LMFDB - Newform search results

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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (1-50 of 125 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
87.1.d.a	$87$	$1$	87.d	87.d	$2$	$1$	$1$	$0.043$	$\Q$	$D_{3}$	$\Q(\sqrt{-87}) $	None	✓	✓			87.1.d.a	$2$	$0$	$-1$	$1$	$0$	$-1$		$1$		$q-q^{2}+q^{3}-q^{6}-q^{7}+q^{8}+q^{9}+\cdots$
87.1.d.b	$87$	$1$	87.d	87.d	$2$	$1$	$1$	$0.043$	$\Q$	$D_{3}$	$\Q(\sqrt{-87}) $	None	✓	✓			87.1.d.a	$2$	$0$	$1$	$-1$	$0$	$-1$		$1$		$q+q^{2}-q^{3}-q^{6}-q^{7}-q^{8}+q^{9}+\cdots$
87.2.a.a	$87$	$2$	87.a	1.a	$1$	$2$	$2$	$0.695$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓	✓	✓	87.2.a.a	$1$	$0$	$1$	$2$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(2-2\beta )q^{5}+\cdots$
87.2.a.b	$87$	$2$	87.a	1.a	$1$	$3$	$3$	$0.695$	3.3.229.1	$_{}$	None	None	✓	✓	✓	✓	87.2.a.b	$1$	$0$	$2$	$-3$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}-q^{3}+(2+\beta _{1})q^{4}-2\beta _{1}q^{5}+\cdots$
87.2.c.a	$87$	$2$	87.c	29.b	$2$	$4$	$4$	$0.695$	$\Q(i, \sqrt{5})$	$_{}$	None	None		✓	✓	✓	87.2.c.a	$2$	$0$	$0$	$0$	$4$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}-2\beta _{2}q^{5}+\cdots$
87.2.f.a	$87$	$2$	87.f	87.f	$4$	$4$	$2$	$0.695$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			87.2.f.a	$2$	$0$	$-2$	$0$	$8$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(-\zeta_{12}+2\zeta_{12}^{3})q^{3}+\cdots$
87.2.f.b	$87$	$2$	87.f	87.f	$4$	$4$	$2$	$0.695$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			87.2.f.a	$2$	$0$	$2$	$6$	$-8$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(1+\cdots)q^{3}+\cdots$
87.2.f.c	$87$	$2$	87.f	87.f	$4$	$8$	$4$	$0.695$	8.0.1871773696.1	$_{}$	None	None		✓	✓		87.2.f.c	$4$	$0$	$0$	$-8$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2}+\beta _{3})q^{3}+(2\beta _{3}+\cdots)q^{4}+\cdots$
87.2.g.a	$87$	$2$	87.g	29.d	$7$	$18$	$3$	$0.695$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		✓			87.2.g.a	$2$	$0$	$-4$	$-3$	$-1$	$-4$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(-\beta _{3}+\beta _{9})q^{2}-\beta _{10}q^{3}+(2\beta _{1}+\beta _{5}+\cdots)q^{4}+\cdots$
87.2.g.b	$87$	$2$	87.g	29.d	$7$	$18$	$3$	$0.695$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		✓			87.2.g.b	$2$	$0$	$-2$	$3$	$-7$	$-4$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q-\beta _{3}q^{2}+\beta _{14}q^{3}+(-\beta _{10}-\beta _{16}+\cdots)q^{4}+\cdots$
87.2.i.a	$87$	$2$	87.i	29.e	$14$	$24$	$4$	$0.695$		$_{}$	None	None		✓	✓	✓	87.2.i.a	$2$	$0$	$0$	$0$	$-4$	$8$			$\mathrm{SU}(2)[C_{14}]$
87.2.k.a	$87$	$2$	87.k	87.k	$28$	$96$	$8$	$0.695$		$_{}$	None	None		✓	✓	✓	87.2.k.a	$4$	$0$	$0$	$-12$	$0$	$-20$			$\mathrm{SU}(2)[C_{28}]$
87.3.b.a	$87$	$3$	87.b	3.b	$2$	$18$	$18$	$2.371$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None		✓	✓	✓	87.3.b.a	$2$	$0$	$0$	$-2$	$0$	$-12$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{9}q^{3}+(-2+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots$
87.3.d.a	$87$	$3$	87.d	87.d	$2$	$3$	$3$	$2.371$	3.3.2349.1	$_{}$	$\Q(\sqrt{-87}) $	None	✓	✓			87.3.d.a	$2$	$0$	$0$	$-9$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}-3q^{3}+(4+2\beta _{1}+\beta _{2})q^{4}+\cdots$
87.3.d.b	$87$	$3$	87.d	87.d	$2$	$3$	$3$	$2.371$	3.3.2349.1	$_{}$	$\Q(\sqrt{-87}) $	None	✓	✓			87.3.d.a	$2$	$0$	$0$	$9$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{2}+3q^{3}+(4+2\beta _{1}+\beta _{2})q^{4}+\cdots$
87.3.d.c	$87$	$3$	87.d	87.d	$2$	$12$	$12$	$2.371$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓	✓		87.3.d.c	$4$	$0$	$0$	$0$	$0$	$4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{2}+\beta _{6}q^{3}+\beta _{5}q^{4}-\beta _{9}q^{5}+\cdots$
87.3.e.a	$87$	$3$	87.e	29.c	$4$	$8$	$4$	$2.371$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		✓			87.3.e.a	$2$	$0$	$-8$	$0$	$0$	$12$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{2}+\beta _{3})q^{2}+\beta _{3}q^{3}+(\beta _{2}+\cdots)q^{4}+\cdots$
87.3.e.b	$87$	$3$	87.e	29.c	$4$	$12$	$6$	$2.371$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		✓	✓		87.3.e.b	$2$	$0$	$0$	$0$	$0$	$-12$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta _{3}-\beta _{6})q^{2}+\beta _{6}q^{3}+(\beta _{2}+\beta _{6}-3\beta _{7}+\cdots)q^{4}+\cdots$
87.3.h.a	$87$	$3$	87.h	87.h	$14$	$108$	$18$	$2.371$		$_{}$	None	None		✓	✓	✓	87.3.h.a	$4$	$0$	$0$	$-7$	$0$	$-18$			$\mathrm{SU}(2)[C_{14}]$
87.3.j.a	$87$	$3$	87.j	87.j	$14$	$108$	$18$	$2.371$		$_{}$	None	None		✓	✓	✓	87.3.j.a	$4$	$0$	$0$	$-5$	$0$	$-2$			$\mathrm{SU}(2)[C_{14}]$
87.3.l.a	$87$	$3$	87.l	29.f	$28$	$120$	$10$	$2.371$		$_{}$	None	None		✓	✓	✓	87.3.l.a	$2$	$0$	$8$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{28}]$
87.4.a.a	$87$	$4$	87.a	1.a	$1$	$2$	$2$	$5.133$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓	✓	✓	87.4.a.a	$1$	$1$	$-5$	$6$	$-11$	$-24$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-2-\beta )q^{2}+3q^{3}+5\beta q^{4}+(-4+\cdots)q^{5}+\cdots$
87.4.a.b	$87$	$4$	87.a	1.a	$1$	$2$	$2$	$5.133$	$\Q(\sqrt{41}) $	$_{}$	None	None	✓	✓	✓	✓	87.4.a.b	$1$	$1$	$-1$	$-6$	$-1$	$-24$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-3q^{3}+(2+\beta )q^{4}+(-2+3\beta )q^{5}+\cdots$
87.4.a.c	$87$	$4$	87.a	1.a	$1$	$5$	$5$	$5.133$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	87.4.a.c	$1$	$0$	$3$	$-15$	$-1$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-3q^{3}+(6-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
87.4.a.d	$87$	$4$	87.a	1.a	$1$	$5$	$5$	$5.133$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	87.4.a.d	$1$	$0$	$3$	$15$	$29$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+3q^{3}+(6+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
87.4.c.a	$87$	$4$	87.c	29.b	$2$	$16$	$16$	$5.133$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	✓	✓	87.4.c.a	$2$	$0$	$0$	$0$	$-28$	$40$		$2^{4}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-3+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots$
87.4.f.a	$87$	$4$	87.f	87.f	$4$	$56$	$28$	$5.133$		$_{}$	None	None		✓	✓	✓	87.4.f.a	$4$	$0$	$0$	$-2$	$0$	$-8$			$\mathrm{SU}(2)[C_{4}]$
87.4.g.a	$87$	$4$	87.g	29.d	$7$	$42$	$7$	$5.133$		$_{}$	None	None		✓			87.4.g.a	$2$	$0$	$-2$	$21$	$-47$	$20$			$\mathrm{SU}(2)[C_{7}]$
87.4.g.b	$87$	$4$	87.g	29.d	$7$	$42$	$7$	$5.133$		$_{}$	None	None		✓			87.4.g.b	$2$	$0$	$2$	$-21$	$31$	$20$			$\mathrm{SU}(2)[C_{7}]$
87.4.i.a	$87$	$4$	87.i	29.e	$14$	$96$	$16$	$5.133$		$_{}$	None	None		✓	✓	✓	87.4.i.a	$2$	$0$	$0$	$0$	$28$	$-40$			$\mathrm{SU}(2)[C_{14}]$
87.4.k.a	$87$	$4$	87.k	87.k	$28$	$336$	$28$	$5.133$		$_{}$	None	None		✓	✓	✓	87.4.k.a	$4$	$0$	$0$	$-12$	$0$	$-20$			$\mathrm{SU}(2)[C_{28}]$
87.5.b.a	$87$	$5$	87.b	3.b	$2$	$38$	$38$	$8.993$		$_{}$	None	None		✓	✓	✓	87.5.b.a	$2$	$0$	$0$	$-2$	$0$	$76$			$\mathrm{SU}(2)[C_{2}]$
87.5.d.a	$87$	$5$	87.d	87.d	$2$	$3$	$3$	$8.993$	3.3.2349.1	$_{}$	$\Q(\sqrt{-87}) $	None	✓	✓			87.5.d.a	$2$	$0$	$0$	$-27$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(-2\beta _{1}-\beta _{2})q^{2}-9q^{3}+(2^{4}+5\beta _{1}+\cdots)q^{4}+\cdots$
87.5.d.b	$87$	$5$	87.d	87.d	$2$	$3$	$3$	$8.993$	3.3.2349.1	$_{}$	$\Q(\sqrt{-87}) $	None	✓	✓			87.5.d.a	$2$	$0$	$0$	$27$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(2\beta _{1}+\beta _{2})q^{2}+9q^{3}+(2^{4}+5\beta _{1}+\cdots)q^{4}+\cdots$
87.5.d.c	$87$	$5$	87.d	87.d	$2$	$32$	$32$	$8.993$		$_{}$	None	None		✓	✓		87.5.d.c	$4$	$0$	$0$	$0$	$0$	$-84$			$\mathrm{SU}(2)[C_{2}]$
87.5.e.a	$87$	$5$	87.e	29.c	$4$	$40$	$20$	$8.993$		$_{}$	None	None		✓	✓	✓	87.5.e.a	$2$	$0$	$12$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
87.5.h.a	$87$	$5$	87.h	87.h	$14$	$228$	$38$	$8.993$		$_{}$	None	None		✓	✓	✓	87.5.h.a	$4$	$0$	$0$	$-7$	$0$	$70$			$\mathrm{SU}(2)[C_{14}]$
87.5.j.a	$87$	$5$	87.j	87.j	$14$	$228$	$38$	$8.993$		$_{}$	None	None		✓	✓	✓	87.5.j.a	$4$	$0$	$0$	$-5$	$0$	$-90$			$\mathrm{SU}(2)[C_{14}]$
87.5.l.a	$87$	$5$	87.l	29.f	$28$	$240$	$20$	$8.993$		$_{}$	None	None		✓	✓	✓	87.5.l.a	$2$	$0$	$-12$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{28}]$
87.6.a.a	$87$	$6$	87.a	1.a	$1$	$4$	$4$	$13.953$	4.4.8167381.1	$_{}$	None	None	✓	✓	✓	✓	87.6.a.a	$1$	$1$	$-3$	$36$	$-136$	$-28$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{2}+9q^{3}+(14+6\beta _{1}+\cdots)q^{4}+\cdots$
87.6.a.b	$87$	$6$	87.a	1.a	$1$	$5$	$5$	$13.953$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	87.6.a.b	$1$	$1$	$-9$	$-45$	$14$	$-68$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-2+\beta _{1})q^{2}-9q^{3}+(11-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$
87.6.a.c	$87$	$6$	87.a	1.a	$1$	$7$	$7$	$13.953$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	87.6.a.c	$1$	$0$	$13$	$63$	$64$	$168$	$-$	$2$	$\mathrm{SU}(2)$	$q+(2-\beta _{1})q^{2}+9q^{3}+(21-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
87.6.a.d	$87$	$6$	87.a	1.a	$1$	$8$	$8$	$13.953$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	87.6.a.d	$1$	$0$	$-1$	$-72$	$14$	$128$	$-$	$2\cdot 5$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-9q^{3}+(19+\beta _{1}+\beta _{2})q^{4}+\cdots$
87.6.c.a	$87$	$6$	87.c	29.b	$2$	$24$	$24$	$13.953$		$_{}$	None	None		✓	✓	✓	87.6.c.a	$2$	$0$	$0$	$0$	$-196$	$-120$			$\mathrm{SU}(2)[C_{2}]$
87.6.f.a	$87$	$6$	87.f	87.f	$4$	$96$	$48$	$13.953$		$_{}$	None	None		✓	✓	✓	87.6.f.a	$4$	$0$	$0$	$-2$	$0$	$-8$			$\mathrm{SU}(2)[C_{4}]$
87.6.g.a	$87$	$6$	87.g	29.d	$7$	$78$	$13$	$13.953$		$_{}$	None	None		✓			87.6.g.a	$2$	$0$	$2$	$-117$	$-17$	$-60$			$\mathrm{SU}(2)[C_{7}]$
87.6.g.b	$87$	$6$	87.g	29.d	$7$	$78$	$13$	$13.953$		$_{}$	None	None		✓			87.6.g.b	$2$	$0$	$10$	$117$	$49$	$-60$			$\mathrm{SU}(2)[C_{7}]$
87.6.i.a	$87$	$6$	87.i	29.e	$14$	$144$	$24$	$13.953$		$_{}$	None	None		✓	✓	✓	87.6.i.a	$2$	$0$	$0$	$0$	$196$	$120$			$\mathrm{SU}(2)[C_{14}]$
87.6.k.a	$87$	$6$	87.k	87.k	$28$	$576$	$48$	$13.953$		$_{}$	None	None		✓	✓	✓	87.6.k.a	$4$	$0$	$0$	$-12$	$0$	$-20$			$\mathrm{SU}(2)[C_{28}]$
87.7.b.a	$87$	$7$	87.b	3.b	$2$	$56$	$56$	$20.015$		$_{}$	None	None		✓	✓	✓	87.7.b.a	$2$	$0$	$0$	$52$	$0$	$160$			$\mathrm{SU}(2)[C_{2}]$

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Elliptic curves over $\Q$
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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.