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 115 matches)

 

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
31.1.b.a	$31$	$1$	31.b	31.b	$2$	$1$	$1$	$0.015$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-31}) \)	None	✓	$2$	$0$	\(-1\)	\(0\)	\(-1\)	\(-1\)		$1$		\(q-q^{2}-q^{5}-q^{7}+q^{8}+q^{9}+q^{10}+\cdots\)
31.2.a.a	$31$	$2$	31.a	1.a	$1$	$2$	$2$	$0.248$	\(\Q(\sqrt{5}) \)	$_{}$	None	None	✓	$1$	$0$	\(1\)	\(-2\)	\(2\)	\(-4\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-2\beta q^{3}+(-1+\beta )q^{4}+q^{5}+\cdots\)
31.2.c.a	$31$	$2$	31.c	31.c	$3$	$4$	$2$	$0.248$	\(\Q(\sqrt{2}, \sqrt{-3})\)	$_{}$	None	None		$2$	$0$	\(-4\)	\(2\)	\(-2\)	\(-2\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+\cdots\)
31.2.d.a	$31$	$2$	31.d	31.d	$5$	$4$	$1$	$0.248$	\(\Q(\zeta_{10})\)	$_{}$	None	None		$2$	$0$	\(-3\)	\(1\)	\(-6\)	\(-3\)		$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1-\zeta_{10}^{2})q^{2}+(1-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)
31.2.g.a	$31$	$2$	31.g	31.g	$15$	$16$	$2$	$0.248$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	$_{}$	None	None		$2$	$0$	\(-6\)	\(-12\)	\(-3\)	\(2\)		$1$	$\mathrm{SU}(2)[C_{15}]$	\(q+(-1-\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots\)
31.3.b.a	$31$	$3$	31.b	31.b	$2$	$2$	$2$	$0.845$	\(\Q(\sqrt{-26}) \)	$_{}$	None	None		$2$	$0$	\(-2\)	\(0\)	\(4\)	\(16\)		$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta q^{3}-3q^{4}+2q^{5}-\beta q^{6}+\cdots\)
31.3.b.b	$31$	$3$	31.b	31.b	$2$	$3$	$3$	$0.845$	3.3.837.1	$_{}$	\(\Q(\sqrt{-31}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{2}+(4+\beta _{1}-2\beta _{2})q^{4}+(-3\beta _{1}+\cdots)q^{5}+\cdots\)
31.3.e.a	$31$	$3$	31.e	31.e	$6$	$2$	$1$	$0.845$	\(\Q(\sqrt{-3}) \)	$_{}$	None	None		$2$	$0$	\(-6\)	\(3\)	\(9\)	\(1\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-3q^{2}+(1+\zeta_{6})q^{3}+5q^{4}+9\zeta_{6}q^{5}+\cdots\)
31.3.e.b	$31$	$3$	31.e	31.e	$6$	$6$	$3$	$0.845$	6.0.954288.1	$_{}$	None	None		$2$	$0$	\(2\)	\(-3\)	\(-7\)	\(-9\)		$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{2}+\beta _{4})q^{2}+(-\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{3}+\cdots\)
31.3.f.a	$31$	$3$	31.f	31.f	$10$	$20$	$5$	$0.845$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	$_{}$	None	None		$2$	$0$	\(-3\)	\(-5\)	\(-14\)	\(-1\)		$1$	$\mathrm{SU}(2)[C_{10}]$	\(q-\beta _{10}q^{2}-\beta _{13}q^{3}+(3\beta _{11}+\beta _{19})q^{4}+\cdots\)
31.3.h.a	$31$	$3$	31.h	31.h	$30$	$32$	$4$	$0.845$		$_{}$	None	None		$2$	$0$	\(-6\)	\(-10\)	\(-7\)	\(-22\)			$\mathrm{SU}(2)[C_{30}]$
31.4.a.a	$31$	$4$	31.a	1.a	$1$	$2$	$2$	$1.829$	\(\Q(\sqrt{17}) \)	$_{}$	None	None	✓	$1$	$1$	\(-5\)	\(-2\)	\(-25\)	\(-19\)	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-2-\beta )q^{2}+(-2+2\beta )q^{3}+5\beta q^{4}+\cdots\)
31.4.a.b	$31$	$4$	31.a	1.a	$1$	$5$	$5$	$1.829$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	$_{}$	None	None	✓	$1$	$0$	\(3\)	\(4\)	\(15\)	\(9\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(-\beta _{2}+\beta _{3}-\beta _{4})q^{3}+\cdots\)
31.4.c.a	$31$	$4$	31.c	31.c	$3$	$14$	$7$	$1.829$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	$_{}$	None	None		$2$	$0$	\(-4\)	\(-11\)	\(-5\)	\(31\)		$2^{6}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{4})q^{2}+(-2+2\beta _{3}-\beta _{8}+\cdots)q^{3}+\cdots\)
31.4.d.a	$31$	$4$	31.d	31.d	$5$	$28$	$7$	$1.829$		$_{}$	None	None		$2$	$0$	\(-3\)	\(-7\)	\(0\)	\(35\)			$\mathrm{SU}(2)[C_{5}]$
31.4.g.a	$31$	$4$	31.g	31.g	$15$	$56$	$7$	$1.829$		$_{}$	None	None		$2$	$0$	\(-6\)	\(1\)	\(0\)	\(-71\)			$\mathrm{SU}(2)[C_{15}]$
31.5.b.a	$31$	$5$	31.b	31.b	$2$	$3$	$3$	$3.204$	3.3.837.1	$_{}$	\(\Q(\sqrt{-31}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$3$	$\mathrm{U}(1)[D_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{2}+(2^{4}-6\beta _{1}+\beta _{2})q^{4}+\cdots\)
31.5.b.b	$31$	$5$	31.b	31.b	$2$	$6$	$6$	$3.204$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	$_{}$	None	None		$2$	$0$	\(-2\)	\(0\)	\(-8\)	\(-132\)		$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+\beta _{1}q^{3}+(4+\beta _{3}+\beta _{4})q^{4}+\cdots\)
31.5.e.a	$31$	$5$	31.e	31.e	$6$	$20$	$10$	$3.204$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	$_{}$	None	None		$2$	$0$	\(-4\)	\(6\)	\(-4\)	\(-98\)		$2^{2}\cdot 3^{11}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{3}q^{2}+\beta _{8}q^{3}+(6+\beta _{2})q^{4}+(-\beta _{11}+\cdots)q^{5}+\cdots\)
31.5.f.a	$31$	$5$	31.f	31.f	$10$	$36$	$9$	$3.204$		$_{}$	None	None		$2$	$0$	\(-3\)	\(-5\)	\(-2\)	\(-73\)			$\mathrm{SU}(2)[C_{10}]$
31.5.h.a	$31$	$5$	31.h	31.h	$30$	$80$	$10$	$3.204$		$_{}$	None	None		$2$	$0$	\(-6\)	\(-16\)	\(-1\)	\(288\)			$\mathrm{SU}(2)[C_{30}]$
31.6.a.a	$31$	$6$	31.a	1.a	$1$	$5$	$5$	$4.972$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	$_{}$	None	None	✓	$1$	$1$	\(-9\)	\(-20\)	\(-72\)	\(-108\)	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-2+\beta _{1})q^{2}+(-4-\beta _{1}-\beta _{3})q^{3}+\cdots\)
31.6.a.b	$31$	$6$	31.a	1.a	$1$	$8$	$8$	$4.972$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	$_{}$	None	None	✓	$1$	$0$	\(7\)	\(-2\)	\(128\)	\(88\)	$-$	$2^{2}\cdot 5\cdot 13$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+\beta _{6}q^{3}+(19-3\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
31.6.c.a	$31$	$6$	31.c	31.c	$3$	$24$	$12$	$4.972$		$_{}$	None	None		$2$	$0$	\(-4\)	\(10\)	\(28\)	\(-134\)			$\mathrm{SU}(2)[C_{3}]$
31.6.d.a	$31$	$6$	31.d	31.d	$5$	$52$	$13$	$4.972$		$_{}$	None	None		$2$	$0$	\(-3\)	\(17\)	\(-66\)	\(205\)			$\mathrm{SU}(2)[C_{5}]$
31.6.g.a	$31$	$6$	31.g	31.g	$15$	$96$	$12$	$4.972$		$_{}$	None	None		$2$	$0$	\(-6\)	\(-20\)	\(-33\)	\(-66\)			$\mathrm{SU}(2)[C_{15}]$
31.7.b.a	$31$	$7$	31.b	31.b	$2$	$1$	$1$	$7.132$	\(\Q\)	$_{}$	\(\Q(\sqrt{-31}) \)	None	✓	$2$	$0$	\(-15\)	\(0\)	\(-246\)	\(-430\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q-15q^{2}+161q^{4}-246q^{5}-430q^{7}+\cdots\)
31.7.b.b	$31$	$7$	31.b	31.b	$2$	$2$	$2$	$7.132$	\(\Q(\sqrt{93}) \)	$_{}$	\(\Q(\sqrt{-31}) \)	None	✓	$2$	$0$	\(15\)	\(0\)	\(246\)	\(430\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(8-\beta )q^{2}+(23-15\beta )q^{4}+(127-8\beta )q^{5}+\cdots\)
31.7.b.c	$31$	$7$	31.b	31.b	$2$	$12$	$12$	$7.132$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	$_{}$	None	None		$2$	$0$	\(-2\)	\(0\)	\(-146\)	\(6\)		$2^{10}\cdot 3^{2}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{8}q^{2}-\beta _{1}q^{3}+(10+\beta _{6}-\beta _{8})q^{4}+\cdots\)
31.7.e.a	$31$	$7$	31.e	31.e	$6$	$30$	$15$	$7.132$		$_{}$	None	None		$2$	$0$	\(-4\)	\(-3\)	\(-73\)	\(723\)			$\mathrm{SU}(2)[C_{6}]$
31.7.f.a	$31$	$7$	31.f	31.f	$10$	$60$	$15$	$7.132$		$_{}$	None	None		$2$	$0$	\(-3\)	\(-5\)	\(136\)	\(1009\)			$\mathrm{SU}(2)[C_{10}]$
31.7.h.a	$31$	$7$	31.h	31.h	$30$	$120$	$15$	$7.132$		$_{}$	None	None		$2$	$0$	\(-6\)	\(-7\)	\(68\)	\(-1753\)			$\mathrm{SU}(2)[C_{30}]$
31.8.a.a	$31$	$8$	31.a	1.a	$1$	$7$	$7$	$9.684$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	$_{}$	None	None	✓	$1$	$1$	\(-17\)	\(-14\)	\(-430\)	\(-832\)	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+(-2-\beta _{1})q^{2}+(-2+\beta _{1}+\beta _{3})q^{3}+\cdots\)
31.8.a.b	$31$	$8$	31.a	1.a	$1$	$10$	$10$	$9.684$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	$_{}$	None	None	✓	$1$	$0$	\(15\)	\(40\)	\(570\)	\(540\)	$+$	$2^{6}$	$\mathrm{SU}(2)$	\(q+(2-\beta _{1})q^{2}+(4+\beta _{2})q^{3}+(61+\beta _{1}+\cdots)q^{4}+\cdots\)
31.8.c.a	$31$	$8$	31.c	31.c	$3$	$36$	$18$	$9.684$		$_{}$	None	None		$2$	$0$	\(-4\)	\(-2\)	\(70\)	\(-2158\)			$\mathrm{SU}(2)[C_{3}]$
31.8.d.a	$31$	$8$	31.d	31.d	$5$	$68$	$17$	$9.684$		$_{}$	None	None		$2$	$0$	\(-3\)	\(-31\)	\(-150\)	\(-3083\)			$\mathrm{SU}(2)[C_{5}]$
31.8.g.a	$31$	$8$	31.g	31.g	$15$	$144$	$18$	$9.684$		$_{}$	None	None		$2$	$0$	\(-6\)	\(-8\)	\(-75\)	\(5518\)			$\mathrm{SU}(2)[C_{15}]$
31.9.b.a	$31$	$9$	31.b	31.b	$2$	$3$	$3$	$12.629$	3.3.837.1	$_{}$	\(\Q(\sqrt{-31}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$3$	$\mathrm{U}(1)[D_{2}]$	\(q+(-6\beta _{1}+\beta _{2})q^{2}+(2^{8}-\beta _{1}+3^{4}\beta _{2})q^{4}+\cdots\)
31.9.b.b	$31$	$9$	31.b	31.b	$2$	$18$	$18$	$12.629$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	$_{}$	None	None		$2$	$0$	\(-2\)	\(0\)	\(292\)	\(-5472\)		$2^{20}\cdot 3^{8}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(140+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
31.9.e.a	$31$	$9$	31.e	31.e	$6$	$40$	$20$	$12.629$		$_{}$	None	None		$2$	$0$	\(-4\)	\(-84\)	\(146\)	\(272\)			$\mathrm{SU}(2)[C_{6}]$
31.9.f.a	$31$	$9$	31.f	31.f	$10$	$84$	$21$	$12.629$		$_{}$	None	None		$2$	$0$	\(-3\)	\(-5\)	\(-302\)	\(5067\)			$\mathrm{SU}(2)[C_{10}]$
31.9.h.a	$31$	$9$	31.h	31.h	$30$	$160$	$20$	$12.629$		$_{}$	None	None		$2$	$0$	\(-6\)	\(74\)	\(-151\)	\(118\)			$\mathrm{SU}(2)[C_{30}]$
31.10.a.a	$31$	$10$	31.a	1.a	$1$	$10$	$10$	$15.966$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	$_{}$	None	None	✓	$1$	$1$	\(-33\)	\(-8\)	\(-3297\)	\(-495\)	$+$	$2^{10}\cdot 23$	$\mathrm{SU}(2)$	\(q+(-3-\beta _{1})q^{2}+(-1+\beta _{1}-\beta _{3})q^{3}+\cdots\)
31.10.a.b	$31$	$10$	31.a	1.a	$1$	$13$	$13$	$15.966$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	$_{}$	None	None	✓	$1$	$0$	\(31\)	\(154\)	\(1703\)	\(9109\)	$-$	$2^{10}\cdot 3^{5}\cdot 5$	$\mathrm{SU}(2)$	\(q+(2+\beta _{1})q^{2}+(12+\beta _{3})q^{3}+(300+6\beta _{1}+\cdots)q^{4}+\cdots\)
31.10.c.a	$31$	$10$	31.c	31.c	$3$	$46$	$23$	$15.966$		$_{}$	None	None		$2$	$0$	\(-4\)	\(13\)	\(-797\)	\(6359\)			$\mathrm{SU}(2)[C_{3}]$
31.10.d.a	$31$	$10$	31.d	31.d	$5$	$92$	$23$	$15.966$		$_{}$	None	None		$2$	$0$	\(-3\)	\(-151\)	\(1584\)	\(15771\)			$\mathrm{SU}(2)[C_{5}]$
31.10.g.a	$31$	$10$	31.g	31.g	$15$	$184$	$23$	$15.966$		$_{}$	None	None		$2$	$0$	\(-6\)	\(-23\)	\(792\)	\(-30759\)			$\mathrm{SU}(2)[C_{15}]$
31.11.b.a	$31$	$11$	31.b	31.b	$2$	$3$	$3$	$19.696$	3.3.837.1	$_{}$	\(\Q(\sqrt{-31}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(-15\beta _{1}+14\beta _{2})q^{2}+(2^{10}-644\beta _{1}+\cdots)q^{4}+\cdots\)
31.11.b.b	$31$	$11$	31.b	31.b	$2$	$22$	$22$	$19.696$		$_{}$	None	None		$2$	$0$	\(-2\)	\(0\)	\(3304\)	\(19916\)			$\mathrm{SU}(2)[C_{2}]$
31.11.e.a	$31$	$11$	31.e	31.e	$6$	$52$	$26$	$19.696$		$_{}$	None	None		$2$	$0$	\(-4\)	\(-246\)	\(1652\)	\(-19306\)			$\mathrm{SU}(2)[C_{6}]$