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-twist	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 110 matches)

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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
76.1.c.a	$1$	$0.038$	$\Q$	$\Q(\sqrt{-19}) $	None	$0$	$0$	$-1$	$-1$		$q-q^{5}-q^{7}+q^{9}-q^{11}-q^{17}+q^{19}+\cdots$
76.2.a.a	$1$	$0.607$	$\Q$	None	None	$0$	$2$	$-1$	$-3$	$-$	$q+2q^{3}-q^{5}-3q^{7}+q^{9}+5q^{11}+\cdots$
76.2.d.a	$8$	$0.607$	8.0.$\cdots$.1	None	None	$0$	$0$	$-4$	$0$		$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
76.2.e.a	$2$	$0.607$	$\Q(\sqrt{-3}) $	None	None	$0$	$1$	$1$	$0$		$q+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots$
76.2.f.a	$16$	$0.607$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	None	$-3$	$0$	$-2$	$0$		$q+(-\beta _{1}-\beta _{14})q^{2}+\beta _{15}q^{3}+(-1+\cdots)q^{4}+\cdots$
76.2.i.a	$12$	$0.607$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	None	$0$	$-3$	$0$	$3$		$q+(-1-\beta _{5}+\beta _{7}+\beta _{9}+\beta _{11})q^{3}+\cdots$
76.2.k.a	$48$	$0.607$		None	None	$-6$	$0$	$-12$	$0$
76.3.b.a	$4$	$2.071$	$\Q(\sqrt{-3}, \sqrt{-19})$	None	None	$-4$	$0$	$-4$	$0$		$q+(-1-\beta _{1})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-2+\cdots)q^{4}+\cdots$
76.3.b.b	$14$	$2.071$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	None	$2$	$0$	$0$	$0$		$q+\beta _{3}q^{2}-\beta _{7}q^{3}+\beta _{5}q^{4}+\beta _{12}q^{5}+\cdots$
76.3.c.a	$2$	$2.071$	$\Q(\sqrt{-29}) $	None	None	$0$	$0$	$-8$	$-2$		$q+\beta q^{3}-4q^{5}-q^{7}-20q^{9}+14q^{11}+\cdots$
76.3.c.b	$2$	$2.071$	$\Q(\sqrt{57}) $	$\Q(\sqrt{-19}) $	None	$0$	$0$	$9$	$5$		$q+(5-\beta )q^{5}+(1+3\beta )q^{7}+9q^{9}+(1+\cdots)q^{11}+\cdots$
76.3.g.a	$4$	$2.071$	$\Q(\sqrt{-3}, \sqrt{-10})$	None	None	$-4$	$6$	$-4$	$0$		$q-2\beta _{2}q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(-4+\cdots)q^{4}+\cdots$
76.3.g.b	$4$	$2.071$	$\Q(\sqrt{-3}, \sqrt{-10})$	None	None	$8$	$-6$	$-4$	$0$		$q+2q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+4q^{4}+\cdots$
76.3.g.c	$28$	$2.071$		None	None	$-5$	$0$	$6$	$0$
76.3.h.a	$8$	$2.071$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	None	$0$	$6$	$-1$	$-12$		$q+(-\beta _{3}-\beta _{4})q^{3}+(\beta _{5}-\beta _{6})q^{5}+(-2+\cdots)q^{7}+\cdots$
76.3.j.a	$18$	$2.071$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	None	None	$0$	$-6$	$0$	$9$		$q+(-\beta _{4}-\beta _{6}-\beta _{8}-\beta _{10}+\beta _{12})q^{3}+\cdots$
76.3.l.a	$108$	$2.071$		None	None	$-6$	$0$	$-12$	$0$
76.4.a.a	$2$	$4.484$	$\Q(\sqrt{33}) $	None	None	$0$	$-5$	$-5$	$-30$	$-$	$q+(-2-\beta )q^{3}+(-5+5\beta )q^{5}+(-13+\cdots)q^{7}+\cdots$
76.4.a.b	$3$	$4.484$	3.3.35529.1	None	None	$0$	$1$	$9$	$44$	$+$	$q+(\beta _{1}+\beta _{2})q^{3}+(3+\beta _{2})q^{5}+(15-\beta _{1}+\cdots)q^{7}+\cdots$
76.4.d.a	$28$	$4.484$		None	None	$0$	$0$	$-4$	$0$
76.4.e.a	$10$	$4.484$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	None	$0$	$7$	$-4$	$-20$		$q+(-\beta _{1}-\beta _{2}-\beta _{3})q^{3}+(\beta _{3}+\beta _{7}+\beta _{8}+\cdots)q^{5}+\cdots$
76.4.f.a	$56$	$4.484$		None	None	$-3$	$0$	$-2$	$0$
76.4.i.a	$30$	$4.484$		None	None	$0$	$-3$	$0$	$6$
76.4.k.a	$168$	$4.484$		None	None	$-6$	$0$	$-12$	$0$
76.5.b.a	$36$	$7.856$		None	None	$6$	$0$	$24$	$0$
76.5.c.a	$2$	$7.856$	$\Q(\sqrt{57}) $	$\Q(\sqrt{-19}) $	None	$0$	$0$	$-31$	$73$		$q+(-17-3\beta )q^{5}+(39+5\beta )q^{7}+3^{4}q^{9}+\cdots$
76.5.c.b	$4$	$7.856$	$\mathbb{Q}[x]/(x^{4} + \cdots)$	None	None	$0$	$0$	$22$	$24$		$q+\beta _{1}q^{3}+(6-\beta _{2})q^{5}+(7-2\beta _{2})q^{7}+\cdots$
76.5.g.a	$76$	$7.856$		None	None	$-1$	$0$	$-2$	$0$
76.5.h.a	$12$	$7.856$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	None	$0$	$-12$	$9$	$-52$		$q+(-\beta _{1}+\beta _{3})q^{3}+(1-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$
76.5.j.a	$42$	$7.856$		None	None	$0$	$12$	$0$	$-45$
76.5.l.a	$228$	$7.856$		None	None	$-6$	$0$	$-12$	$0$
76.6.a.a	$3$	$12.189$	3.3.272193.1	None	None	$0$	$-8$	$-9$	$-13$	$+$	$q+(-3-\beta _{1}-\beta _{2})q^{3}+(-2+3\beta _{1}+\cdots)q^{5}+\cdots$
76.6.a.b	$4$	$12.189$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	None	$0$	$10$	$-110$	$30$	$-$	$q+(3+\beta _{3})q^{3}+(-26+\beta _{1}+2\beta _{2}+3\beta _{3})q^{5}+\cdots$
76.6.d.a	$48$	$12.189$		None	None	$0$	$0$	$-4$	$0$
76.6.e.a	$18$	$12.189$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	None	$0$	$-11$	$11$	$336$		$q+(\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(\beta _{2}+\beta _{6}+\beta _{8}+\cdots)q^{5}+\cdots$
76.6.f.a	$96$	$12.189$		None	None	$-3$	$0$	$-2$	$0$
76.6.i.a	$48$	$12.189$		None	None	$0$	$33$	$0$	$-177$
76.6.k.a	$288$	$12.189$		None	None	$-6$	$0$	$-12$	$0$
76.7.b.a	$54$	$17.484$		None	None	$-10$	$0$	$-44$	$0$
76.7.c.a	$2$	$17.484$	$\Q(\sqrt{57}) $	$\Q(\sqrt{-19}) $	None	$0$	$0$	$54$	$-610$		$q+(3^{3}+7\beta )q^{5}+(-305+9\beta )q^{7}+3^{6}q^{9}+\cdots$
76.7.c.b	$8$	$17.484$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None	None	$0$	$0$	$2$	$362$		$q+\beta _{1}q^{3}+\beta _{7}q^{5}+(46+\beta _{2}+2\beta _{3}+\cdots)q^{7}+\cdots$
76.7.g.a	$116$	$17.484$		None	None	$-1$	$0$	$-2$	$0$
76.7.h.a	$20$	$17.484$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None	None	$0$	$-30$	$-56$	$464$		$q+(-1+\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(-6+6\beta _{3}+\cdots)q^{5}+\cdots$
76.7.j.a	$60$	$17.484$		None	None	$0$	$30$	$0$	$-216$
76.7.l.a	$348$	$17.484$		None	None	$-6$	$0$	$-12$	$0$
76.8.a.a	$5$	$23.741$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	None	$0$	$-14$	$-280$	$414$	$-$	$q+(-3-\beta _{1})q^{3}+(-56+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
76.8.a.b	$6$	$23.741$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	None	$0$	$40$	$279$	$-1565$	$+$	$q+(7-\beta _{1})q^{3}+(47-\beta _{1}-\beta _{2})q^{5}+(-262+\cdots)q^{7}+\cdots$
76.8.d.a	$68$	$23.741$		None	None	$0$	$0$	$-4$	$0$
76.8.e.a	$22$	$23.741$		None	None	$0$	$13$	$1$	$560$
76.8.f.a	$136$	$23.741$		None	None	$-3$	$0$	$-2$	$0$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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
76.1.c.a	\(1\)	\(0.038\)	\(\Q\)	\(\Q(\sqrt{-19}) \)	None	\(0\)	\(0\)	\(-1\)	\(-1\)		\(q-q^{5}-q^{7}+q^{9}-q^{11}-q^{17}+q^{19}+\cdots\)
76.2.a.a	\(1\)	\(0.607\)	\(\Q\)	None	None	\(0\)	\(2\)	\(-1\)	\(-3\)	\(-\)	\(q+2q^{3}-q^{5}-3q^{7}+q^{9}+5q^{11}+\cdots\)
76.2.d.a	\(8\)	\(0.607\)	8.0.\(\cdots\).1	None	None	\(0\)	\(0\)	\(-4\)	\(0\)		\(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
76.2.e.a	\(2\)	\(0.607\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(1\)	\(1\)	\(0\)		\(q+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
76.2.f.a	\(16\)	\(0.607\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	None	\(-3\)	\(0\)	\(-2\)	\(0\)		\(q+(-\beta _{1}-\beta _{14})q^{2}+\beta _{15}q^{3}+(-1+\cdots)q^{4}+\cdots\)
76.2.i.a	\(12\)	\(0.607\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	None	\(0\)	\(-3\)	\(0\)	\(3\)		\(q+(-1-\beta _{5}+\beta _{7}+\beta _{9}+\beta _{11})q^{3}+\cdots\)
76.2.k.a	\(48\)	\(0.607\)		None	None	\(-6\)	\(0\)	\(-12\)	\(0\)
76.3.b.a	\(4\)	\(2.071\)	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None	None	\(-4\)	\(0\)	\(-4\)	\(0\)		\(q+(-1-\beta _{1})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-2+\cdots)q^{4}+\cdots\)
76.3.b.b	\(14\)	\(2.071\)	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	None	\(2\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{3}q^{2}-\beta _{7}q^{3}+\beta _{5}q^{4}+\beta _{12}q^{5}+\cdots\)
76.3.c.a	\(2\)	\(2.071\)	\(\Q(\sqrt{-29}) \)	None	None	\(0\)	\(0\)	\(-8\)	\(-2\)		\(q+\beta q^{3}-4q^{5}-q^{7}-20q^{9}+14q^{11}+\cdots\)
76.3.c.b	\(2\)	\(2.071\)	\(\Q(\sqrt{57}) \)	\(\Q(\sqrt{-19}) \)	None	\(0\)	\(0\)	\(9\)	\(5\)		\(q+(5-\beta )q^{5}+(1+3\beta )q^{7}+9q^{9}+(1+\cdots)q^{11}+\cdots\)
76.3.g.a	\(4\)	\(2.071\)	\(\Q(\sqrt{-3}, \sqrt{-10})\)	None	None	\(-4\)	\(6\)	\(-4\)	\(0\)		\(q-2\beta _{2}q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(-4+\cdots)q^{4}+\cdots\)
76.3.g.b	\(4\)	\(2.071\)	\(\Q(\sqrt{-3}, \sqrt{-10})\)	None	None	\(8\)	\(-6\)	\(-4\)	\(0\)		\(q+2q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+4q^{4}+\cdots\)
76.3.g.c	\(28\)	\(2.071\)		None	None	\(-5\)	\(0\)	\(6\)	\(0\)
76.3.h.a	\(8\)	\(2.071\)	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	None	\(0\)	\(6\)	\(-1\)	\(-12\)		\(q+(-\beta _{3}-\beta _{4})q^{3}+(\beta _{5}-\beta _{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
76.3.j.a	\(18\)	\(2.071\)	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None	None	\(0\)	\(-6\)	\(0\)	\(9\)		\(q+(-\beta _{4}-\beta _{6}-\beta _{8}-\beta _{10}+\beta _{12})q^{3}+\cdots\)
76.3.l.a	\(108\)	\(2.071\)		None	None	\(-6\)	\(0\)	\(-12\)	\(0\)
76.4.a.a	\(2\)	\(4.484\)	\(\Q(\sqrt{33}) \)	None	None	\(0\)	\(-5\)	\(-5\)	\(-30\)	\(-\)	\(q+(-2-\beta )q^{3}+(-5+5\beta )q^{5}+(-13+\cdots)q^{7}+\cdots\)
76.4.a.b	\(3\)	\(4.484\)	3.3.35529.1	None	None	\(0\)	\(1\)	\(9\)	\(44\)	\(+\)	\(q+(\beta _{1}+\beta _{2})q^{3}+(3+\beta _{2})q^{5}+(15-\beta _{1}+\cdots)q^{7}+\cdots\)
76.4.d.a	\(28\)	\(4.484\)		None	None	\(0\)	\(0\)	\(-4\)	\(0\)
76.4.e.a	\(10\)	\(4.484\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	None	\(0\)	\(7\)	\(-4\)	\(-20\)		\(q+(-\beta _{1}-\beta _{2}-\beta _{3})q^{3}+(\beta _{3}+\beta _{7}+\beta _{8}+\cdots)q^{5}+\cdots\)
76.4.f.a	\(56\)	\(4.484\)		None	None	\(-3\)	\(0\)	\(-2\)	\(0\)
76.4.i.a	\(30\)	\(4.484\)		None	None	\(0\)	\(-3\)	\(0\)	\(6\)
76.4.k.a	\(168\)	\(4.484\)		None	None	\(-6\)	\(0\)	\(-12\)	\(0\)
76.5.b.a	\(36\)	\(7.856\)		None	None	\(6\)	\(0\)	\(24\)	\(0\)
76.5.c.a	\(2\)	\(7.856\)	\(\Q(\sqrt{57}) \)	\(\Q(\sqrt{-19}) \)	None	\(0\)	\(0\)	\(-31\)	\(73\)		\(q+(-17-3\beta )q^{5}+(39+5\beta )q^{7}+3^{4}q^{9}+\cdots\)
76.5.c.b	\(4\)	\(7.856\)	\(\mathbb{Q}[x]/(x^{4} + \cdots)\)	None	None	\(0\)	\(0\)	\(22\)	\(24\)		\(q+\beta _{1}q^{3}+(6-\beta _{2})q^{5}+(7-2\beta _{2})q^{7}+\cdots\)
76.5.g.a	\(76\)	\(7.856\)		None	None	\(-1\)	\(0\)	\(-2\)	\(0\)
76.5.h.a	\(12\)	\(7.856\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	None	\(0\)	\(-12\)	\(9\)	\(-52\)		\(q+(-\beta _{1}+\beta _{3})q^{3}+(1-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
76.5.j.a	\(42\)	\(7.856\)		None	None	\(0\)	\(12\)	\(0\)	\(-45\)
76.5.l.a	\(228\)	\(7.856\)		None	None	\(-6\)	\(0\)	\(-12\)	\(0\)
76.6.a.a	\(3\)	\(12.189\)	3.3.272193.1	None	None	\(0\)	\(-8\)	\(-9\)	\(-13\)	\(+\)	\(q+(-3-\beta _{1}-\beta _{2})q^{3}+(-2+3\beta _{1}+\cdots)q^{5}+\cdots\)
76.6.a.b	\(4\)	\(12.189\)	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	None	\(0\)	\(10\)	\(-110\)	\(30\)	\(-\)	\(q+(3+\beta _{3})q^{3}+(-26+\beta _{1}+2\beta _{2}+3\beta _{3})q^{5}+\cdots\)
76.6.d.a	\(48\)	\(12.189\)		None	None	\(0\)	\(0\)	\(-4\)	\(0\)
76.6.e.a	\(18\)	\(12.189\)	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	None	\(0\)	\(-11\)	\(11\)	\(336\)		\(q+(\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(\beta _{2}+\beta _{6}+\beta _{8}+\cdots)q^{5}+\cdots\)
76.6.f.a	\(96\)	\(12.189\)		None	None	\(-3\)	\(0\)	\(-2\)	\(0\)
76.6.i.a	\(48\)	\(12.189\)		None	None	\(0\)	\(33\)	\(0\)	\(-177\)
76.6.k.a	\(288\)	\(12.189\)		None	None	\(-6\)	\(0\)	\(-12\)	\(0\)
76.7.b.a	\(54\)	\(17.484\)		None	None	\(-10\)	\(0\)	\(-44\)	\(0\)
76.7.c.a	\(2\)	\(17.484\)	\(\Q(\sqrt{57}) \)	\(\Q(\sqrt{-19}) \)	None	\(0\)	\(0\)	\(54\)	\(-610\)		\(q+(3^{3}+7\beta )q^{5}+(-305+9\beta )q^{7}+3^{6}q^{9}+\cdots\)
76.7.c.b	\(8\)	\(17.484\)	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None	None	\(0\)	\(0\)	\(2\)	\(362\)		\(q+\beta _{1}q^{3}+\beta _{7}q^{5}+(46+\beta _{2}+2\beta _{3}+\cdots)q^{7}+\cdots\)
76.7.g.a	\(116\)	\(17.484\)		None	None	\(-1\)	\(0\)	\(-2\)	\(0\)
76.7.h.a	\(20\)	\(17.484\)	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None	None	\(0\)	\(-30\)	\(-56\)	\(464\)		\(q+(-1+\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(-6+6\beta _{3}+\cdots)q^{5}+\cdots\)
76.7.j.a	\(60\)	\(17.484\)		None	None	\(0\)	\(30\)	\(0\)	\(-216\)
76.7.l.a	\(348\)	\(17.484\)		None	None	\(-6\)	\(0\)	\(-12\)	\(0\)
76.8.a.a	\(5\)	\(23.741\)	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	None	\(0\)	\(-14\)	\(-280\)	\(414\)	\(-\)	\(q+(-3-\beta _{1})q^{3}+(-56+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
76.8.a.b	\(6\)	\(23.741\)	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	None	\(0\)	\(40\)	\(279\)	\(-1565\)	\(+\)	\(q+(7-\beta _{1})q^{3}+(47-\beta _{1}-\beta _{2})q^{5}+(-262+\cdots)q^{7}+\cdots\)
76.8.d.a	\(68\)	\(23.741\)		None	None	\(0\)	\(0\)	\(-4\)	\(0\)
76.8.e.a	\(22\)	\(23.741\)		None	None	\(0\)	\(13\)	\(1\)	\(560\)
76.8.f.a	\(136\)	\(23.741\)		None	None	\(-3\)	\(0\)	\(-2\)	\(0\)

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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.