LMFDB - Newform Search Results

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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.	Only for weight 1:	Projective image	Projective image type
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Results (displaying matches 1-50 of 115) Next

Label	Dim.	$A$	Field	CM	RM	Traces				Fricke sign	$q$-expansion
Label	Dim.	$A$	Field	CM	RM	$a_2$	$a_3$	$a_5$	$a_7$	Fricke sign	$q$-expansion
31.1.b.a	$1$	$0.015$	$\Q$	$\Q(\sqrt{-31}) $	None	$-1$	$0$	$-1$	$-1$		$q-q^{2}-q^{5}-q^{7}+q^{8}+q^{9}+q^{10}+\cdots$
31.2.a.a	$2$	$0.248$	$\Q(\sqrt{5}) $	None	None	$1$	$-2$	$2$	$-4$	$-$	$q+\beta q^{2}-2\beta q^{3}+(-1+\beta )q^{4}+q^{5}+\cdots$
31.2.c.a	$4$	$0.248$	$\Q(\sqrt{2}, \sqrt{-3})$	None	None	$-4$	$2$	$-2$	$-2$		$q+(-1+\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+\cdots$
31.2.d.a	$4$	$0.248$	$\Q(\zeta_{10})$	None	None	$-3$	$1$	$-6$	$-3$		$q+(-1-\zeta_{10}^{2})q^{2}+(1-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{3}+\cdots$
31.2.g.a	$16$	$0.248$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	None	$-6$	$-12$	$-3$	$2$		$q+(-1-\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots$
31.3.b.a	$2$	$0.845$	$\Q(\sqrt{-26}) $	None	None	$-2$	$0$	$4$	$16$		$q-q^{2}+\beta q^{3}-3q^{4}+2q^{5}-\beta q^{6}+\cdots$
31.3.b.b	$3$	$0.845$	3.3.837.1	$\Q(\sqrt{-31}) $	None	$0$	$0$	$0$	$0$		$q+\beta _{2}q^{2}+(4+\beta _{1}-2\beta _{2})q^{4}+(-3\beta _{1}+\cdots)q^{5}+\cdots$
31.3.e.a	$2$	$0.845$	$\Q(\sqrt{-3}) $	None	None	$-6$	$3$	$9$	$1$		$q-3q^{2}+(1+\zeta_{6})q^{3}+5q^{4}+9\zeta_{6}q^{5}+\cdots$
31.3.e.b	$6$	$0.845$	6.0.954288.1	None	None	$2$	$-3$	$-7$	$-9$		$q+(-\beta _{2}+\beta _{4})q^{2}+(-\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{3}+\cdots$
31.3.f.a	$20$	$0.845$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	None	$-3$	$-5$	$-14$	$-1$		$q-\beta _{10}q^{2}-\beta _{13}q^{3}+(3\beta _{11}+\beta _{19})q^{4}+\cdots$
31.3.h.a	$32$	$0.845$		None	None	$-6$	$-10$	$-7$	$-22$
31.4.a.a	$2$	$1.829$	$\Q(\sqrt{17}) $	None	None	$-5$	$-2$	$-25$	$-19$	$-$	$q+(-2-\beta )q^{2}+(-2+2\beta )q^{3}+5\beta q^{4}+\cdots$
31.4.a.b	$5$	$1.829$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	None	$3$	$4$	$15$	$9$	$+$	$q+(1-\beta _{1})q^{2}+(-\beta _{2}+\beta _{3}-\beta _{4})q^{3}+\cdots$
31.4.c.a	$14$	$1.829$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	None	$-4$	$-11$	$-5$	$31$		$q+(-\beta _{1}+\beta _{4})q^{2}+(-2+2\beta _{3}-\beta _{8}+\cdots)q^{3}+\cdots$
31.4.d.a	$28$	$1.829$		None	None	$-3$	$-7$	$0$	$35$
31.4.g.a	$56$	$1.829$		None	None	$-6$	$1$	$0$	$-71$
31.5.b.a	$3$	$3.204$	3.3.837.1	$\Q(\sqrt{-31}) $	None	$0$	$0$	$0$	$0$		$q+(-\beta _{1}+\beta _{2})q^{2}+(2^{4}-6\beta _{1}+\beta _{2})q^{4}+\cdots$
31.5.b.b	$6$	$3.204$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None	None	$-2$	$0$	$-8$	$-132$		$q-\beta _{3}q^{2}+\beta _{1}q^{3}+(4+\beta _{3}+\beta _{4})q^{4}+\cdots$
31.5.e.a	$20$	$3.204$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	None	$-4$	$6$	$-4$	$-98$		$q-\beta _{3}q^{2}+\beta _{8}q^{3}+(6+\beta _{2})q^{4}+(-\beta _{11}+\cdots)q^{5}+\cdots$
31.5.f.a	$36$	$3.204$		None	None	$-3$	$-5$	$-2$	$-73$
31.5.h.a	$80$	$3.204$		None	None	$-6$	$-16$	$-1$	$288$
31.6.a.a	$5$	$4.972$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	None	$-9$	$-20$	$-72$	$-108$	$+$	$q+(-2+\beta _{1})q^{2}+(-4-\beta _{1}-\beta _{3})q^{3}+\cdots$
31.6.a.b	$8$	$4.972$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	None	$7$	$-2$	$128$	$88$	$-$	$q+(1-\beta _{1})q^{2}+\beta _{6}q^{3}+(19-3\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
31.6.c.a	$24$	$4.972$		None	None	$-4$	$10$	$28$	$-134$
31.6.d.a	$52$	$4.972$		None	None	$-3$	$17$	$-66$	$205$
31.6.g.a	$96$	$4.972$		None	None	$-6$	$-20$	$-33$	$-66$
31.7.b.a	$1$	$7.132$	$\Q$	$\Q(\sqrt{-31}) $	None	$-15$	$0$	$-246$	$-430$		$q-15q^{2}+161q^{4}-246q^{5}-430q^{7}+\cdots$
31.7.b.b	$2$	$7.132$	$\Q(\sqrt{93}) $	$\Q(\sqrt{-31}) $	None	$15$	$0$	$246$	$430$		$q+(8-\beta )q^{2}+(23-15\beta )q^{4}+(127-8\beta )q^{5}+\cdots$
31.7.b.c	$12$	$7.132$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None	None	$-2$	$0$	$-146$	$6$		$q-\beta _{8}q^{2}-\beta _{1}q^{3}+(10+\beta _{6}-\beta _{8})q^{4}+\cdots$
31.7.e.a	$30$	$7.132$		None	None	$-4$	$-3$	$-73$	$723$
31.7.f.a	$60$	$7.132$		None	None	$-3$	$-5$	$136$	$1009$
31.7.h.a	$120$	$7.132$		None	None	$-6$	$-7$	$68$	$-1753$
31.8.a.a	$7$	$9.684$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	None	$-17$	$-14$	$-430$	$-832$	$-$	$q+(-2-\beta _{1})q^{2}+(-2+\beta _{1}+\beta _{3})q^{3}+\cdots$
31.8.a.b	$10$	$9.684$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	None	$15$	$40$	$570$	$540$	$+$	$q+(2-\beta _{1})q^{2}+(4+\beta _{2})q^{3}+(61+\beta _{1}+\cdots)q^{4}+\cdots$
31.8.c.a	$36$	$9.684$		None	None	$-4$	$-2$	$70$	$-2158$
31.8.d.a	$68$	$9.684$		None	None	$-3$	$-31$	$-150$	$-3083$
31.8.g.a	$144$	$9.684$		None	None	$-6$	$-8$	$-75$	$5518$
31.9.b.a	$3$	$12.629$	3.3.837.1	$\Q(\sqrt{-31}) $	None	$0$	$0$	$0$	$0$		$q+(-6\beta _{1}+\beta _{2})q^{2}+(2^{8}-\beta _{1}+3^{4}\beta _{2})q^{4}+\cdots$
31.9.b.b	$18$	$12.629$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	None	None	$-2$	$0$	$292$	$-5472$		$q-\beta _{2}q^{2}+\beta _{1}q^{3}+(140+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
31.9.e.a	$40$	$12.629$		None	None	$-4$	$-84$	$146$	$272$
31.9.f.a	$84$	$12.629$		None	None	$-3$	$-5$	$-302$	$5067$
31.9.h.a	$160$	$12.629$		None	None	$-6$	$74$	$-151$	$118$
31.10.a.a	$10$	$15.966$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	None	$-33$	$-8$	$-3297$	$-495$	$+$	$q+(-3-\beta _{1})q^{2}+(-1+\beta _{1}-\beta _{3})q^{3}+\cdots$
31.10.a.b	$13$	$15.966$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	None	$31$	$154$	$1703$	$9109$	$-$	$q+(2+\beta _{1})q^{2}+(12+\beta _{3})q^{3}+(300+6\beta _{1}+\cdots)q^{4}+\cdots$
31.10.c.a	$46$	$15.966$		None	None	$-4$	$13$	$-797$	$6359$
31.10.d.a	$92$	$15.966$		None	None	$-3$	$-151$	$1584$	$15771$
31.10.g.a	$184$	$15.966$		None	None	$-6$	$-23$	$792$	$-30759$
31.11.b.a	$3$	$19.696$	3.3.837.1	$\Q(\sqrt{-31}) $	None	$0$	$0$	$0$	$0$		$q+(-15\beta _{1}+14\beta _{2})q^{2}+(2^{10}-644\beta _{1}+\cdots)q^{4}+\cdots$
31.11.b.b	$22$	$19.696$		None	None	$-2$	$0$	$3304$	$19916$
31.11.e.a	$52$	$19.696$		None	None	$-4$	$-246$	$1652$	$-19306$

Introduction	Features
Universe	News

Label	Dim.	\(A\)	Field	CM	RM	Traces				Fricke sign	$q$-expansion
Label	Dim.	\(A\)	Field	CM	RM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	Fricke sign	$q$-expansion
31.1.b.a	\(1\)	\(0.015\)	\(\Q\)	\(\Q(\sqrt{-31}) \)	None	\(-1\)	\(0\)	\(-1\)	\(-1\)		\(q-q^{2}-q^{5}-q^{7}+q^{8}+q^{9}+q^{10}+\cdots\)
31.2.a.a	\(2\)	\(0.248\)	\(\Q(\sqrt{5}) \)	None	None	\(1\)	\(-2\)	\(2\)	\(-4\)	\(-\)	\(q+\beta q^{2}-2\beta q^{3}+(-1+\beta )q^{4}+q^{5}+\cdots\)
31.2.c.a	\(4\)	\(0.248\)	\(\Q(\sqrt{2}, \sqrt{-3})\)	None	None	\(-4\)	\(2\)	\(-2\)	\(-2\)		\(q+(-1+\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+\cdots\)
31.2.d.a	\(4\)	\(0.248\)	\(\Q(\zeta_{10})\)	None	None	\(-3\)	\(1\)	\(-6\)	\(-3\)		\(q+(-1-\zeta_{10}^{2})q^{2}+(1-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)
31.2.g.a	\(16\)	\(0.248\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	None	\(-6\)	\(-12\)	\(-3\)	\(2\)		\(q+(-1-\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots\)
31.3.b.a	\(2\)	\(0.845\)	\(\Q(\sqrt{-26}) \)	None	None	\(-2\)	\(0\)	\(4\)	\(16\)		\(q-q^{2}+\beta q^{3}-3q^{4}+2q^{5}-\beta q^{6}+\cdots\)
31.3.b.b	\(3\)	\(0.845\)	3.3.837.1	\(\Q(\sqrt{-31}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{2}q^{2}+(4+\beta _{1}-2\beta _{2})q^{4}+(-3\beta _{1}+\cdots)q^{5}+\cdots\)
31.3.e.a	\(2\)	\(0.845\)	\(\Q(\sqrt{-3}) \)	None	None	\(-6\)	\(3\)	\(9\)	\(1\)		\(q-3q^{2}+(1+\zeta_{6})q^{3}+5q^{4}+9\zeta_{6}q^{5}+\cdots\)
31.3.e.b	\(6\)	\(0.845\)	6.0.954288.1	None	None	\(2\)	\(-3\)	\(-7\)	\(-9\)		\(q+(-\beta _{2}+\beta _{4})q^{2}+(-\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{3}+\cdots\)
31.3.f.a	\(20\)	\(0.845\)	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	None	\(-3\)	\(-5\)	\(-14\)	\(-1\)		\(q-\beta _{10}q^{2}-\beta _{13}q^{3}+(3\beta _{11}+\beta _{19})q^{4}+\cdots\)
31.3.h.a	\(32\)	\(0.845\)		None	None	\(-6\)	\(-10\)	\(-7\)	\(-22\)
31.4.a.a	\(2\)	\(1.829\)	\(\Q(\sqrt{17}) \)	None	None	\(-5\)	\(-2\)	\(-25\)	\(-19\)	\(-\)	\(q+(-2-\beta )q^{2}+(-2+2\beta )q^{3}+5\beta q^{4}+\cdots\)
31.4.a.b	\(5\)	\(1.829\)	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	None	\(3\)	\(4\)	\(15\)	\(9\)	\(+\)	\(q+(1-\beta _{1})q^{2}+(-\beta _{2}+\beta _{3}-\beta _{4})q^{3}+\cdots\)
31.4.c.a	\(14\)	\(1.829\)	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	None	\(-4\)	\(-11\)	\(-5\)	\(31\)		\(q+(-\beta _{1}+\beta _{4})q^{2}+(-2+2\beta _{3}-\beta _{8}+\cdots)q^{3}+\cdots\)
31.4.d.a	\(28\)	\(1.829\)		None	None	\(-3\)	\(-7\)	\(0\)	\(35\)
31.4.g.a	\(56\)	\(1.829\)		None	None	\(-6\)	\(1\)	\(0\)	\(-71\)
31.5.b.a	\(3\)	\(3.204\)	3.3.837.1	\(\Q(\sqrt{-31}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(-\beta _{1}+\beta _{2})q^{2}+(2^{4}-6\beta _{1}+\beta _{2})q^{4}+\cdots\)
31.5.b.b	\(6\)	\(3.204\)	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None	None	\(-2\)	\(0\)	\(-8\)	\(-132\)		\(q-\beta _{3}q^{2}+\beta _{1}q^{3}+(4+\beta _{3}+\beta _{4})q^{4}+\cdots\)
31.5.e.a	\(20\)	\(3.204\)	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	None	\(-4\)	\(6\)	\(-4\)	\(-98\)		\(q-\beta _{3}q^{2}+\beta _{8}q^{3}+(6+\beta _{2})q^{4}+(-\beta _{11}+\cdots)q^{5}+\cdots\)
31.5.f.a	\(36\)	\(3.204\)		None	None	\(-3\)	\(-5\)	\(-2\)	\(-73\)
31.5.h.a	\(80\)	\(3.204\)		None	None	\(-6\)	\(-16\)	\(-1\)	\(288\)
31.6.a.a	\(5\)	\(4.972\)	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	None	\(-9\)	\(-20\)	\(-72\)	\(-108\)	\(+\)	\(q+(-2+\beta _{1})q^{2}+(-4-\beta _{1}-\beta _{3})q^{3}+\cdots\)
31.6.a.b	\(8\)	\(4.972\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	None	\(7\)	\(-2\)	\(128\)	\(88\)	\(-\)	\(q+(1-\beta _{1})q^{2}+\beta _{6}q^{3}+(19-3\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
31.6.c.a	\(24\)	\(4.972\)		None	None	\(-4\)	\(10\)	\(28\)	\(-134\)
31.6.d.a	\(52\)	\(4.972\)		None	None	\(-3\)	\(17\)	\(-66\)	\(205\)
31.6.g.a	\(96\)	\(4.972\)		None	None	\(-6\)	\(-20\)	\(-33\)	\(-66\)
31.7.b.a	\(1\)	\(7.132\)	\(\Q\)	\(\Q(\sqrt{-31}) \)	None	\(-15\)	\(0\)	\(-246\)	\(-430\)		\(q-15q^{2}+161q^{4}-246q^{5}-430q^{7}+\cdots\)
31.7.b.b	\(2\)	\(7.132\)	\(\Q(\sqrt{93}) \)	\(\Q(\sqrt{-31}) \)	None	\(15\)	\(0\)	\(246\)	\(430\)		\(q+(8-\beta )q^{2}+(23-15\beta )q^{4}+(127-8\beta )q^{5}+\cdots\)
31.7.b.c	\(12\)	\(7.132\)	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None	None	\(-2\)	\(0\)	\(-146\)	\(6\)		\(q-\beta _{8}q^{2}-\beta _{1}q^{3}+(10+\beta _{6}-\beta _{8})q^{4}+\cdots\)
31.7.e.a	\(30\)	\(7.132\)		None	None	\(-4\)	\(-3\)	\(-73\)	\(723\)
31.7.f.a	\(60\)	\(7.132\)		None	None	\(-3\)	\(-5\)	\(136\)	\(1009\)
31.7.h.a	\(120\)	\(7.132\)		None	None	\(-6\)	\(-7\)	\(68\)	\(-1753\)
31.8.a.a	\(7\)	\(9.684\)	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	None	\(-17\)	\(-14\)	\(-430\)	\(-832\)	\(-\)	\(q+(-2-\beta _{1})q^{2}+(-2+\beta _{1}+\beta _{3})q^{3}+\cdots\)
31.8.a.b	\(10\)	\(9.684\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	None	\(15\)	\(40\)	\(570\)	\(540\)	\(+\)	\(q+(2-\beta _{1})q^{2}+(4+\beta _{2})q^{3}+(61+\beta _{1}+\cdots)q^{4}+\cdots\)
31.8.c.a	\(36\)	\(9.684\)		None	None	\(-4\)	\(-2\)	\(70\)	\(-2158\)
31.8.d.a	\(68\)	\(9.684\)		None	None	\(-3\)	\(-31\)	\(-150\)	\(-3083\)
31.8.g.a	\(144\)	\(9.684\)		None	None	\(-6\)	\(-8\)	\(-75\)	\(5518\)
31.9.b.a	\(3\)	\(12.629\)	3.3.837.1	\(\Q(\sqrt{-31}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(-6\beta _{1}+\beta _{2})q^{2}+(2^{8}-\beta _{1}+3^{4}\beta _{2})q^{4}+\cdots\)
31.9.b.b	\(18\)	\(12.629\)	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None	None	\(-2\)	\(0\)	\(292\)	\(-5472\)		\(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(140+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
31.9.e.a	\(40\)	\(12.629\)		None	None	\(-4\)	\(-84\)	\(146\)	\(272\)
31.9.f.a	\(84\)	\(12.629\)		None	None	\(-3\)	\(-5\)	\(-302\)	\(5067\)
31.9.h.a	\(160\)	\(12.629\)		None	None	\(-6\)	\(74\)	\(-151\)	\(118\)
31.10.a.a	\(10\)	\(15.966\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	None	\(-33\)	\(-8\)	\(-3297\)	\(-495\)	\(+\)	\(q+(-3-\beta _{1})q^{2}+(-1+\beta _{1}-\beta _{3})q^{3}+\cdots\)
31.10.a.b	\(13\)	\(15.966\)	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	None	\(31\)	\(154\)	\(1703\)	\(9109\)	\(-\)	\(q+(2+\beta _{1})q^{2}+(12+\beta _{3})q^{3}+(300+6\beta _{1}+\cdots)q^{4}+\cdots\)
31.10.c.a	\(46\)	\(15.966\)		None	None	\(-4\)	\(13\)	\(-797\)	\(6359\)
31.10.d.a	\(92\)	\(15.966\)		None	None	\(-3\)	\(-151\)	\(1584\)	\(15771\)
31.10.g.a	\(184\)	\(15.966\)		None	None	\(-6\)	\(-23\)	\(792\)	\(-30759\)
31.11.b.a	\(3\)	\(19.696\)	3.3.837.1	\(\Q(\sqrt{-31}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(-15\beta _{1}+14\beta _{2})q^{2}+(2^{10}-644\beta _{1}+\cdots)q^{4}+\cdots\)
31.11.b.b	\(22\)	\(19.696\)		None	None	\(-2\)	\(0\)	\(3304\)	\(19916\)
31.11.e.a	\(52\)	\(19.696\)		None	None	\(-4\)	\(-246\)	\(1652\)	\(-19306\)

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.