Newform search results

Results (1-50 of 191 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4.5.b.a	$4$	$5$	4.b	4.b	$2$	$1$	$1$	$0.413$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(-4\)	\(0\)	\(-14\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-4q^{2}+2^{4}q^{4}-14q^{5}-2^{6}q^{8}+3^{4}q^{9}+\cdots\)
4.6.a.a	$4$	$6$	4.a	1.a	$1$	$1$	$1$	$0.642$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-12\)	\(54\)	\(-88\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-12q^{3}+54q^{5}-88q^{7}-99q^{9}+\cdots\)
4.7.b.a	$4$	$7$	4.b	4.b	$2$	$2$	$2$	$0.920$	\(\Q(\sqrt{-15}) \)	None		$2$	$0$	\(4\)	\(0\)	\(20\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2+\beta )q^{2}-4\beta q^{3}+(-56+4\beta )q^{4}+\cdots\)
4.9.b.a	$4$	$9$	4.b	4.b	$2$	$1$	$1$	$1.630$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(16\)	\(0\)	\(-1054\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{4}q^{2}+2^{8}q^{4}-1054q^{5}+2^{12}q^{8}+\cdots\)
4.9.b.b	$4$	$9$	4.b	4.b	$2$	$2$	$2$	$1.630$	\(\Q(\sqrt{-39}) \)	None		$2$	$0$	\(-20\)	\(0\)	\(1220\)	\(0\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-10-\beta )q^{2}-8\beta q^{3}+(-56+20\beta )q^{4}+\cdots\)
4.10.a.a	$4$	$10$	4.a	1.a	$1$	$1$	$1$	$2.060$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(228\)	\(-666\)	\(-6328\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+228q^{3}-666q^{5}-6328q^{7}+32301q^{9}+\cdots\)
4.11.b.a	$4$	$11$	4.b	4.b	$2$	$4$	$4$	$2.541$	4.0.26777625.2	None		$2$	$0$	\(-12\)	\(0\)	\(-1560\)	\(0\)		$2^{12}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-3+\beta _{1})q^{2}+(-2\beta _{1}+\beta _{2})q^{3}+\cdots\)
4.12.a.a	$4$	$12$	4.a	1.a	$1$	$1$	$1$	$3.073$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-516\)	\(-10530\)	\(49304\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-516q^{3}-10530q^{5}+49304q^{7}+\cdots\)
4.13.b.a	$4$	$13$	4.b	4.b	$2$	$1$	$1$	$3.656$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(-64\)	\(0\)	\(23506\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{6}q^{2}+2^{12}q^{4}+23506q^{5}-2^{18}q^{8}+\cdots\)
4.13.b.b	$4$	$13$	4.b	4.b	$2$	$4$	$4$	$3.656$	4.0.8546467905.1	None		$2$	$0$	\(108\)	\(0\)	\(-18360\)	\(0\)		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(3^{3}+\beta _{1})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(-380+\cdots)q^{4}+\cdots\)
4.14.a.a	$4$	$14$	4.a	1.a	$1$	$1$	$1$	$4.289$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(468\)	\(56214\)	\(333032\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+468q^{3}+56214q^{5}+333032q^{7}+\cdots\)
4.15.b.a	$4$	$15$	4.b	4.b	$2$	$6$	$6$	$4.973$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		$2$	$0$	\(-92\)	\(0\)	\(8060\)	\(0\)		$2^{30}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-15+\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{3}+\cdots\)
4.16.a.a	$4$	$16$	4.a	1.a	$1$	$1$	$1$	$5.708$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-276\)	\(-132210\)	\(-3585736\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-276q^{3}-132210q^{5}-3585736q^{7}+\cdots\)
4.17.b.a	$4$	$17$	4.b	4.b	$2$	$1$	$1$	$6.493$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(256\)	\(0\)	\(329666\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{8}q^{2}+2^{16}q^{4}+329666q^{5}+2^{24}q^{8}+\cdots\)
4.17.b.b	$4$	$17$	4.b	4.b	$2$	$6$	$6$	$6.493$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		$2$	$0$	\(-164\)	\(0\)	\(-506740\)	\(0\)		$2^{30}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-3^{3}-\beta _{1})q^{2}+(1-3\beta _{1}+\beta _{2})q^{3}+\cdots\)
4.18.a.a	$4$	$18$	4.a	1.a	$1$	$2$	$2$	$7.329$	\(\Q(\sqrt{9361}) \)	None	✓	$1$	$0$	\(0\)	\(-5880\)	\(604044\)	\(25350160\)	$-$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	\(q+(-2940-\beta )q^{3}+(302022+6^{2}\beta )q^{5}+\cdots\)
4.19.b.a	$4$	$19$	4.b	4.b	$2$	$8$	$8$	$8.215$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(84\)	\(0\)	\(860880\)	\(0\)		$2^{56}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(11-\beta _{1})q^{2}-\beta _{2}q^{3}+(44007-9\beta _{1}+\cdots)q^{4}+\cdots\)
4.20.a.a	$4$	$20$	4.a	1.a	$1$	$1$	$1$	$9.153$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-36\)	\(-196290\)	\(-35905576\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-6^{2}q^{3}-196290q^{5}-35905576q^{7}+\cdots\)
4.21.b.a	$4$	$21$	4.b	4.b	$2$	$1$	$1$	$10.141$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(-1024\)	\(0\)	\(-19306574\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{10}q^{2}+2^{20}q^{4}-19306574q^{5}+\cdots\)
4.21.b.b	$4$	$21$	4.b	4.b	$2$	$8$	$8$	$10.141$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(396\)	\(0\)	\(18568080\)	\(0\)		$2^{56}\cdot 3^{5}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(7^{2}+\beta _{1})q^{2}+(6-12\beta _{1}-\beta _{2})q^{3}+\cdots\)
4.22.a.a	$4$	$22$	4.a	1.a	$1$	$2$	$2$	$11.179$	\(\Q(\sqrt{2161}) \)	None	✓	$1$	$0$	\(0\)	\(65640\)	\(13689324\)	\(-260508080\)	$-$	$2^{8}\cdot 3\cdot 7$	$\mathrm{SU}(2)$	\(q+(32820-\beta )q^{3}+(6844662-204\beta )q^{5}+\cdots\)
4.23.b.a	$4$	$23$	4.b	4.b	$2$	$10$	$10$	$12.268$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(1540\)	\(0\)	\(-17091100\)	\(0\)		$2^{90}\cdot 3^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(154-\beta _{1})q^{2}+(-19\beta _{1}-\beta _{2})q^{3}+\cdots\)
4.24.a.a	$4$	$24$	4.a	1.a	$1$	$2$	$2$	$13.408$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(170520\)	\(-92266020\)	\(192083440\)	$-$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	\(q+(85260-\beta )q^{3}+(-46133010+540\beta )q^{5}+\cdots\)
4.25.b.a	$4$	$25$	4.b	4.b	$2$	$1$	$1$	$14.599$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(4096\)	\(0\)	\(64250786\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{12}q^{2}+2^{24}q^{4}+64250786q^{5}+\cdots\)
4.25.b.b	$4$	$25$	4.b	4.b	$2$	$10$	$10$	$14.599$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(-6212\)	\(0\)	\(56758100\)	\(0\)		$2^{90}\cdot 3^{8}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-621+\beta _{1})q^{2}+(-3-15\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
4.26.a.a	$4$	$26$	4.a	1.a	$1$	$2$	$2$	$15.840$	\(\Q(\sqrt{358121}) \)	None	✓	$1$	$0$	\(0\)	\(-899640\)	\(-399350196\)	\(-40518462320\)	$-$	$2^{7}\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q+(-449820-\beta )q^{3}+(-199675098+\cdots)q^{5}+\cdots\)
4.27.b.a	$4$	$27$	4.b	4.b	$2$	$12$	$12$	$17.132$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(180\)	\(0\)	\(-298775880\)	\(0\)		$2^{132}\cdot 3^{17}\cdot 5^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(15-\beta _{1})q^{2}-\beta _{2}q^{3}+(-1879252+\cdots)q^{4}+\cdots\)
4.28.a.a	$4$	$28$	4.a	1.a	$1$	$2$	$2$	$18.474$	\(\Q(\sqrt{1059289}) \)	None	✓	$1$	$1$	\(0\)	\(-483720\)	\(145079100\)	\(60475251760\)	$-$	$2^{8}\cdot 3\cdot 7$	$\mathrm{SU}(2)$	\(q+(-241860-\beta )q^{3}+(72539550+\cdots)q^{5}+\cdots\)
4.29.b.a	$4$	$29$	4.b	4.b	$2$	$1$	$1$	$19.867$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(-16384\)	\(0\)	\(11167097746\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{14}q^{2}+2^{28}q^{4}+11167097746q^{5}+\cdots\)
4.29.b.b	$4$	$29$	4.b	4.b	$2$	$12$	$12$	$19.867$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(24300\)	\(0\)	\(-12399664680\)	\(0\)		$2^{132}\cdot 3^{15}\cdot 5^{2}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(45^{2}+\beta _{1})q^{2}+(-6\beta _{1}+\beta _{2})q^{3}+\cdots\)
4.30.a.a	$4$	$30$	4.a	1.a	$1$	$3$	$3$	$21.311$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(6139068\)	\(13945023234\)	\(360544308792\)	$-$	$2^{24}\cdot 3^{5}\cdot 7^{2}\cdot 23$	$\mathrm{SU}(2)$	\(q+(2046356-\beta _{1})q^{3}+(4648341078+\cdots)q^{5}+\cdots\)
4.31.b.a	$4$	$31$	4.b	4.b	$2$	$14$	$14$	$22.806$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(-24476\)	\(0\)	\(14864798540\)	\(0\)		$2^{182}\cdot 3^{19}\cdot 5^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1748+\beta _{1})q^{2}+(9+30\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
4.32.a.a	$4$	$32$	4.a	1.a	$1$	$2$	$2$	$24.351$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-31205160\)	\(1872305820\)	\(60\!\cdots\!80\)	$-$	$2^{7}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(-15602580-\beta )q^{3}+(936152910+\cdots)q^{5}+\cdots\)
4.33.b.a	$4$	$33$	4.b	4.b	$2$	$1$	$1$	$25.947$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(65536\)	\(0\)	\(-196496109694\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{16}q^{2}+2^{32}q^{4}-196496109694q^{5}+\cdots\)
4.33.b.b	$4$	$33$	4.b	4.b	$2$	$14$	$14$	$25.947$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(-23780\)	\(0\)	\(138121491740\)	\(0\)		$2^{182}\cdot 3^{20}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1699+\beta _{1})q^{2}+(9-21\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
4.34.a.a	$4$	$34$	4.a	1.a	$1$	$3$	$3$	$27.593$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(92491788\)	\(-53880683886\)	\(45\!\cdots\!92\)	$-$	$2^{22}\cdot 3^{3}\cdot 7\cdot 11\cdot 29$	$\mathrm{SU}(2)$	\(q+(30830596+\beta _{1})q^{3}+(-17960227962+\cdots)q^{5}+\cdots\)
4.35.b.a	$4$	$35$	4.b	4.b	$2$	$16$	$16$	$29.290$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(-27372\)	\(0\)	\(-21372255840\)	\(0\)		$2^{240}\cdot 3^{26}\cdot 5^{6}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1711+\beta _{1})q^{2}+(19-76\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
4.36.a.a	$4$	$36$	4.a	1.a	$1$	$3$	$3$	$31.038$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(50908884\)	\(280720890\)	\(-55\!\cdots\!16\)	$-$	$2^{24}\cdot 3^{4}\cdot 5\cdot 7$	$\mathrm{SU}(2)$	\(q+(16969628+\beta _{1})q^{3}+(93573630+\cdots)q^{5}+\cdots\)
4.37.b.a	$4$	$37$	4.b	4.b	$2$	$1$	$1$	$32.837$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(-262144\)	\(0\)	\(-42\!\cdots\!34\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{18}q^{2}+2^{36}q^{4}-4228490555534q^{5}+\cdots\)
4.37.b.b	$4$	$37$	4.b	4.b	$2$	$16$	$16$	$32.837$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(177228\)	\(0\)	\(58\!\cdots\!60\)	\(0\)		$2^{240}\cdot 3^{24}\cdot 5^{6}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(11077+\beta _{1})q^{2}+(50+198\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
4.38.a.a	$4$	$38$	4.a	1.a	$1$	$3$	$3$	$34.686$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-272163492\)	\(36\!\cdots\!94\)	\(15\!\cdots\!92\)	$-$	$2^{24}\cdot 3^{5}\cdot 7$	$\mathrm{SU}(2)$	\(q+(-90721164-\beta _{1})q^{3}+(1213681705398+\cdots)q^{5}+\cdots\)
4.39.b.a	$4$	$39$	4.b	4.b	$2$	$18$	$18$	$36.585$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(364228\)	\(0\)	\(-89\!\cdots\!20\)	\(0\)		$2^{306}\cdot 3^{34}\cdot 5^{10}\cdot 19^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(20235-\beta _{1})q^{2}+(-18+165\beta _{1}+\cdots)q^{3}+\cdots\)
4.40.a.a	$4$	$40$	4.a	1.a	$1$	$3$	$3$	$38.536$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-1269987036\)	\(-81\!\cdots\!90\)	\(26\!\cdots\!24\)	$-$	$2^{22}\cdot 3^{3}\cdot 5\cdot 7\cdot 13$	$\mathrm{SU}(2)$	\(q+(-423329012+\beta _{1})q^{3}+(-27008612411730+\cdots)q^{5}+\cdots\)
4.41.b.a	$4$	$41$	4.b	4.b	$2$	$1$	$1$	$40.537$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(1048576\)	\(0\)	\(18\!\cdots\!26\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{20}q^{2}+2^{40}q^{4}+182008936336226q^{5}+\cdots\)
4.41.b.b	$4$	$41$	4.b	4.b	$2$	$18$	$18$	$40.537$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(-1801604\)	\(0\)	\(-16\!\cdots\!20\)	\(0\)		$2^{306}\cdot 3^{36}\cdot 5^{8}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-100089-\beta _{1})q^{2}+(4-6^{2}\beta _{1}+\cdots)q^{3}+\cdots\)
4.42.a.a	$4$	$42$	4.a	1.a	$1$	$4$	$4$	$42.589$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(1162346640\)	\(22\!\cdots\!24\)	\(-40\!\cdots\!80\)	$-$	$2^{45}\cdot 3^{8}\cdot 5\cdot 7$	$\mathrm{SU}(2)$	\(q+(290586660-\beta _{1})q^{3}+(55732604152806+\cdots)q^{5}+\cdots\)
4.43.b.a	$4$	$43$	4.b	4.b	$2$	$20$	$20$	$44.691$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(802164\)	\(0\)	\(13\!\cdots\!00\)	\(0\)		$2^{380}\cdot 3^{41}\cdot 5^{10}\cdot 7^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(40108+\beta _{1})q^{2}+(2^{4}-78\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
4.44.a.a	$4$	$44$	4.a	1.a	$1$	$3$	$3$	$46.844$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(7902569844\)	\(29\!\cdots\!30\)	\(-25\!\cdots\!36\)	$-$	$2^{24}\cdot 3^{6}\cdot 5\cdot 7\cdot 11$	$\mathrm{SU}(2)$	\(q+(2634189948-\beta _{1})q^{3}+(9956588758110+\cdots)q^{5}+\cdots\)
4.45.b.a	$4$	$45$	4.b	4.b	$2$	$1$	$1$	$49.048$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(-4194304\)	\(0\)	\(94\!\cdots\!86\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{22}q^{2}+2^{44}q^{4}+94681488501586q^{5}+\cdots\)
4.45.b.b	$4$	$45$	4.b	4.b	$2$	$20$	$20$	$49.048$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(4799916\)	\(0\)	\(-12\!\cdots\!00\)	\(0\)		$2^{380}\cdot 3^{44}\cdot 5^{12}\cdot 7^{2}\cdot 11^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(239996+\beta _{1})q^{2}+(86+431\beta _{1}+\cdots)q^{3}+\cdots\)