Newform search results

Results (1-50 of 191 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4.5.b.a	$4$	$5$	4.b	4.b	$2$	$1$	$1$	$0.413$	$\Q$	$\Q(\sqrt{-1})$	✓	✓	✓	✓	4.5.b.a	$2$	$0$	$-4$	$0$	$-14$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-4q^{2}+2^{4}q^{4}-14q^{5}-2^{6}q^{8}+3^{4}q^{9}+\cdots$
4.6.a.a	$4$	$6$	4.a	1.a	$1$	$1$	$1$	$0.642$	$\Q$	None	✓	✓	✓	✓	4.6.a.a	$1$	$0$	$0$	$-12$	$54$	$-88$	$-$	$1$	$\mathrm{SU}(2)$	$q-12q^{3}+54q^{5}-88q^{7}-99q^{9}+\cdots$
4.7.b.a	$4$	$7$	4.b	4.b	$2$	$2$	$2$	$0.920$	$\Q(\sqrt{-15})$	None		✓	✓	✓	4.7.b.a	$2$	$0$	$4$	$0$	$20$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(2+\beta )q^{2}-4\beta q^{3}+(-56+4\beta )q^{4}+\cdots$
4.9.b.a	$4$	$9$	4.b	4.b	$2$	$1$	$1$	$1.630$	$\Q$	$\Q(\sqrt{-1})$	✓	✓			4.9.b.a	$2$	$0$	$16$	$0$	$-1054$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{4}q^{2}+2^{8}q^{4}-1054q^{5}+2^{12}q^{8}+\cdots$
4.9.b.b	$4$	$9$	4.b	4.b	$2$	$2$	$2$	$1.630$	$\Q(\sqrt{-39})$	None		✓	✓		4.9.b.b	$2$	$0$	$-20$	$0$	$1220$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-10-\beta )q^{2}-8\beta q^{3}+(-56+20\beta )q^{4}+\cdots$
4.10.a.a	$4$	$10$	4.a	1.a	$1$	$1$	$1$	$2.060$	$\Q$	None	✓	✓	✓	✓	4.10.a.a	$1$	$0$	$0$	$228$	$-666$	$-6328$	$-$	$1$	$\mathrm{SU}(2)$	$q+228q^{3}-666q^{5}-6328q^{7}+32301q^{9}+\cdots$
4.11.b.a	$4$	$11$	4.b	4.b	$2$	$4$	$4$	$2.541$	4.0.26777625.2	None		✓	✓	✓	4.11.b.a	$2$	$0$	$-12$	$0$	$-1560$	$0$		$2^{12}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+(-3+\beta _{1})q^{2}+(-2\beta _{1}+\beta _{2})q^{3}+\cdots$
4.12.a.a	$4$	$12$	4.a	1.a	$1$	$1$	$1$	$3.073$	$\Q$	None	✓	✓	✓	✓	4.12.a.a	$1$	$1$	$0$	$-516$	$-10530$	$49304$	$-$	$1$	$\mathrm{SU}(2)$	$q-516q^{3}-10530q^{5}+49304q^{7}+\cdots$
4.13.b.a	$4$	$13$	4.b	4.b	$2$	$1$	$1$	$3.656$	$\Q$	$\Q(\sqrt{-1})$	✓	✓			4.13.b.a	$2$	$0$	$-64$	$0$	$23506$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2^{6}q^{2}+2^{12}q^{4}+23506q^{5}-2^{18}q^{8}+\cdots$
4.13.b.b	$4$	$13$	4.b	4.b	$2$	$4$	$4$	$3.656$	4.0.8546467905.1	None		✓	✓		4.13.b.b	$2$	$0$	$108$	$0$	$-18360$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+(3^{3}+\beta _{1})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(-380+\cdots)q^{4}+\cdots$
4.14.a.a	$4$	$14$	4.a	1.a	$1$	$1$	$1$	$4.289$	$\Q$	None	✓	✓	✓	✓	4.14.a.a	$1$	$0$	$0$	$468$	$56214$	$333032$	$-$	$1$	$\mathrm{SU}(2)$	$q+468q^{3}+56214q^{5}+333032q^{7}+\cdots$
4.15.b.a	$4$	$15$	4.b	4.b	$2$	$6$	$6$	$4.973$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None		✓	✓	✓	4.15.b.a	$2$	$0$	$-92$	$0$	$8060$	$0$		$2^{30}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-15+\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{3}+\cdots$
4.16.a.a	$4$	$16$	4.a	1.a	$1$	$1$	$1$	$5.708$	$\Q$	None	✓	✓	✓	✓	4.16.a.a	$1$	$1$	$0$	$-276$	$-132210$	$-3585736$	$-$	$1$	$\mathrm{SU}(2)$	$q-276q^{3}-132210q^{5}-3585736q^{7}+\cdots$
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	$2$	$0$	$-164$	$0$	$-506740$	$0$		$2^{30}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-3^{3}-\beta _{1})q^{2}+(1-3\beta _{1}+\beta _{2})q^{3}+\cdots$
4.18.a.a	$4$	$18$	4.a	1.a	$1$	$2$	$2$	$7.329$	$\Q(\sqrt{9361})$	None	✓	✓	✓	✓	4.18.a.a	$1$	$0$	$0$	$-5880$	$604044$	$25350160$	$-$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	$q+(-2940-\beta )q^{3}+(302022+6^{2}\beta )q^{5}+\cdots$
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	$2$	$0$	$84$	$0$	$860880$	$0$		$2^{56}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+(11-\beta _{1})q^{2}-\beta _{2}q^{3}+(44007-9\beta _{1}+\cdots)q^{4}+\cdots$
4.20.a.a	$4$	$20$	4.a	1.a	$1$	$1$	$1$	$9.153$	$\Q$	None	✓	✓	✓	✓	4.20.a.a	$1$	$1$	$0$	$-36$	$-196290$	$-35905576$	$-$	$1$	$\mathrm{SU}(2)$	$q-6^{2}q^{3}-196290q^{5}-35905576q^{7}+\cdots$
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	$2$	$0$	$396$	$0$	$18568080$	$0$		$2^{56}\cdot 3^{5}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(7^{2}+\beta _{1})q^{2}+(6-12\beta _{1}-\beta _{2})q^{3}+\cdots$
4.22.a.a	$4$	$22$	4.a	1.a	$1$	$2$	$2$	$11.179$	$\Q(\sqrt{2161})$	None	✓	✓	✓	✓	4.22.a.a	$1$	$0$	$0$	$65640$	$13689324$	$-260508080$	$-$	$2^{8}\cdot 3\cdot 7$	$\mathrm{SU}(2)$	$q+(32820-\beta )q^{3}+(6844662-204\beta )q^{5}+\cdots$
4.23.b.a	$4$	$23$	4.b	4.b	$2$	$10$	$10$	$12.268$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		✓	✓	✓	4.23.b.a	$2$	$0$	$1540$	$0$	$-17091100$	$0$		$2^{90}\cdot 3^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q+(154-\beta _{1})q^{2}+(-19\beta _{1}-\beta _{2})q^{3}+\cdots$
4.24.a.a	$4$	$24$	4.a	1.a	$1$	$2$	$2$	$13.408$	$\mathbb{Q}[x]/(x^{2} - \cdots)$	None	✓	✓	✓	✓	4.24.a.a	$1$	$1$	$0$	$170520$	$-92266020$	$192083440$	$-$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	$q+(85260-\beta )q^{3}+(-46133010+540\beta )q^{5}+\cdots$
4.25.b.a	$4$	$25$	4.b	4.b	$2$	$1$	$1$	$14.599$	$\Q$	$\Q(\sqrt{-1})$	✓	✓			4.25.b.a	$2$	$0$	$4096$	$0$	$64250786$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{12}q^{2}+2^{24}q^{4}+64250786q^{5}+\cdots$
4.25.b.b	$4$	$25$	4.b	4.b	$2$	$10$	$10$	$14.599$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None		✓	✓		4.25.b.b	$2$	$0$	$-6212$	$0$	$56758100$	$0$		$2^{90}\cdot 3^{8}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-621+\beta _{1})q^{2}+(-3-15\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
4.26.a.a	$4$	$26$	4.a	1.a	$1$	$2$	$2$	$15.840$	$\Q(\sqrt{358121})$	None	✓	✓	✓	✓	4.26.a.a	$1$	$0$	$0$	$-899640$	$-399350196$	$-40518462320$	$-$	$2^{7}\cdot 3^{3}$	$\mathrm{SU}(2)$	$q+(-449820-\beta )q^{3}+(-199675098+\cdots)q^{5}+\cdots$
4.27.b.a	$4$	$27$	4.b	4.b	$2$	$12$	$12$	$17.132$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓	✓	✓	4.27.b.a	$2$	$0$	$180$	$0$	$-298775880$	$0$		$2^{132}\cdot 3^{17}\cdot 5^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+(15-\beta _{1})q^{2}-\beta _{2}q^{3}+(-1879252+\cdots)q^{4}+\cdots$
4.28.a.a	$4$	$28$	4.a	1.a	$1$	$2$	$2$	$18.474$	$\Q(\sqrt{1059289})$	None	✓	✓	✓	✓	4.28.a.a	$1$	$1$	$0$	$-483720$	$145079100$	$60475251760$	$-$	$2^{8}\cdot 3\cdot 7$	$\mathrm{SU}(2)$	$q+(-241860-\beta )q^{3}+(72539550+\cdots)q^{5}+\cdots$
4.29.b.a	$4$	$29$	4.b	4.b	$2$	$1$	$1$	$19.867$	$\Q$	$\Q(\sqrt{-1})$	✓	✓			4.29.b.a	$2$	$0$	$-16384$	$0$	$11167097746$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2^{14}q^{2}+2^{28}q^{4}+11167097746q^{5}+\cdots$
4.29.b.b	$4$	$29$	4.b	4.b	$2$	$12$	$12$	$19.867$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓	✓		4.29.b.b	$2$	$0$	$24300$	$0$	$-12399664680$	$0$		$2^{132}\cdot 3^{15}\cdot 5^{2}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(45^{2}+\beta _{1})q^{2}+(-6\beta _{1}+\beta _{2})q^{3}+\cdots$
4.30.a.a	$4$	$30$	4.a	1.a	$1$	$3$	$3$	$21.311$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	✓	✓	✓	4.30.a.a	$1$	$0$	$0$	$6139068$	$13945023234$	$360544308792$	$-$	$2^{24}\cdot 3^{5}\cdot 7^{2}\cdot 23$	$\mathrm{SU}(2)$	$q+(2046356-\beta _{1})q^{3}+(4648341078+\cdots)q^{5}+\cdots$
4.31.b.a	$4$	$31$	4.b	4.b	$2$	$14$	$14$	$22.806$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None		✓	✓	✓	4.31.b.a	$2$	$0$	$-24476$	$0$	$14864798540$	$0$		$2^{182}\cdot 3^{19}\cdot 5^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1748+\beta _{1})q^{2}+(9+30\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots$
4.32.a.a	$4$	$32$	4.a	1.a	$1$	$2$	$2$	$24.351$	$\mathbb{Q}[x]/(x^{2} - \cdots)$	None	✓	✓	✓	✓	4.32.a.a	$1$	$1$	$0$	$-31205160$	$1872305820$	$60\!\cdots\!80$	$-$	$2^{7}\cdot 3^{2}$	$\mathrm{SU}(2)$	$q+(-15602580-\beta )q^{3}+(936152910+\cdots)q^{5}+\cdots$
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	$2$	$0$	$-23780$	$0$	$138121491740$	$0$		$2^{182}\cdot 3^{20}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1699+\beta _{1})q^{2}+(9-21\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
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	$1$	$0$	$0$	$92491788$	$-53880683886$	$45\!\cdots\!92$	$-$	$2^{22}\cdot 3^{3}\cdot 7\cdot 11\cdot 29$	$\mathrm{SU}(2)$	$q+(30830596+\beta _{1})q^{3}+(-17960227962+\cdots)q^{5}+\cdots$
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	$2$	$0$	$-27372$	$0$	$-21372255840$	$0$		$2^{240}\cdot 3^{26}\cdot 5^{6}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1711+\beta _{1})q^{2}+(19-76\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots$
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	$1$	$1$	$0$	$50908884$	$280720890$	$-55\!\cdots\!16$	$-$	$2^{24}\cdot 3^{4}\cdot 5\cdot 7$	$\mathrm{SU}(2)$	$q+(16969628+\beta _{1})q^{3}+(93573630+\cdots)q^{5}+\cdots$
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	$2$	$0$	$177228$	$0$	$58\!\cdots\!60$	$0$		$2^{240}\cdot 3^{24}\cdot 5^{6}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(11077+\beta _{1})q^{2}+(50+198\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
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	$1$	$0$	$0$	$-272163492$	$36\!\cdots\!94$	$15\!\cdots\!92$	$-$	$2^{24}\cdot 3^{5}\cdot 7$	$\mathrm{SU}(2)$	$q+(-90721164-\beta _{1})q^{3}+(1213681705398+\cdots)q^{5}+\cdots$
4.39.b.a	$4$	$39$	4.b	4.b	$2$	$18$	$18$	$36.585$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		✓	✓	✓	4.39.b.a	$2$	$0$	$364228$	$0$	$-89\!\cdots\!20$	$0$		$2^{306}\cdot 3^{34}\cdot 5^{10}\cdot 19^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(20235-\beta _{1})q^{2}+(-18+165\beta _{1}+\cdots)q^{3}+\cdots$
4.40.a.a	$4$	$40$	4.a	1.a	$1$	$3$	$3$	$38.536$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	✓	✓	✓	4.40.a.a	$1$	$1$	$0$	$-1269987036$	$-81\!\cdots\!90$	$26\!\cdots\!24$	$-$	$2^{22}\cdot 3^{3}\cdot 5\cdot 7\cdot 13$	$\mathrm{SU}(2)$	$q+(-423329012+\beta _{1})q^{3}+(-27008612411730+\cdots)q^{5}+\cdots$
4.41.b.a	$4$	$41$	4.b	4.b	$2$	$1$	$1$	$40.537$	$\Q$	$\Q(\sqrt{-1})$	✓	✓			4.41.b.a	$2$	$0$	$1048576$	$0$	$18\!\cdots\!26$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2^{20}q^{2}+2^{40}q^{4}+182008936336226q^{5}+\cdots$
4.41.b.b	$4$	$41$	4.b	4.b	$2$	$18$	$18$	$40.537$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	None		✓	✓		4.41.b.b	$2$	$0$	$-1801604$	$0$	$-16\!\cdots\!20$	$0$		$2^{306}\cdot 3^{36}\cdot 5^{8}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-100089-\beta _{1})q^{2}+(4-6^{2}\beta _{1}+\cdots)q^{3}+\cdots$
4.42.a.a	$4$	$42$	4.a	1.a	$1$	$4$	$4$	$42.589$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	✓	✓	✓	4.42.a.a	$1$	$0$	$0$	$1162346640$	$22\!\cdots\!24$	$-40\!\cdots\!80$	$-$	$2^{45}\cdot 3^{8}\cdot 5\cdot 7$	$\mathrm{SU}(2)$	$q+(290586660-\beta _{1})q^{3}+(55732604152806+\cdots)q^{5}+\cdots$
4.43.b.a	$4$	$43$	4.b	4.b	$2$	$20$	$20$	$44.691$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓	✓	✓	4.43.b.a	$2$	$0$	$802164$	$0$	$13\!\cdots\!00$	$0$		$2^{380}\cdot 3^{41}\cdot 5^{10}\cdot 7^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+(40108+\beta _{1})q^{2}+(2^{4}-78\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots$
4.44.a.a	$4$	$44$	4.a	1.a	$1$	$3$	$3$	$46.844$	$\mathbb{Q}[x]/(x^{3} - \cdots)$	None	✓	✓	✓	✓	4.44.a.a	$1$	$1$	$0$	$7902569844$	$29\!\cdots\!30$	$-25\!\cdots\!36$	$-$	$2^{24}\cdot 3^{6}\cdot 5\cdot 7\cdot 11$	$\mathrm{SU}(2)$	$q+(2634189948-\beta _{1})q^{3}+(9956588758110+\cdots)q^{5}+\cdots$
4.45.b.a	$4$	$45$	4.b	4.b	$2$	$1$	$1$	$49.048$	$\Q$	$\Q(\sqrt{-1})$	✓	✓			4.45.b.a	$2$	$0$	$-4194304$	$0$	$94\!\cdots\!86$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2^{22}q^{2}+2^{44}q^{4}+94681488501586q^{5}+\cdots$
4.45.b.b	$4$	$45$	4.b	4.b	$2$	$20$	$20$	$49.048$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		✓	✓		4.45.b.b	$2$	$0$	$4799916$	$0$	$-12\!\cdots\!00$	$0$		$2^{380}\cdot 3^{44}\cdot 5^{12}\cdot 7^{2}\cdot 11^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(239996+\beta _{1})q^{2}+(86+431\beta _{1}+\cdots)q^{3}+\cdots$

  Download displayed columns for results to