	✓	1.90.a.a	$1$	$1$	$-31\!\cdots\!08$	$-13\!\cdots\!64$	$10\!\cdots\!50$	$38\!\cdots\!92$	$+$	$2^{83}\cdot 3^{29}\cdot 5^{9}\cdot 7^{5}\cdot 11^{2}\cdot 13^{2}$	$\mathrm{SU}(2)$	$q+(-4486761478773-\beta _{1})q^{2}+\cdots$
1.92.a.a	$1$	$92$	1.a	1.a	$1$	$7$	$7$	$52.442$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓	✓	1.92.a.a	$1$	$0$	$38\!\cdots\!56$	$62\!\cdots\!32$	$23\!\cdots\!30$	$-17\!\cdots\!44$	$+$	$2^{83}\cdot 3^{31}\cdot 5^{8}\cdot 7^{6}\cdot 11\cdot 13^{3}\cdot 23$	$\mathrm{SU}(2)$	$q+(548816691151+\beta _{1})q^{2}+\cdots$
2.66.a.a	$2$	$66$	2.a	1.a	$1$	$2$	$2$	$53.514$	$\mathbb{Q}[x]/(x^{2} - \cdots)$	None	✓	✓	✓	✓	2.66.a.a	$1$	$1$	$-8589934592$	$11\!\cdots\!92$	$-74\!\cdots\!00$	$27\!\cdots\!24$	$+$	$2^{7}\cdot 3^{4}\cdot 5\cdot 11$	$\mathrm{SU}(2)$	$q-2^{32}q^{2}+(574529980102596-111\beta )q^{3}+\cdots$
2.66.a.b	$2$	$66$	2.a	1.a	$1$	$3$	$3$	$53.514$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	✓	✓	✓	2.66.a.b	$1$	$0$	$12884901888$	$29\!\cdots\!12$	$39\!\cdots\!50$	$42\!\cdots\!64$	$-$	$2^{22}\cdot 3^{8}\cdot 5^{3}\cdot 7\cdot 11\cdot 13$	$\mathrm{SU}(2)$	$q+2^{32}q^{2}+(994852866070404-\beta _{1}+\cdots)q^{3}+\cdots$
1.94.a.a	$1$	$94$	1.a	1.a	$1$	$7$	$7$	$54.773$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓	✓	1.94.a.a	$1$	$1$	$43\!\cdots\!92$	$-36\!\cdots\!84$	$-24\!\cdots\!50$	$-92\!\cdots\!08$	$+$	$2^{88}\cdot 3^{34}\cdot 5^{10}\cdot 7^{6}\cdot 13^{2}\cdot 19\cdot 23\cdot 31^{2}$	$\mathrm{SU}(2)$	$q+(6247918101970+\beta _{1})q^{2}+\cdots$
2.68.a.a	$2$	$68$	2.a	1.a	$1$	$3$	$3$	$56.858$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	✓	✓	✓	2.68.a.a	$1$	$0$	$-25769803776$	$-52\!\cdots\!16$	$-26\!\cdots\!50$	$21\!\cdots\!12$	$+$	$2^{24}\cdot 3^{5}\cdot 5^{3}\cdot 11\cdot 17$	$\mathrm{SU}(2)$	$q-2^{33}q^{2}+(-1741882068537572+\cdots)q^{3}+\cdots$
2.68.a.b	$2$	$68$	2.a	1.a	$1$	$3$	$3$	$56.858$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	✓	✓	✓	2.68.a.b	$1$	$1$	$25769803776$	$-23\!\cdots\!44$	$69\!\cdots\!90$	$-46\!\cdots\!92$	$-$	$2^{24}\cdot 3^{7}\cdot 5^{2}\cdot 7\cdot 11$	$\mathrm{SU}(2)$	$q+2^{33}q^{2}+(-794134480773348+\cdots)q^{3}+\cdots$
1.96.a.a	$1$	$96$	1.a	1.a	$1$	$8$	$8$	$57.154$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓	✓	✓	1.96.a.a	$1$	$0$	$-58\!\cdots\!80$	$-95\!\cdots\!80$	$19\!\cdots\!60$	$31\!\cdots\!00$	$+$	$2^{104}\cdot 3^{38}\cdot 5^{12}\cdot 7^{7}\cdot 11\cdot 13\cdot 19^{3}$	$\mathrm{SU}(2)$	$q+(-729457392285+\beta _{1})q^{2}+\cdots$
1.98.a.a	$1$	$98$	1.a	1.a	$1$	$7$	$7$	$59.585$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓	✓	1.98.a.a	$1$	$1$	$-16\!\cdots\!08$	$10\!\cdots\!96$	$-36\!\cdots\!50$	$-18\!\cdots\!08$	$+$	$2^{83}\cdot 3^{30}\cdot 5^{10}\cdot 7^{8}\cdot 11^{2}\cdot 19$	$\mathrm{SU}(2)$	$q+(-2385320155001+\beta _{1})q^{2}+\cdots$
2.70.a.a	$2$	$70$	2.a	1.a	$1$	$3$	$3$	$60.303$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	✓	✓	✓	2.70.a.a	$1$	$1$	$-51539607552$	$15\!\cdots\!12$	$20\!\cdots\!70$	$-20\!\cdots\!96$	$+$	$2^{24}\cdot 3^{10}\cdot 5^{2}\cdot 7\cdot 11\cdot 17\cdot 23$	$\mathrm{SU}(2)$	$q-2^{34}q^{2}+(5160893455497204+\cdots)q^{3}+\cdots$
2.70.a.b	$2$	$70$	2.a	1.a	$1$	$3$	$3$	$60.303$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	✓	✓	✓	2.70.a.b	$1$	$0$	$51539607552$	$-23\!\cdots\!52$	$-58\!\cdots\!50$	$92\!\cdots\!16$	$-$	$2^{24}\cdot 3^{5}\cdot 5^{4}\cdot 7\cdot 23$	$\mathrm{SU}(2)$	$q+2^{34}q^{2}+(-7866377652201484+\cdots)q^{3}+\cdots$
1.100.a.a	$1$	$100$	1.a	1.a	$1$	$8$	$8$	$62.068$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓	✓	✓	1.100.a.a	$1$	$0$	$-20\!\cdots\!20$	$-28\!\cdots\!20$	$-48\!\cdots\!60$	$-56\!\cdots\!00$	$+$	$2^{109}\cdot 3^{44}\cdot 5^{13}\cdot 7^{9}\cdot 11^{3}\cdot 13\cdot 17$	$\mathrm{SU}(2)$	$q+(-26005077112815+\beta _{1})q^{2}+\cdots$
2.72.a.a	$2$	$72$	2.a	1.a	$1$	$2$	$2$	$63.849$	$\mathbb{Q}[x]/(x^{2} - \cdots)$	None	✓	✓	✓	✓	2.72.a.a	$1$	$1$	$68719476736$	$-73\!\cdots\!24$	$40\!\cdots\!00$	$-29\!\cdots\!52$	$-$	$2^{7}\cdot 3^{6}\cdot 5^{2}$	$\mathrm{SU}(2)$	$q+2^{35}q^{2}+(-36645276287423412+\cdots)q^{3}+\cdots$
2.72.a.b	$2$	$72$	2.a	1.a	$1$	$3$	$3$	$63.849$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	✓	✓	✓	2.72.a.b	$1$	$0$	$-103079215104$	$23\!\cdots\!36$	$47\!\cdots\!50$	$-68\!\cdots\!72$	$+$	$2^{22}\cdot 3^{6}\cdot 5^{3}\cdot 7$	$\mathrm{SU}(2)$	$q-2^{35}q^{2}+(787523430902412+\beta _{1}+\cdots)q^{3}+\cdots$
1.102.a.a	$1$	$102$	1.a	1.a	$1$	$8$	$8$	$64.601$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓	✓	✓	1.102.a.a	$1$	$1$	$-43\!\cdots\!40$	$-12\!\cdots\!60$	$38\!\cdots\!00$	$-57\!\cdots\!00$	$+$	$2^{119}\cdot 3^{37}\cdot 5^{14}\cdot 7^{7}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2}$	$\mathrm{SU}(2)$	$q+(-54373636474380-\beta _{1})q^{2}+\cdots$
1.104.a.a	$1$	$104$	1.a	1.a	$1$	$8$	$8$	$67.184$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓	✓	✓	1.104.a.a	$1$	$0$	$43\!\cdots\!40$	$50\!\cdots\!40$	$55\!\cdots\!20$	$41\!\cdots\!00$	$+$	$2^{104}\cdot 3^{40}\cdot 5^{12}\cdot 7^{8}\cdot 11\cdot 13^{3}\cdot 17^{2}$	$\mathrm{SU}(2)$	$q+(548616194585055-\beta _{1})q^{2}+\cdots$
2.74.a.a	$2$	$74$	2.a	1.a	$1$	$3$	$3$	$67.497$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	✓	✓	✓	2.74.a.a	$1$	$1$	$-206158430208$	$-30\!\cdots\!72$	$-32\!\cdots\!50$	$-23\!\cdots\!64$	$+$	$2^{23}\cdot 3^{7}\cdot 5^{3}$	$\mathrm{SU}(2)$	$q-2^{36}q^{2}+(-101346400339911324+\cdots)q^{3}+\cdots$
2.74.a.b	$2$	$74$	2.a	1.a	$1$	$4$	$4$	$67.497$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	✓	✓	✓	2.74.a.b	$1$	$0$	$274877906944$	$30\!\cdots\!76$	$-78\!\cdots\!60$	$36\!\cdots\!12$	$-$	$2^{45}\cdot 3^{14}\cdot 5^{5}\cdot 7^{2}\cdot 11$	$\mathrm{SU}(2)$	$q+2^{36}q^{2}+(76266581430811044+\cdots)q^{3}+\cdots$
1.106.a.a	$1$	$106$	1.a	1.a	$1$	$8$	$8$	$69.819$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓	✓	✓	1.106.a.a	$1$	$1$	$-91\!\cdots\!20$	$-35\!\cdots\!80$	$74\!\cdots\!00$	$70\!\cdots\!00$	$+$	$2^{111}\cdot 3^{44}\cdot 5^{13}\cdot 7^{7}\cdot 11\cdot 13^{3}\cdot 17$	$\mathrm{SU}(2)$	$q+(-1146879061146990+\beta _{1})q^{2}+\cdots$
2.76.a.a	$2$	$76$	2.a	1.a	$1$	$3$	$3$	$71.246$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	✓	✓	✓	2.76.a.a	$1$	$0$	$-412316860416$	$12\!\cdots\!04$	$16\!\cdots\!50$	$49\!\cdots\!12$	$+$	$2^{24}\cdot 3^{7}\cdot 5^{4}\cdot 7\cdot 11\cdot 19$	$\mathrm{SU}(2)$	$q-2^{37}q^{2}+(415752245544732668+\cdots)q^{3}+\cdots$
2.76.a.b	$2$	$76$	2.a	1.a	$1$	$3$	$3$	$71.246$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	✓	✓	✓	2.76.a.b	$1$	$1$	$412316860416$	$45\!\cdots\!16$	$-19\!\cdots\!90$	$-37\!\cdots\!52$	$-$	$2^{24}\cdot 3^{8}\cdot 5^{3}\cdot 7\cdot 11$	$\mathrm{SU}(2)$	$q+2^{37}q^{2}+(152747388742936572+\cdots)q^{3}+\cdots$
1.108.a.a	$1$	$108$	1.a	1.a	$1$	$9$	$9$	$72.504$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓	✓	✓	1.108.a.a	$1$	$0$	$54\!\cdots\!96$	$15\!\cdots\!12$	$24\!\cdots\!50$	$-93\!\cdots\!44$	$+$	$2^{143}\cdot 3^{48}\cdot 5^{18}\cdot 7^{8}\cdot 11^{2}\cdot 13^{2}$	$\mathrm{SU}(2)$	$q+(607308845937277-\beta _{1})q^{2}+\cdots$
2.78.a.a	$2$	$78$	2.a	1.a	$1$	$3$	$3$	$75.096$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	✓	✓	✓	2.78.a.a	$1$	$1$	$-824633720832$	$-25\!\cdots\!88$	$30\!\cdots\!10$	$-23\!\cdots\!16$	$+$	$2^{24}\cdot 3^{11}\cdot 5^{2}\cdot 7\cdot 11\cdot 13\cdot 19$	$\mathrm{SU}(2)$	$q-2^{38}q^{2}+(-842429601461527596+\cdots)q^{3}+\cdots$
2.78.a.b	$2$	$78$	2.a	1.a	$1$	$3$	$3$	$75.096$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	✓	✓	✓	2.78.a.b	$1$	$0$	$824633720832$	$-11\!\cdots\!92$	$64\!\cdots\!50$	$-17\!\cdots\!44$	$-$	$2^{24}\cdot 3^{8}\cdot 5^{4}\cdot 7\cdot 11$	$\mathrm{SU}(2)$	$q+2^{38}q^{2}+(-37139225154949164+\cdots)q^{3}+\cdots$
1.110.a.a	$1$	$110$	1.a	1.a	$1$	$8$	$8$	$75.239$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓	✓	✓	1.110.a.a	$1$	$1$	$22\!\cdots\!00$	$-79\!\cdots\!00$	$-21\!\cdots\!00$	$23\!\cdots\!00$	$+$	$2^{118}\cdot 3^{40}\cdot 5^{14}\cdot 7^{6}\cdot 11^{3}\cdot 13$	$\mathrm{SU}(2)$	$q+(286049075864400-\beta _{1})q^{2}+\cdots$
3.65.b.a	$3$	$65$	3.b	3.b	$2$	$20$	$20$	$77.821$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		✓	✓	✓	3.65.b.a	$2$	$0$	$0$	$-14\!\cdots\!92$	$0$	$68\!\cdots\!76$		$2^{190}\cdot 3^{282}\cdot 5^{19}\cdot 7^{8}\cdot 11^{4}\cdot 13^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-71037898477915+13312\beta _{1}+\cdots)q^{3}+\cdots$
1.112.a.a	$1$	$112$	1.a	1.a	$1$	$9$	$9$	$78.026$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓	✓	✓	1.112.a.a	$1$	$0$	$73\!\cdots\!76$	$23\!\cdots\!52$	$81\!\cdots\!30$	$78\!\cdots\!56$	$+$	$2^{135}\cdot 3^{56}\cdot 5^{16}\cdot 7^{7}\cdot 11^{3}\cdot 13\cdot 19\cdot 37^{3}$	$\mathrm{SU}(2)$	$q+(811166749386264+\beta _{1})q^{2}+\cdots$
2.80.a.a	$2$	$80$	2.a	1.a	$1$	$3$	$3$	$79.047$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	✓	✓	✓	2.80.a.a	$1$	$1$	$16\!\cdots\!64$	$-45\!\cdots\!36$	$-40\!\cdots\!50$	$14\!\cdots\!12$	$-$	$2^{23}\cdot 3^{9}\cdot 5^{4}\cdot 7\cdot 11$	$\mathrm{SU}(2)$	$q+2^{39}q^{2}+(-1528323113916241812+\cdots)q^{3}+\cdots$
2.80.a.b	$2$	$80$	2.a	1.a	$1$	$4$	$4$	$79.047$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	✓	✓	✓	2.80.a.b	$1$	$0$	$-21\!\cdots\!52$	$43\!\cdots\!88$	$-20\!\cdots\!80$	$25\!\cdots\!04$	$+$	$2^{45}\cdot 3^{12}\cdot 5^{5}\cdot 7\cdot 11\cdot 13$	$\mathrm{SU}(2)$	$q-2^{39}q^{2}+(1099291558848636972+\cdots)q^{3}+\cdots$
3.66.a.a	$3$	$66$	3.a	1.a	$1$	$5$	$5$	$80.272$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	✓	✓	✓	3.66.a.a	$1$	$1$	$-2586530964$	$-92\!\cdots\!05$	$-86\!\cdots\!94$	$57\!\cdots\!24$	$+$	$2^{37}\cdot 3^{20}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}$	$\mathrm{SU}(2)$	$q+(-517306193-\beta _{1})q^{2}-3^{32}q^{3}+\cdots$
3.66.a.b	$3$	$66$	3.a	1.a	$1$	$6$	$6$	$80.272$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	✓	✓	✓	3.66.a.b	$1$	$0$	$6210982962$	$11\!\cdots\!46$	$35\!\cdots\!00$	$13\!\cdots\!04$	$-$	$2^{43}\cdot 3^{29}\cdot 5^{6}\cdot 7^{2}\cdot 11\cdot 13$	$\mathrm{SU}(2)$	$q+(1035163827+\beta _{1})q^{2}+3^{32}q^{3}+\cdots$
1.114.a.a	$1$	$114$	1.a	1.a	$1$	$9$	$9$	$80.863$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓	✓	✓	1.114.a.a	$1$	$1$	$49\!\cdots\!32$	$-10\!\cdots\!24$	$-31\!\cdots\!50$	$-17\!\cdots\!08$	$+$	$2^{144}\cdot 3^{48}\cdot 5^{19}\cdot 7^{7}\cdot 11^{2}\cdot 13^{2}\cdot 19^{3}\cdot 23$	$\mathrm{SU}(2)$	$q+(552636039763781+\beta _{1})q^{2}+\cdots$
3.67.b.a	$3$	$67$	3.b	3.b	$2$	$1$	$1$	$82.760$	$\Q$	$\Q(\sqrt{-3}) $	✓	✓			3.67.b.a	$2$	$0$	$0$	$-55\!\cdots\!23$	$0$	$-15\!\cdots\!14$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-3^{33}q^{3}+2^{66}q^{4}+\cdots$
3.67.b.b	$3$	$67$	3.b	3.b	$2$	$20$	$20$	$82.760$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		✓	✓		3.67.b.b	$2$	$0$	$0$	$48\!\cdots\!16$	$0$	$12\!\cdots\!88$		$2^{216}\cdot 3^{291}\cdot 5^{20}\cdot 7^{10}\cdot 11^{6}\cdot 13^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(243548779847726+15513\beta _{1}+\cdots)q^{3}+\cdots$
2.82.a.a	$2$	$82$	2.a	1.a	$1$	$3$	$3$	$83.100$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	✓	✓	✓	2.82.a.a	$1$	$1$	$-32\!\cdots\!28$	$12\!\cdots\!88$	$-20\!\cdots\!50$	$-55\!\cdots\!24$	$+$	$2^{23}\cdot 3^{10}\cdot 5^{3}\cdot 7$	$\mathrm{SU}(2)$	$q-2^{40}q^{2}+(4201453557463404996+\cdots)q^{3}+\cdots$
2.82.a.b	$2$	$82$	2.a	1.a	$1$	$4$	$4$	$83.100$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	✓	✓	✓	2.82.a.b	$1$	$0$	$43\!\cdots\!04$	$-71\!\cdots\!04$	$24\!\cdots\!80$	$18\!\cdots\!92$	$-$	$2^{45}\cdot 3^{15}\cdot 5^{5}\cdot 7^{2}\cdot 11$	$\mathrm{SU}(2)$	$q+2^{40}q^{2}+(-1777934344659239676+\cdots)q^{3}+\cdots$
1.116.a.a	$1$	$116$	1.a	1.a	$1$	$9$	$9$	$83.750$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓	✓	✓	1.116.a.a	$1$	$0$	$-11\!\cdots\!44$	$34\!\cdots\!92$	$-94\!\cdots\!90$	$18\!\cdots\!56$	$+$	$2^{142}\cdot 3^{52}\cdot 5^{17}\cdot 7^{8}\cdot 11^{3}\cdot 13^{3}\cdot 17\cdot 19^{3}\cdot 23^{3}\cdot 29^{2}$	$\mathrm{SU}(2)$	$q+(-12908974454383949-\beta _{1}+\cdots)q^{2}+\cdots$
3.68.a.a	$3$	$68$	3.a	1.a	$1$	$5$	$5$	$85.287$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	✓	✓	✓	3.68.a.a	$1$	$1$	$-16255223088$	$27\!\cdots\!15$	$-78\!\cdots\!10$	$28\!\cdots\!08$	$-$	$2^{40}\cdot 3^{20}\cdot 5^{3}\cdot 7^{2}\cdot 11\cdot 17$	$\mathrm{SU}(2)$	$q+(-3251044618-\beta _{1})q^{2}+3^{33}q^{3}+\cdots$

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Elliptic curves over $\Q$
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