Newform search results

Level	Weight	Analytic conductor	\(Nk^2\)	Dim.
Bad \(p\)	Char.	Primitive character	Character order	Coefficient field
Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank
Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 271 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
8.3.d.a	$8$	$3$	8.d	8.d	$2$	$1$	$1$	$0.218$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓	$2$	$0$	\(-2\)	\(-2\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2q^{2}-2q^{3}+4q^{4}+4q^{6}-8q^{8}+\cdots\)
8.4.a.a	$8$	$4$	8.a	1.a	$1$	$1$	$1$	$0.472$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-4\)	\(-2\)	\(24\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{3}-2q^{5}+24q^{7}-11q^{9}-44q^{11}+\cdots\)
8.4.b.a	$8$	$4$	8.b	8.b	$2$	$2$	$2$	$0.472$	\(\Q(\sqrt{-7}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(-16\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta )q^{2}+2\beta q^{3}+(-6+2\beta )q^{4}+\cdots\)
8.5.d.a	$8$	$5$	8.d	8.d	$2$	$1$	$1$	$0.827$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓	$2$	$0$	\(4\)	\(-14\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4q^{2}-14q^{3}+2^{4}q^{4}-56q^{6}+2^{6}q^{8}+\cdots\)
8.5.d.b	$8$	$5$	8.d	8.d	$2$	$2$	$2$	$0.827$	\(\Q(\sqrt{-15}) \)	None		$2$	$0$	\(-2\)	\(12\)	\(0\)	\(0\)		$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta )q^{2}+6q^{3}+(-14+2\beta )q^{4}+\cdots\)
8.6.a.a	$8$	$6$	8.a	1.a	$1$	$1$	$1$	$1.283$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(20\)	\(-74\)	\(-24\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+20q^{3}-74q^{5}-24q^{7}+157q^{9}+\cdots\)
8.6.b.a	$8$	$6$	8.b	8.b	$2$	$4$	$4$	$1.283$	4.0.218489.1	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(96\)		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(5+\cdots)q^{4}+\cdots\)
8.7.d.a	$8$	$7$	8.d	8.d	$2$	$1$	$1$	$1.840$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓	$2$	$0$	\(-8\)	\(46\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-8q^{2}+46q^{3}+2^{6}q^{4}-368q^{6}+\cdots\)
8.7.d.b	$8$	$7$	8.d	8.d	$2$	$4$	$4$	$1.840$	4.0.3803625.2	None		$2$	$0$	\(2\)	\(-48\)	\(0\)	\(0\)		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-13+2\beta _{1}+\beta _{2})q^{3}+(-12+\cdots)q^{4}+\cdots\)
8.8.a.a	$8$	$8$	8.a	1.a	$1$	$1$	$1$	$2.499$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-84\)	\(-82\)	\(-456\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-84q^{3}-82q^{5}-456q^{7}+4869q^{9}+\cdots\)
8.8.a.b	$8$	$8$	8.a	1.a	$1$	$1$	$1$	$2.499$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(44\)	\(430\)	\(-1224\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+44q^{3}+430q^{5}-1224q^{7}-251q^{9}+\cdots\)
8.8.b.a	$8$	$8$	8.b	8.b	$2$	$6$	$6$	$2.499$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		$2$	$0$	\(6\)	\(0\)	\(0\)	\(-688\)		$2^{15}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{1})q^{2}+\beta _{4}q^{3}+(19+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
8.9.d.a	$8$	$9$	8.d	8.d	$2$	$1$	$1$	$3.259$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓	$2$	$0$	\(16\)	\(34\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{4}q^{2}+34q^{3}+2^{8}q^{4}+544q^{6}+\cdots\)
8.9.d.b	$8$	$9$	8.d	8.d	$2$	$6$	$6$	$3.259$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		$2$	$0$	\(-14\)	\(-36\)	\(0\)	\(0\)		$2^{15}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2+\beta _{1})q^{2}+(-6-\beta _{1}-\beta _{2})q^{3}+\cdots\)
8.10.a.a	$8$	$10$	8.a	1.a	$1$	$1$	$1$	$4.120$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-60\)	\(-2074\)	\(-4344\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-60q^{3}-2074q^{5}-4344q^{7}-16083q^{9}+\cdots\)
8.10.a.b	$8$	$10$	8.a	1.a	$1$	$1$	$1$	$4.120$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(68\)	\(1510\)	\(10248\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+68q^{3}+1510q^{5}+10248q^{7}-15059q^{9}+\cdots\)
8.10.b.a	$8$	$10$	8.b	8.b	$2$	$8$	$8$	$4.120$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(-18\)	\(0\)	\(0\)	\(4800\)		$2^{28}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2-\beta _{1})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(-54+\cdots)q^{4}+\cdots\)
8.11.d.a	$8$	$11$	8.d	8.d	$2$	$1$	$1$	$5.083$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓	$2$	$0$	\(-32\)	\(-482\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{5}q^{2}-482q^{3}+2^{10}q^{4}+15424q^{6}+\cdots\)
8.11.d.b	$8$	$11$	8.d	8.d	$2$	$8$	$8$	$5.083$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(42\)	\(480\)	\(0\)	\(0\)		$2^{28}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(5-\beta _{1})q^{2}+(60+\beta _{1}+\beta _{2})q^{3}+(5^{2}+\cdots)q^{4}+\cdots\)
8.12.a.a	$8$	$12$	8.a	1.a	$1$	$1$	$1$	$6.147$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-36\)	\(-3490\)	\(-55464\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-6^{2}q^{3}-3490q^{5}-55464q^{7}-175851q^{9}+\cdots\)
8.12.a.b	$8$	$12$	8.a	1.a	$1$	$2$	$2$	$6.147$	\(\Q(\sqrt{109}) \)	None	✓	$1$	$0$	\(0\)	\(56\)	\(7868\)	\(91056\)	$+$	$2^{7}$	$\mathrm{SU}(2)$	\(q+(28+\beta )q^{3}+(3934-12\beta )q^{5}+(45528+\cdots)q^{7}+\cdots\)
8.12.b.a	$8$	$12$	8.b	8.b	$2$	$10$	$10$	$6.147$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(22\)	\(0\)	\(0\)	\(-33616\)		$2^{45}\cdot 3^{2}\cdot 7$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2+\beta _{1})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(43+2\beta _{1}+\cdots)q^{4}+\cdots\)
8.13.d.a	$8$	$13$	8.d	8.d	$2$	$1$	$1$	$7.312$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓	$2$	$0$	\(64\)	\(658\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{6}q^{2}+658q^{3}+2^{12}q^{4}+42112q^{6}+\cdots\)
8.13.d.b	$8$	$13$	8.d	8.d	$2$	$10$	$10$	$7.312$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(-110\)	\(-660\)	\(0\)	\(0\)		$2^{45}\cdot 3^{3}\cdot 23$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-11-\beta _{1})q^{2}+(-66+3\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
8.14.a.a	$8$	$14$	8.a	1.a	$1$	$1$	$1$	$8.578$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-12\)	\(-4330\)	\(-139992\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-12q^{3}-4330q^{5}-139992q^{7}+\cdots\)
8.14.a.b	$8$	$14$	8.a	1.a	$1$	$2$	$2$	$8.578$	\(\Q(\sqrt{781}) \)	None	✓	$1$	$0$	\(0\)	\(872\)	\(18476\)	\(110928\)	$-$	$2^{7}$	$\mathrm{SU}(2)$	\(q+(436-\beta )q^{3}+(9238-12\beta )q^{5}+(55464+\cdots)q^{7}+\cdots\)
8.14.b.a	$8$	$14$	8.b	8.b	$2$	$2$	$2$	$8.578$	\(\Q(\sqrt{-79}) \)	None		$2$	$1$	\(-112\)	\(0\)	\(0\)	\(-351664\)		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-56-4\beta )q^{2}+129\beta q^{3}+(-1920+\cdots)q^{4}+\cdots\)
8.14.b.b	$8$	$14$	8.b	8.b	$2$	$10$	$10$	$8.578$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(110\)	\(0\)	\(0\)	\(586960\)		$2^{48}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(11+\beta _{1})q^{2}+(3\beta _{1}+\beta _{3})q^{3}+(-472+\cdots)q^{4}+\cdots\)
8.15.d.a	$8$	$15$	8.d	8.d	$2$	$1$	$1$	$9.946$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓	$2$	$0$	\(-128\)	\(3022\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{7}q^{2}+3022q^{3}+2^{14}q^{4}-386816q^{6}+\cdots\)
8.15.d.b	$8$	$15$	8.d	8.d	$2$	$12$	$12$	$9.946$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(218\)	\(-3024\)	\(0\)	\(0\)		$2^{66}\cdot 3^{6}\cdot 5^{2}\cdot 7$	$\mathrm{SU}(2)[C_{2}]$	\(q+(18+\beta _{1})q^{2}+(-252+3\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots\)
8.16.a.a	$8$	$16$	8.a	1.a	$1$	$1$	$1$	$11.415$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-3444\)	\(313358\)	\(-2324616\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-3444q^{3}+313358q^{5}-2324616q^{7}+\cdots\)
8.16.a.b	$8$	$16$	8.a	1.a	$1$	$1$	$1$	$11.415$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2700\)	\(-251890\)	\(1374072\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+2700q^{3}-251890q^{5}+1374072q^{7}+\cdots\)
8.16.a.c	$8$	$16$	8.a	1.a	$1$	$2$	$2$	$11.415$	\(\Q(\sqrt{58}) \)	None	✓	$1$	$0$	\(0\)	\(-4072\)	\(-140260\)	\(126192\)	$+$	$2^{7}\cdot 5$	$\mathrm{SU}(2)$	\(q+(-2036+\beta )q^{3}+(-70130+6^{2}\beta )q^{5}+\cdots\)
8.16.b.a	$8$	$16$	8.b	8.b	$2$	$14$	$14$	$11.415$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(-90\)	\(0\)	\(0\)	\(-1647088\)		$2^{91}\cdot 3^{6}\cdot 5^{4}\cdot 31^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-6-\beta _{1})q^{2}+\beta _{2}q^{3}+(3672+5\beta _{1}+\cdots)q^{4}+\cdots\)
8.17.d.a	$8$	$17$	8.d	8.d	$2$	$1$	$1$	$12.986$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓	$2$	$0$	\(256\)	\(-11966\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{8}q^{2}-11966q^{3}+2^{16}q^{4}-3063296q^{6}+\cdots\)
8.17.d.b	$8$	$17$	8.d	8.d	$2$	$14$	$14$	$12.986$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(-350\)	\(11964\)	\(0\)	\(0\)		$2^{91}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-5^{2}-\beta _{1})q^{2}+(855-6\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots\)
8.18.a.a	$8$	$18$	8.a	1.a	$1$	$2$	$2$	$14.658$	\(\Q(\sqrt{2146}) \)	None	✓	$1$	$0$	\(0\)	\(-952\)	\(-53620\)	\(-333168\)	$-$	$2^{8}$	$\mathrm{SU}(2)$	\(q+(-476+\beta )q^{3}+(-26810+60\beta )q^{5}+\cdots\)
8.18.a.b	$8$	$18$	8.a	1.a	$1$	$2$	$2$	$14.658$	\(\Q(\sqrt{114}) \)	None	✓	$1$	$1$	\(0\)	\(11592\)	\(-791924\)	\(-18932592\)	$+$	$2^{7}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(5796+\beta )q^{3}+(-395962-68\beta )q^{5}+\cdots\)
8.18.b.a	$8$	$18$	8.b	8.b	$2$	$16$	$16$	$14.658$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(270\)	\(0\)	\(0\)	\(11529600\)		$2^{120}\cdot 3^{14}\cdot 7$	$\mathrm{SU}(2)[C_{2}]$	\(q+(17-\beta _{1})q^{2}+(3\beta _{1}-\beta _{2})q^{3}+(-1712+\cdots)q^{4}+\cdots\)
8.19.d.a	$8$	$19$	8.d	8.d	$2$	$1$	$1$	$16.431$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓	$2$	$0$	\(-512\)	\(-3266\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{9}q^{2}-3266q^{3}+2^{18}q^{4}+1672192q^{6}+\cdots\)
8.19.d.b	$8$	$19$	8.d	8.d	$2$	$16$	$16$	$16.431$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(426\)	\(3264\)	\(0\)	\(0\)		$2^{120}\cdot 3^{13}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(3^{3}+\beta _{1})q^{2}+(203-4\beta _{1}-\beta _{2})q^{3}+\cdots\)
8.20.a.a	$8$	$20$	8.a	1.a	$1$	$2$	$2$	$18.305$	\(\Q(\sqrt{1453}) \)	None	✓	$1$	$1$	\(0\)	\(-27912\)	\(1226620\)	\(88510512\)	$-$	$2^{7}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q+(-13956-\beta )q^{3}+(613310+44\beta )q^{5}+\cdots\)
8.20.a.b	$8$	$20$	8.a	1.a	$1$	$3$	$3$	$18.305$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(23732\)	\(2140218\)	\(55851720\)	$+$	$2^{21}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(7911-\beta _{1})q^{3}+(713429-70\beta _{1}+\cdots)q^{5}+\cdots\)
8.20.b.a	$8$	$20$	8.b	8.b	$2$	$18$	$18$	$18.305$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(-458\)	\(0\)	\(0\)	\(-80707216\)		$2^{153}\cdot 3^{16}\cdot 5^{4}\cdot 7$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-5^{2}+\beta _{1})q^{2}+(2+5\beta _{1}-\beta _{2})q^{3}+\cdots\)
8.21.d.a	$8$	$21$	8.d	8.d	$2$	$1$	$1$	$20.281$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓	$2$	$0$	\(1024\)	\(114226\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{10}q^{2}+114226q^{3}+2^{20}q^{4}+\cdots\)
8.21.d.b	$8$	$21$	8.d	8.d	$2$	$18$	$18$	$20.281$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(-398\)	\(-114228\)	\(0\)	\(0\)		$2^{153}\cdot 3^{15}\cdot 5^{4}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-22+\beta _{1})q^{2}+(-6347-5\beta _{1}+\cdots)q^{3}+\cdots\)
8.22.a.a	$8$	$22$	8.a	1.a	$1$	$2$	$2$	$22.358$	\(\Q(\sqrt{358549}) \)	None	✓	$1$	$1$	\(0\)	\(-105432\)	\(2108140\)	\(444771792\)	$+$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	\(q+(-52716-\beta )q^{3}+(1054070+20\beta )q^{5}+\cdots\)
8.22.a.b	$8$	$22$	8.a	1.a	$1$	$3$	$3$	$22.358$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(96764\)	\(-24111774\)	\(295988280\)	$-$	$2^{21}\cdot 3\cdot 5\cdot 7$	$\mathrm{SU}(2)$	\(q+(32255-\beta _{1})q^{3}+(-8037261+9\beta _{1}+\cdots)q^{5}+\cdots\)
8.22.b.a	$8$	$22$	8.b	8.b	$2$	$20$	$20$	$22.358$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(286\)	\(0\)	\(0\)	\(564950496\)		$2^{190}\cdot 3^{14}\cdot 5^{4}\cdot 7^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(14-\beta _{1})q^{2}+(1+3\beta _{1}-\beta _{2})q^{3}+\cdots\)
8.23.d.a	$8$	$23$	8.d	8.d	$2$	$1$	$1$	$24.537$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓	$2$	$0$	\(-2048\)	\(-199058\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{11}q^{2}-199058q^{3}+2^{22}q^{4}+\cdots\)