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 364 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
9.3.d.a	$9$	$3$	9.d	9.d	$6$	$2$	$1$	$0.245$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-3\)	\(-3\)	\(6\)	\(-2\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
9.4.a.a	$9$	$4$	9.a	1.a	$1$	$1$	$1$	$0.531$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(20\)	$+$	$1$	$N(\mathrm{U}(1))$	\(q-8q^{4}+20q^{7}-70q^{13}+2^{6}q^{16}+\cdots\)
9.4.c.a	$9$	$4$	9.c	9.c	$3$	$4$	$2$	$0.531$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(-3\)	\(-3\)	\(-15\)	\(-7\)		$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
9.5.b.a	$9$	$5$	9.b	3.b	$2$	$2$	$2$	$0.930$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-56\)		$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-2q^{4}-7\beta q^{5}-28q^{7}+14\beta q^{8}+\cdots\)
9.5.d.a	$9$	$5$	9.d	9.d	$6$	$6$	$3$	$0.930$	6.0.39400128.1	None		$2$	$0$	\(-3\)	\(-3\)	\(-12\)	\(12\)		$3^{3}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{2}+(-3+\beta _{1}-3\beta _{3}+\beta _{4})q^{3}+\cdots\)
9.6.a.a	$9$	$6$	9.a	1.a	$1$	$1$	$1$	$1.443$	\(\Q\)	None	✓	$1$	$0$	\(6\)	\(0\)	\(-6\)	\(-40\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+6q^{2}+4q^{4}-6q^{5}-40q^{7}-168q^{8}+\cdots\)
9.6.c.a	$9$	$6$	9.c	9.c	$3$	$8$	$4$	$1.443$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(3\)	\(-12\)	\(78\)	\(28\)		$2^{2}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{1}+\beta _{4}+\beta _{5})q^{2}+(-3+3\beta _{1}+\cdots)q^{3}+\cdots\)
9.7.b.a	$9$	$7$	9.b	3.b	$2$	$2$	$2$	$2.070$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(1048\)		$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-98q^{4}+5\beta q^{5}+524q^{7}+\cdots\)
9.7.d.a	$9$	$7$	9.d	9.d	$6$	$10$	$5$	$2.070$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(-3\)	\(24\)	\(-219\)	\(-121\)		$2^{2}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{1}q^{2}+(2+\beta _{1}-\beta _{2}+\beta _{3}+\beta _{6}+\cdots)q^{3}+\cdots\)
9.8.a.a	$9$	$8$	9.a	1.a	$1$	$1$	$1$	$2.811$	\(\Q\)	None	✓	$1$	$1$	\(-6\)	\(0\)	\(-390\)	\(-64\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-6q^{2}-92q^{4}-390q^{5}-2^{6}q^{7}+\cdots\)
9.8.a.b	$9$	$8$	9.a	1.a	$1$	$2$	$2$	$2.811$	\(\Q(\sqrt{10}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(520\)	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+232q^{4}-2^{4}\beta q^{5}+260q^{7}+\cdots\)
9.8.c.a	$9$	$8$	9.c	9.c	$3$	$12$	$6$	$2.811$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(-9\)	\(24\)	\(-180\)	\(-84\)		$2^{8}\cdot 3^{15}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{2}-\beta _{3})q^{2}+(1-\beta _{1}-\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots\)
9.9.b.a	$9$	$9$	9.b	3.b	$2$	$2$	$2$	$3.666$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(3304\)		$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+238q^{4}+233\beta q^{5}+1652q^{7}+\cdots\)
9.9.d.a	$9$	$9$	9.d	9.d	$6$	$14$	$7$	$3.666$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		$2$	$0$	\(-3\)	\(-93\)	\(438\)	\(922\)		$2^{6}\cdot 3^{21}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{1}q^{2}+(-5-3\beta _{3}+\beta _{4}+\beta _{6})q^{3}+\cdots\)
9.10.a.a	$9$	$10$	9.a	1.a	$1$	$1$	$1$	$4.635$	\(\Q\)	None	✓	$1$	$0$	\(-18\)	\(0\)	\(1530\)	\(9128\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-18q^{2}-188q^{4}+1530q^{5}+9128q^{7}+\cdots\)
9.10.a.b	$9$	$10$	9.a	1.a	$1$	$1$	$1$	$4.635$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-12580\)	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2^{9}q^{4}-12580q^{7}+118370q^{13}+\cdots\)
9.10.a.c	$9$	$10$	9.a	1.a	$1$	$1$	$1$	$4.635$	\(\Q\)	None	✓	$1$	$0$	\(36\)	\(0\)	\(1314\)	\(-4480\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+6^{2}q^{2}+28^{2}q^{4}+1314q^{5}-4480q^{7}+\cdots\)
9.10.c.a	$9$	$10$	9.c	9.c	$3$	$16$	$8$	$4.635$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(15\)	\(-3\)	\(453\)	\(-343\)		$2^{14}\cdot 3^{28}\cdot 17^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2+\beta _{2}-2\beta _{3})q^{2}+(9-18\beta _{3}+\beta _{5}+\cdots)q^{3}+\cdots\)
9.11.b.a	$9$	$11$	9.b	3.b	$2$	$4$	$4$	$5.718$	\(\Q(\sqrt{-2}, \sqrt{385})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-44464\)		$2\cdot 3^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(-1073-\beta _{2})q^{4}+(-35\beta _{1}+\cdots)q^{5}+\cdots\)
9.11.d.a	$9$	$11$	9.d	9.d	$6$	$18$	$9$	$5.718$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(-3\)	\(51\)	\(4956\)	\(-6120\)		$2^{14}\cdot 3^{36}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{3}q^{2}+(3-\beta _{1}+\beta _{3}+\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)
9.12.a.a	$9$	$12$	9.a	1.a	$1$	$1$	$1$	$6.915$	\(\Q\)	None	✓	$1$	$1$	\(-78\)	\(0\)	\(5370\)	\(-27760\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-78q^{2}+4036q^{4}+5370q^{5}-27760q^{7}+\cdots\)
9.12.a.b	$9$	$12$	9.a	1.a	$1$	$1$	$1$	$6.915$	\(\Q\)	None	✓	$1$	$1$	\(24\)	\(0\)	\(-4830\)	\(-16744\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+24q^{2}-1472q^{4}-4830q^{5}-16744q^{7}+\cdots\)
9.12.a.c	$9$	$12$	9.a	1.a	$1$	$2$	$2$	$6.915$	\(\Q(\sqrt{70}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(116200\)	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+472q^{4}+224\beta q^{5}+58100q^{7}+\cdots\)
9.12.c.a	$9$	$12$	9.c	9.c	$3$	$20$	$10$	$6.915$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(-33\)	\(-12\)	\(-7230\)	\(8512\)		$2^{24}\cdot 3^{45}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-3\beta _{3})q^{2}+(24-51\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots\)
9.13.b.a	$9$	$13$	9.b	3.b	$2$	$2$	$2$	$8.226$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-223736\)		$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+8\beta q^{2}-6272q^{4}-2291\beta q^{5}-111868q^{7}+\cdots\)
9.13.b.b	$9$	$13$	9.b	3.b	$2$	$2$	$2$	$8.226$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(232456\)		$3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+2638q^{4}-175\beta q^{5}+116228q^{7}+\cdots\)
9.13.d.a	$9$	$13$	9.d	9.d	$6$	$22$	$11$	$8.226$		None		$2$	$0$	\(-3\)	\(618\)	\(-15987\)	\(34319\)			$\mathrm{SU}(2)[C_{6}]$
9.14.a.a	$9$	$14$	9.a	1.a	$1$	$1$	$1$	$9.651$	\(\Q\)	None	✓	$1$	$0$	\(12\)	\(0\)	\(30210\)	\(235088\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+12q^{2}-8048q^{4}+30210q^{5}+235088q^{7}+\cdots\)
9.14.a.b	$9$	$14$	9.a	1.a	$1$	$2$	$2$	$9.651$	\(\Q(\sqrt{55}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-266600\)	$+$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-272q^{4}-520\beta q^{5}-133300q^{7}+\cdots\)
9.14.a.c	$9$	$14$	9.a	1.a	$1$	$2$	$2$	$9.651$	\(\Q(\sqrt{1969}) \)	None	✓	$1$	$0$	\(54\)	\(0\)	\(-40716\)	\(-21008\)	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(3^{3}-\beta )q^{2}+(10258-54\beta )q^{4}+(-20358+\cdots)q^{5}+\cdots\)
9.14.c.a	$9$	$14$	9.c	9.c	$3$	$24$	$12$	$9.651$		None		$2$	$0$	\(63\)	\(-732\)	\(52128\)	\(-93912\)			$\mathrm{SU}(2)[C_{3}]$
9.15.b.a	$9$	$15$	9.b	3.b	$2$	$4$	$4$	$11.190$	\(\Q(\sqrt{-2}, \sqrt{3745})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-1065904\)		$2\cdot 3^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+(-833-\beta _{2})q^{4}+(-7\beta _{1}+\cdots)q^{5}+\cdots\)
9.15.d.a	$9$	$15$	9.d	9.d	$6$	$26$	$13$	$11.190$		None		$2$	$0$	\(-3\)	\(-2199\)	\(-107994\)	\(-146330\)			$\mathrm{SU}(2)[C_{6}]$
9.16.a.a	$9$	$16$	9.a	1.a	$1$	$1$	$1$	$12.842$	\(\Q\)	None	✓	$1$	$1$	\(-216\)	\(0\)	\(-52110\)	\(2822456\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-6^{3}q^{2}+13888q^{4}-52110q^{5}+\cdots\)
9.16.a.b	$9$	$16$	9.a	1.a	$1$	$1$	$1$	$12.842$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(1244900\)	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2^{15}q^{4}+1244900q^{7}+397771850q^{13}+\cdots\)
9.16.a.c	$9$	$16$	9.a	1.a	$1$	$1$	$1$	$12.842$	\(\Q\)	None	✓	$1$	$1$	\(72\)	\(0\)	\(221490\)	\(-2149000\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+72q^{2}-27584q^{4}+221490q^{5}+\cdots\)
9.16.a.d	$9$	$16$	9.a	1.a	$1$	$1$	$1$	$12.842$	\(\Q\)	None	✓	$1$	$1$	\(234\)	\(0\)	\(-280710\)	\(-1373344\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+234q^{2}+21988q^{4}-280710q^{5}+\cdots\)
9.16.a.e	$9$	$16$	9.a	1.a	$1$	$2$	$2$	$12.842$	\(\Q(\sqrt{370}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-5182520\)	$+$	$2\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+87112q^{4}+464\beta q^{5}-2591260q^{7}+\cdots\)
9.16.c.a	$9$	$16$	9.c	9.c	$3$	$28$	$14$	$12.842$		None		$2$	$0$	\(-129\)	\(3345\)	\(-152655\)	\(803705\)			$\mathrm{SU}(2)[C_{3}]$
9.17.b.a	$9$	$17$	9.b	3.b	$2$	$6$	$6$	$14.609$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(5400696\)		$2^{12}\cdot 3^{29}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(-61382-\beta _{4})q^{4}+(-189\beta _{1}+\cdots)q^{5}+\cdots\)
9.17.d.a	$9$	$17$	9.d	9.d	$6$	$30$	$15$	$14.609$		None		$2$	$0$	\(-3\)	\(2049\)	\(507588\)	\(220596\)			$\mathrm{SU}(2)[C_{6}]$
9.18.a.a	$9$	$18$	9.a	1.a	$1$	$1$	$1$	$16.490$	\(\Q\)	None	✓	$1$	$0$	\(-204\)	\(0\)	\(163554\)	\(-20846560\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-204q^{2}-89456q^{4}+163554q^{5}+\cdots\)
9.18.a.b	$9$	$18$	9.a	1.a	$1$	$1$	$1$	$16.490$	\(\Q\)	None	✓	$1$	$0$	\(528\)	\(0\)	\(1025850\)	\(3225992\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+528q^{2}+147712q^{4}+1025850q^{5}+\cdots\)
9.18.a.c	$9$	$18$	9.a	1.a	$1$	$2$	$2$	$16.490$	\(\Q(\sqrt{14569}) \)	None	✓	$1$	$0$	\(-594\)	\(0\)	\(-382860\)	\(24471568\)	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(-297-\beta )q^{2}+(88258+594\beta )q^{4}+\cdots\)
9.18.a.d	$9$	$18$	9.a	1.a	$1$	$2$	$2$	$16.490$	\(\Q(\sqrt{910}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-392840\)	$+$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-2^{5}q^{4}-280\beta q^{5}-196420q^{7}+\cdots\)
9.18.c.a	$9$	$18$	9.c	9.c	$3$	$32$	$16$	$16.490$		None		$2$	$0$	\(255\)	\(-2280\)	\(255678\)	\(-5846540\)			$\mathrm{SU}(2)[C_{3}]$
9.19.b.a	$9$	$19$	9.b	3.b	$2$	$6$	$6$	$18.485$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(19180488\)		$2^{7}\cdot 3^{33}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-42038-\beta _{2})q^{4}+(1082\beta _{1}+\cdots)q^{5}+\cdots\)
9.19.d.a	$9$	$19$	9.d	9.d	$6$	$34$	$17$	$18.485$		None		$2$	$0$	\(-3\)	\(3804\)	\(2192181\)	\(4302359\)			$\mathrm{SU}(2)[C_{6}]$
9.20.a.a	$9$	$20$	9.a	1.a	$1$	$1$	$1$	$20.594$	\(\Q\)	None	✓	$1$	$1$	\(-456\)	\(0\)	\(2377410\)	\(-16917544\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-456q^{2}-316352q^{4}+2377410q^{5}+\cdots\)
9.20.a.b	$9$	$20$	9.a	1.a	$1$	$1$	$1$	$20.594$	\(\Q\)	None	✓	$1$	$1$	\(1104\)	\(0\)	\(-3516270\)	\(-195590584\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+1104q^{2}+694528q^{4}-3516270q^{5}+\cdots\)