Newform search results

Results (1-50 of 4855 matches)

  Download displayed columns for results to

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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1.18.a.a	$1$	$18$	1.a	1.a	$1$	$1$	$1$	$1.832$	$\Q$	None	✓	✓	✓	✓	1.18.a.a	$1$	$1$	$-528$	$-4284$	$-1025850$	$3225992$	$+$	$1$	$\mathrm{SU}(2)$	$q-528q^{2}-4284q^{3}+147712q^{4}+\cdots$
1.20.a.a	$1$	$20$	1.a	1.a	$1$	$1$	$1$	$2.288$	$\Q$	None	✓	✓	✓	✓	1.20.a.a	$1$	$0$	$456$	$50652$	$-2377410$	$-16917544$	$+$	$1$	$\mathrm{SU}(2)$	$q+456q^{2}+50652q^{3}-316352q^{4}+\cdots$
1.22.a.a	$1$	$22$	1.a	1.a	$1$	$1$	$1$	$2.795$	$\Q$	None	✓	✓	✓	✓	1.22.a.a	$1$	$1$	$-288$	$-128844$	$21640950$	$-768078808$	$+$	$1$	$\mathrm{SU}(2)$	$q-288q^{2}-128844q^{3}-2014208q^{4}+\cdots$
1.24.a.a	$1$	$24$	1.a	1.a	$1$	$2$	$2$	$3.352$	$\Q(\sqrt{144169})$	None	✓	✓	✓	✓	1.24.a.a	$1$	$0$	$1080$	$339480$	$73069020$	$-1359184400$	$+$	$2^{3}\cdot 3$	$\mathrm{SU}(2)$	$q+(540-\beta )q^{2}+(169740+48\beta )q^{3}+\cdots$
2.18.a.a	$2$	$18$	2.a	1.a	$1$	$1$	$1$	$3.664$	$\Q$	None	✓	✓	✓	✓	2.18.a.a	$1$	$0$	$256$	$6084$	$1255110$	$-22465912$	$-$	$1$	$\mathrm{SU}(2)$	$q+2^{8}q^{2}+78^{2}q^{3}+2^{16}q^{4}+1255110q^{5}+\cdots$
1.26.a.a	$1$	$26$	1.a	1.a	$1$	$1$	$1$	$3.960$	$\Q$	None	✓	✓	✓	✓	1.26.a.a	$1$	$1$	$-48$	$-195804$	$-741989850$	$39080597192$	$+$	$1$	$\mathrm{SU}(2)$	$q-48q^{2}-195804q^{3}-33552128q^{4}+\cdots$
2.20.a.a	$2$	$20$	2.a	1.a	$1$	$1$	$1$	$4.576$	$\Q$	None	✓	✓	✓	✓	2.20.a.a	$1$	$0$	$-512$	$-13092$	$6546750$	$96674264$	$+$	$1$	$\mathrm{SU}(2)$	$q-2^{9}q^{2}-13092q^{3}+2^{18}q^{4}+6546750q^{5}+\cdots$
2.20.a.b	$2$	$20$	2.a	1.a	$1$	$1$	$1$	$4.576$	$\Q$	None	✓	✓	✓	✓	2.20.a.b	$1$	$1$	$512$	$-53028$	$-5556930$	$-44496424$	$-$	$1$	$\mathrm{SU}(2)$	$q+2^{9}q^{2}-53028q^{3}+2^{18}q^{4}-5556930q^{5}+\cdots$
1.28.a.a	$1$	$28$	1.a	1.a	$1$	$2$	$2$	$4.619$	$\Q(\sqrt{18209})$	None	✓	✓	✓	✓	1.28.a.a	$1$	$0$	$-8280$	$-1286280$	$5443587900$	$-175391963600$	$+$	$2^{3}\cdot 3^{3}$	$\mathrm{SU}(2)$	$q+(-4140-\beta )q^{2}+(-643140-192\beta )q^{3}+\cdots$
3.17.b.a	$3$	$17$	3.b	3.b	$2$	$4$	$4$	$4.870$	$\mathbb{Q}[x]/(x^{4} + \cdots)$	None		✓	✓	✓	3.17.b.a	$2$	$0$	$0$	$-2052$	$0$	$-3141544$		$2^{6}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-513+\beta _{1}+\beta _{2})q^{3}+(-3116+\cdots)q^{4}+\cdots$
1.30.a.a	$1$	$30$	1.a	1.a	$1$	$2$	$2$	$5.328$	$\Q(\sqrt{51349})$	None	✓	✓	✓	✓	1.30.a.a	$1$	$1$	$8640$	$-4967640$	$-17477788500$	$-30\!\cdots\!00$	$+$	$2^{6}\cdot 3$	$\mathrm{SU}(2)$	$q+(4320-\beta )q^{2}+(-2483820+552\beta )q^{3}+\cdots$
3.18.a.a	$3$	$18$	3.a	1.a	$1$	$1$	$1$	$5.497$	$\Q$	None	✓	✓	✓	✓	3.18.a.a	$1$	$1$	$204$	$-6561$	$-163554$	$-20846560$	$+$	$1$	$\mathrm{SU}(2)$	$q+204q^{2}-3^{8}q^{3}-89456q^{4}-163554q^{5}+\cdots$
3.18.a.b	$3$	$18$	3.a	1.a	$1$	$2$	$2$	$5.497$	$\Q(\sqrt{14569})$	None	✓	✓	✓	✓	3.18.a.b	$1$	$0$	$594$	$13122$	$382860$	$24471568$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	$q+(297-\beta )q^{2}+3^{8}q^{3}+(88258-594\beta )q^{4}+\cdots$
2.22.a.a	$2$	$22$	2.a	1.a	$1$	$1$	$1$	$5.590$	$\Q$	None	✓	✓	✓	✓	2.22.a.a	$1$	$1$	$-1024$	$71604$	$-28693770$	$-853202392$	$+$	$1$	$\mathrm{SU}(2)$	$q-2^{10}q^{2}+71604q^{3}+2^{20}q^{4}-28693770q^{5}+\cdots$
2.22.a.b	$2$	$22$	2.a	1.a	$1$	$1$	$1$	$5.590$	$\Q$	None	✓	✓	✓	✓	2.22.a.b	$1$	$0$	$1024$	$59316$	$4975350$	$1427425832$	$-$	$1$	$\mathrm{SU}(2)$	$q+2^{10}q^{2}+59316q^{3}+2^{20}q^{4}+4975350q^{5}+\cdots$
1.32.a.a	$1$	$32$	1.a	1.a	$1$	$2$	$2$	$6.088$	$\mathbb{Q}[x]/(x^{2} - \cdots)$	None	✓	✓	✓	✓	1.32.a.a	$1$	$0$	$39960$	$17363160$	$-19391218020$	$30\!\cdots\!00$	$+$	$2^{3}\cdot 3$	$\mathrm{SU}(2)$	$q+(19980-\beta )q^{2}+(8681580-432\beta )q^{3}+\cdots$
3.19.b.a	$3$	$19$	3.b	3.b	$2$	$1$	$1$	$6.162$	$\Q$	$\Q(\sqrt{-3})$	✓	✓			3.19.b.a	$2$	$0$	$0$	$-19683$	$0$	$77549186$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-3^{9}q^{3}+2^{18}q^{4}+77549186q^{7}+\cdots$
3.19.b.b	$3$	$19$	3.b	3.b	$2$	$4$	$4$	$6.162$	4.0.601940665.1	None		✓	✓		3.19.b.b	$2$	$0$	$0$	$15876$	$0$	$-95744152$		$2^{11}\cdot 3^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(63^{2}+11\beta _{1}+\beta _{2})q^{3}+(-263384+\cdots)q^{4}+\cdots$
4.17.b.a	$4$	$17$	4.b	4.b	$2$	$1$	$1$	$6.493$	$\Q$	$\Q(\sqrt{-1})$	✓	✓			4.17.b.a	$2$	$0$	$256$	$0$	$329666$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{8}q^{2}+2^{16}q^{4}+329666q^{5}+2^{24}q^{8}+\cdots$
4.17.b.b	$4$	$17$	4.b	4.b	$2$	$6$	$6$	$6.493$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None		✓	✓		4.17.b.b	$2$	$0$	$-164$	$0$	$-506740$	$0$		$2^{30}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-3^{3}-\beta _{1})q^{2}+(1-3\beta _{1}+\beta _{2})q^{3}+\cdots$
2.24.a.a	$2$	$24$	2.a	1.a	$1$	$1$	$1$	$6.704$	$\Q$	None	✓	✓	✓	✓	2.24.a.a	$1$	$0$	$-2048$	$-505908$	$-90135570$	$6872255096$	$+$	$1$	$\mathrm{SU}(2)$	$q-2^{11}q^{2}-505908q^{3}+2^{22}q^{4}+\cdots$
3.20.a.a	$3$	$20$	3.a	1.a	$1$	$1$	$1$	$6.865$	$\Q$	None	✓	✓	✓	✓	3.20.a.a	$1$	$1$	$-1104$	$19683$	$3516270$	$-195590584$	$-$	$1$	$\mathrm{SU}(2)$	$q-1104q^{2}+3^{9}q^{3}+694528q^{4}+\cdots$
3.20.a.b	$3$	$20$	3.a	1.a	$1$	$2$	$2$	$6.865$	$\Q(\sqrt{87481})$	None	✓	✓	✓	✓	3.20.a.b	$1$	$0$	$702$	$-39366$	$6016140$	$113892064$	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	$q+(351-\beta )q^{2}-3^{9}q^{3}+(386242-702\beta )q^{4}+\cdots$
4.18.a.a	$4$	$18$	4.a	1.a	$1$	$2$	$2$	$7.329$	$\Q(\sqrt{9361})$	None	✓	✓	✓	✓	4.18.a.a	$1$	$0$	$0$	$-5880$	$604044$	$25350160$	$-$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	$q+(-2940-\beta )q^{3}+(302022+6^{2}\beta )q^{5}+\cdots$
3.21.b.a	$3$	$21$	3.b	3.b	$2$	$6$	$6$	$7.605$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		✓	✓	✓	3.21.b.a	$2$	$0$	$0$	$-4122$	$0$	$559607916$		$2^{14}\cdot 3^{19}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-687+11\beta _{1}+\beta _{2})q^{3}+\cdots$
2.26.a.a	$2$	$26$	2.a	1.a	$1$	$1$	$1$	$7.920$	$\Q$	None	✓	✓	✓	✓	2.26.a.a	$1$	$1$	$-4096$	$97956$	$341005350$	$-40882637368$	$+$	$1$	$\mathrm{SU}(2)$	$q-2^{12}q^{2}+97956q^{3}+2^{24}q^{4}+341005350q^{5}+\cdots$
2.26.a.b	$2$	$26$	2.a	1.a	$1$	$2$	$2$	$7.920$	$\Q(\sqrt{106705})$	None	✓	✓	✓	✓	2.26.a.b	$1$	$0$	$8192$	$379848$	$741953100$	$-376536944$	$-$	$2^{7}\cdot 3\cdot 5^{2}$	$\mathrm{SU}(2)$	$q+2^{12}q^{2}+(189924-\beta )q^{3}+2^{24}q^{4}+\cdots$
5.17.c.a	$5$	$17$	5.c	5.c	$4$	$14$	$7$	$8.116$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None		✓	✓	✓	5.17.c.a	$2$	$0$	$-2$	$7908$	$192880$	$-386452$		$2^{34}\cdot 3^{10}\cdot 5^{18}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{2}q^{2}+(565-3\beta _{1}-565\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots$
4.19.b.a	$4$	$19$	4.b	4.b	$2$	$8$	$8$	$8.215$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓	✓	✓	4.19.b.a	$2$	$0$	$84$	$0$	$860880$	$0$		$2^{56}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+(11-\beta _{1})q^{2}-\beta _{2}q^{3}+(44007-9\beta _{1}+\cdots)q^{4}+\cdots$
3.22.a.a	$3$	$22$	3.a	1.a	$1$	$1$	$1$	$8.384$	$\Q$	None	✓	✓			3.22.a.a	$1$	$1$	$-2844$	$-59049$	$3109950$	$363303920$	$+$	$1$	$\mathrm{SU}(2)$	$q-2844q^{2}-3^{10}q^{3}+5991184q^{4}+\cdots$
3.22.a.b	$3$	$22$	3.a	1.a	$1$	$1$	$1$	$8.384$	$\Q$	None	✓	✓			3.22.a.b	$1$	$1$	$1728$	$-59049$	$-41512770$	$538429808$	$+$	$1$	$\mathrm{SU}(2)$	$q+12^{3}q^{2}-3^{10}q^{3}+888832q^{4}+\cdots$
3.22.a.c	$3$	$22$	3.a	1.a	$1$	$2$	$2$	$8.384$	$\Q(\sqrt{649})$	None	✓	✓	✓	✓	3.22.a.c	$1$	$0$	$666$	$118098$	$996876$	$679896112$	$-$	$2\cdot 3^{2}\cdot 7$	$\mathrm{SU}(2)$	$q+(333-\beta )q^{2}+3^{10}q^{3}+(589618+\cdots)q^{4}+\cdots$
4.20.a.a	$4$	$20$	4.a	1.a	$1$	$1$	$1$	$9.153$	$\Q$	None	✓	✓	✓	✓	4.20.a.a	$1$	$1$	$0$	$-36$	$-196290$	$-35905576$	$-$	$1$	$\mathrm{SU}(2)$	$q-6^{2}q^{3}-196290q^{5}-35905576q^{7}+\cdots$
5.18.a.a	$5$	$18$	5.a	1.a	$1$	$2$	$2$	$9.161$	$\Q(\sqrt{39})$	None	✓	✓	✓	✓	5.18.a.a	$1$	$1$	$680$	$-10980$	$-781250$	$-22820700$	$+$	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)$	$q+(340+\beta )q^{2}+(-5490-52\beta )q^{3}+\cdots$
5.18.a.b	$5$	$18$	5.a	1.a	$1$	$3$	$3$	$9.161$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	✓	✓	✓	5.18.a.b	$1$	$0$	$118$	$15944$	$1171875$	$2139308$	$-$	$2^{3}\cdot 5$	$\mathrm{SU}(2)$	$q+(39-\beta _{1})q^{2}+(5317+8\beta _{1}+\beta _{2})q^{3}+\cdots$
5.18.b.a	$5$	$18$	5.b	5.b	$2$	$8$	$8$	$9.161$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		✓	✓	✓	5.18.b.a	$2$	$0$	$0$	$0$	$379200$	$0$		$2^{21}\cdot 3^{8}\cdot 5^{12}\cdot 11$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-72387+\beta _{3}+\cdots)q^{4}+\cdots$
3.23.b.a	$3$	$23$	3.b	3.b	$2$	$6$	$6$	$9.201$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		✓	✓	✓	3.23.b.a	$2$	$0$	$0$	$86670$	$0$	$-3447063060$		$2^{21}\cdot 3^{22}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(14445-8\beta _{1}+\beta _{2})q^{3}+\cdots$
2.28.a.a	$2$	$28$	2.a	1.a	$1$	$1$	$1$	$9.237$	$\Q$	None	✓	✓	✓	✓	2.28.a.a	$1$	$0$	$-8192$	$3984828$	$-2851889250$	$368721063704$	$+$	$1$	$\mathrm{SU}(2)$	$q-2^{13}q^{2}+3984828q^{3}+2^{26}q^{4}+\cdots$
2.28.a.b	$2$	$28$	2.a	1.a	$1$	$1$	$1$	$9.237$	$\Q$	None	✓	✓	✓	✓	2.28.a.b	$1$	$1$	$8192$	$-1016388$	$-3341197410$	$-51021361384$	$-$	$1$	$\mathrm{SU}(2)$	$q+2^{13}q^{2}-1016388q^{3}+2^{26}q^{4}+\cdots$
6.17.b.a	$6$	$17$	6.b	3.b	$2$	$6$	$6$	$9.739$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		✓	✓	✓	6.17.b.a	$2$	$0$	$0$	$6006$	$0$	$-167892$		$2^{27}\cdot 3^{13}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(1001+\beta _{1}-\beta _{2})q^{3}-2^{15}q^{4}+\cdots$
3.24.a.a	$3$	$24$	3.a	1.a	$1$	$1$	$1$	$10.056$	$\Q$	None	✓	✓	✓	✓	3.24.a.a	$1$	$1$	$1128$	$177147$	$-48863730$	$-1723688680$	$-$	$1$	$\mathrm{SU}(2)$	$q+1128q^{2}+3^{11}q^{3}-7116224q^{4}+\cdots$
3.24.a.b	$3$	$24$	3.a	1.a	$1$	$2$	$2$	$10.056$	$\Q(\sqrt{530401})$	None	✓	✓	✓	✓	3.24.a.b	$1$	$0$	$-1242$	$-354294$	$-46808820$	$-211963904$	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	$q+(-621-\beta )q^{2}-3^{11}q^{3}+(-3229358+\cdots)q^{4}+\cdots$
4.21.b.a	$4$	$21$	4.b	4.b	$2$	$1$	$1$	$10.141$	$\Q$	$\Q(\sqrt{-1})$	✓	✓			4.21.b.a	$2$	$0$	$-1024$	$0$	$-19306574$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2^{10}q^{2}+2^{20}q^{4}-19306574q^{5}+\cdots$
4.21.b.b	$4$	$21$	4.b	4.b	$2$	$8$	$8$	$10.141$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓	✓		4.21.b.b	$2$	$0$	$396$	$0$	$18568080$	$0$		$2^{56}\cdot 3^{5}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(7^{2}+\beta _{1})q^{2}+(6-12\beta _{1}-\beta _{2})q^{3}+\cdots$
5.19.c.a	$5$	$19$	5.c	5.c	$4$	$16$	$8$	$10.269$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓	✓	✓	5.19.c.a	$2$	$0$	$510$	$-20130$	$3145170$	$78767350$		$2^{39}\cdot 3^{12}\cdot 5^{25}$	$\mathrm{SU}(2)[C_{4}]$	$q+(2^{5}+\beta _{2}+2^{5}\beta _{4})q^{2}+(-1259-5\beta _{1}+\cdots)q^{3}+\cdots$
2.30.a.a	$2$	$30$	2.a	1.a	$1$	$1$	$1$	$10.656$	$\Q$	None	✓	✓	✓	✓	2.30.a.a	$1$	$1$	$-16384$	$-2792556$	$6651856470$	$14\!\cdots\!48$	$+$	$1$	$\mathrm{SU}(2)$	$q-2^{14}q^{2}-2792556q^{3}+2^{28}q^{4}+\cdots$
2.30.a.b	$2$	$30$	2.a	1.a	$1$	$1$	$1$	$10.656$	$\Q$	None	✓	✓	✓	✓	2.30.a.b	$1$	$0$	$16384$	$4782996$	$6065841750$	$904018883432$	$-$	$1$	$\mathrm{SU}(2)$	$q+2^{14}q^{2}+4782996q^{3}+2^{28}q^{4}+\cdots$
3.25.b.a	$3$	$25$	3.b	3.b	$2$	$1$	$1$	$10.949$	$\Q$	$\Q(\sqrt{-3})$	✓	✓			3.25.b.a	$2$	$0$	$0$	$531441$	$0$	$-4119710398$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+3^{12}q^{3}+2^{24}q^{4}-4119710398q^{7}+\cdots$
3.25.b.b	$3$	$25$	3.b	3.b	$2$	$6$	$6$	$10.949$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		✓	✓		3.25.b.b	$2$	$0$	$0$	$-616842$	$0$	$1988064876$		$2^{13}\cdot 3^{24}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-102807+2^{4}\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
6.18.a.a	$6$	$18$	6.a	1.a	$1$	$1$	$1$	$10.993$	$\Q$	None	✓	✓	✓	✓	6.18.a.a	$1$	$1$	$-256$	$-6561$	$645150$	$3974432$	$+$	$1$	$\mathrm{SU}(2)$	$q-2^{8}q^{2}-3^{8}q^{3}+2^{16}q^{4}+645150q^{5}+\cdots$

  Download displayed columns for results to