LMFDB - Newform search results

Refine search

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

				Sort order	Select

Results (1-50 of 124 matches)

Next Download displayed columns for results to

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
285.1.n.a	$285$	$1$	285.n	285.n	$6$	$2$	$1$	$0.142$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-15}) $	None		✓			285.1.n.a	$4$	$0$	$-1$	$1$	$1$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{6}+\cdots$
285.1.n.b	$285$	$1$	285.n	285.n	$6$	$2$	$1$	$0.142$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-15}) $	None		✓			285.1.n.a	$4$	$0$	$1$	$-1$	$-1$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{6}+\cdots$
285.1.bd.a	$285$	$1$	285.bd	285.ad	$18$	$6$	$1$	$0.142$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-15}) $	None		✓			285.1.bd.a	$4$	$0$	$-3$	$0$	$0$	$0$		$1$		$q+(\zeta_{18}^{4}+\zeta_{18}^{6})q^{2}+\zeta_{18}^{2}q^{3}+(-\zeta_{18}+\cdots)q^{4}+\cdots$
285.1.bd.b	$285$	$1$	285.bd	285.ad	$18$	$6$	$1$	$0.142$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-15}) $	None		✓			285.1.bd.a	$4$	$0$	$3$	$0$	$0$	$0$		$1$		$q+(-\zeta_{18}^{4}-\zeta_{18}^{6})q^{2}-\zeta_{18}^{2}q^{3}+\cdots$
285.2.a.a	$285$	$2$	285.a	1.a	$1$	$1$	$1$	$2.276$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	285.2.a.a	$1$	$1$	$-1$	$1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}-2q^{7}+\cdots$
285.2.a.b	$285$	$2$	285.a	1.a	$1$	$1$	$1$	$2.276$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	285.2.a.b	$1$	$1$	$1$	$-1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}-2q^{7}+\cdots$
285.2.a.c	$285$	$2$	285.a	1.a	$1$	$1$	$1$	$2.276$	$\Q$	$_{}$	None	None	✓	✓			285.2.a.c	$1$	$0$	$1$	$-1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}+4q^{7}+\cdots$
285.2.a.d	$285$	$2$	285.a	1.a	$1$	$2$	$2$	$2.276$	$\Q(\sqrt{7}) $	$_{}$	None	None	✓	✓	✓		285.2.a.d	$1$	$0$	$0$	$-2$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+5q^{4}+q^{5}-\beta q^{6}+(-1+\cdots)q^{7}+\cdots$
285.2.a.e	$285$	$2$	285.a	1.a	$1$	$2$	$2$	$2.276$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓	✓	✓	285.2.a.e	$1$	$0$	$0$	$2$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+q^{4}+q^{5}+\beta q^{6}+(-1+\cdots)q^{7}+\cdots$
285.2.a.f	$285$	$2$	285.a	1.a	$1$	$2$	$2$	$2.276$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓	✓	✓	285.2.a.f	$1$	$0$	$2$	$-2$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}-q^{5}+\cdots$
285.2.a.g	$285$	$2$	285.a	1.a	$1$	$2$	$2$	$2.276$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓	✓	✓	285.2.a.g	$1$	$0$	$2$	$2$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}-q^{5}+\cdots$
285.2.b.a	$285$	$2$	285.b	285.b	$2$	$4$	$4$	$2.276$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	$\Q(\sqrt{-15}) $	None		✓			285.2.b.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}+\beta _{2}q^{3}-q^{4}-\beta _{1}q^{5}-3q^{6}+\cdots$
285.2.b.b	$285$	$2$	285.b	285.b	$2$	$16$	$16$	$2.276$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	$\Q(\sqrt{-95}) $	None		✓			285.2.b.b	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3^{3}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{9}q^{2}-\beta _{3}q^{3}+(-2+\beta _{7})q^{4}-\beta _{2}q^{5}+\cdots$
285.2.b.c	$285$	$2$	285.b	285.b	$2$	$16$	$16$	$2.276$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓			285.2.b.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{11}q^{2}-\beta _{12}q^{3}-\beta _{4}q^{4}+(-\beta _{5}+\cdots)q^{5}+\cdots$
285.2.c.a	$285$	$2$	285.c	5.b	$2$	$6$	$6$	$2.276$	6.0.350464.1	$_{}$	None	None		✓			285.2.c.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}-\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{4}+\cdots$
285.2.c.b	$285$	$2$	285.c	5.b	$2$	$14$	$14$	$2.276$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		✓	✓		285.2.c.b	$2$	$0$	$0$	$0$	$2$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{6}q^{3}+(-2+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots$
285.2.h.a	$285$	$2$	285.h	57.d	$2$	$28$	$28$	$2.276$		$_{}$	None	None		✓	✓	✓	285.2.h.a	$4$	$0$	$0$	$0$	$0$	$-16$			$\mathrm{SU}(2)[C_{2}]$
285.2.i.a	$285$	$2$	285.i	19.c	$3$	$2$	$1$	$2.276$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			285.2.i.a	$2$	$1$	$-2$	$-1$	$1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots$
285.2.i.b	$285$	$2$	285.i	19.c	$3$	$2$	$1$	$2.276$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			285.2.i.b	$2$	$0$	$0$	$-1$	$-1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots$
285.2.i.c	$285$	$2$	285.i	19.c	$3$	$2$	$1$	$2.276$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			285.2.i.c	$2$	$0$	$2$	$1$	$1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots$
285.2.i.d	$285$	$2$	285.i	19.c	$3$	$4$	$2$	$2.276$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		✓			285.2.i.d	$2$	$0$	$-2$	$2$	$2$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}-\beta _{2})q^{2}+(1+\beta _{2})q^{3}+\cdots$
285.2.i.e	$285$	$2$	285.i	19.c	$3$	$4$	$2$	$2.276$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		✓			285.2.i.e	$2$	$0$	$1$	$-2$	$2$	$12$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
285.2.i.f	$285$	$2$	285.i	19.c	$3$	$10$	$5$	$2.276$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		✓	✓		285.2.i.f	$2$	$0$	$1$	$5$	$-5$	$4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{2})q^{2}-\beta _{4}q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots$
285.2.k.a	$285$	$2$	285.k	15.e	$4$	$4$	$2$	$2.276$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			285.2.k.a	$2$	$1$	$-4$	$0$	$-4$	$-6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\zeta_{12}^{3})q^{2}+(1-2\zeta_{12}^{2})q^{3}+\cdots$
285.2.k.b	$285$	$2$	285.k	15.e	$4$	$4$	$2$	$2.276$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			285.2.k.a	$2$	$0$	$4$	$0$	$4$	$-6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\zeta_{12}^{3})q^{2}+(2\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots$
285.2.k.c	$285$	$2$	285.k	15.e	$4$	$28$	$14$	$2.276$		$_{}$	None	None		✓			285.2.k.c	$4$	$0$	$0$	$-2$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
285.2.k.d	$285$	$2$	285.k	15.e	$4$	$36$	$18$	$2.276$		$_{}$	None	None		✓	✓		285.2.k.d	$4$	$0$	$0$	$-2$	$0$	$4$			$\mathrm{SU}(2)[C_{4}]$
285.2.m.a	$285$	$2$	285.m	95.g	$4$	$4$	$2$	$2.276$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			285.2.m.a	$4$	$0$	$0$	$0$	$-4$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}-\zeta_{8}^{3}q^{3}-\zeta_{8}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots$
285.2.m.b	$285$	$2$	285.m	95.g	$4$	$36$	$18$	$2.276$		$_{}$	None	None		✓	✓		285.2.m.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
285.2.p.a	$285$	$2$	285.p	57.f	$6$	$4$	$2$	$2.276$	$\Q(\zeta_{12})$	$_{}$	None	None		✓			285.2.p.a	$4$	$0$	$0$	$6$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{12}-\zeta_{12}^{3})q^{2}+(2-\zeta_{12}^{2})q^{3}+\cdots$
285.2.p.b	$285$	$2$	285.p	57.f	$6$	$52$	$26$	$2.276$		$_{}$	None	None		✓	✓		285.2.p.b	$4$	$0$	$0$	$-12$	$0$	$12$			$\mathrm{SU}(2)[C_{6}]$
285.2.q.a	$285$	$2$	285.q	285.q	$6$	$4$	$2$	$2.276$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	$\Q(\sqrt{-15}) $	None		✓			285.2.q.a	$4$	$0$	$-3$	$6$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-\beta _{1}+\beta _{2})q^{2}+(2+\beta _{3})q^{3}+(1+3\beta _{1}+\cdots)q^{4}+\cdots$
285.2.q.b	$285$	$2$	285.q	285.q	$6$	$4$	$2$	$2.276$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	$\Q(\sqrt{-15}) $	None		✓			285.2.q.a	$4$	$0$	$3$	$-6$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(\beta _{1}-\beta _{2})q^{2}+(-2-\beta _{3})q^{3}+(1+3\beta _{1}+\cdots)q^{4}+\cdots$
285.2.q.c	$285$	$2$	285.q	285.q	$6$	$8$	$4$	$2.276$	8.0.3317760000.3	$_{}$	None	None		✓			285.2.q.c	$8$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{3}+(-2+2\beta _{3})q^{4}-\beta _{2}q^{5}+\cdots$
285.2.q.d	$285$	$2$	285.q	285.q	$6$	$56$	$28$	$2.276$		$_{}$	None	None		✓	✓		285.2.q.d	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
285.2.r.a	$285$	$2$	285.r	95.i	$6$	$40$	$20$	$2.276$		$_{}$	None	None		✓	✓	✓	285.2.r.a	$4$	$0$	$0$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{6}]$
285.2.u.a	$285$	$2$	285.u	19.e	$9$	$12$	$2$	$2.276$	12.0.$\cdots$.1	$_{}$	None	None		✓			285.2.u.a	$2$	$0$	$3$	$0$	$0$	$6$		$3$	$\mathrm{SU}(2)[C_{9}]$	$q+(1-\beta _{5}-\beta _{8}+\beta _{9}-\beta _{11})q^{2}+\beta _{10}q^{3}+\cdots$
285.2.u.b	$285$	$2$	285.u	19.e	$9$	$18$	$3$	$2.276$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		✓			285.2.u.b	$2$	$0$	$-3$	$0$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q-\beta _{4}q^{2}+\beta _{5}q^{3}+(-\beta _{2}-\beta _{5}-\beta _{8}+\cdots)q^{4}+\cdots$
285.2.u.c	$285$	$2$	285.u	19.e	$9$	$24$	$4$	$2.276$		$_{}$	None	None		✓			285.2.u.c	$2$	$0$	$0$	$0$	$0$	$-6$			$\mathrm{SU}(2)[C_{9}]$
285.2.u.d	$285$	$2$	285.u	19.e	$9$	$30$	$5$	$2.276$		$_{}$	None	None		✓	✓		285.2.u.d	$2$	$0$	$0$	$0$	$0$	$-6$			$\mathrm{SU}(2)[C_{9}]$
285.2.v.a	$285$	$2$	285.v	285.v	$12$	$144$	$36$	$2.276$		$_{}$	None	None		✓	✓	✓	285.2.v.a	$8$	$0$	$0$	$-2$	$0$	$-16$			$\mathrm{SU}(2)[C_{12}]$
285.2.x.a	$285$	$2$	285.x	95.l	$12$	$80$	$20$	$2.276$		$_{}$	None	None		✓	✓	✓	285.2.x.a	$4$	$0$	$0$	$0$	$4$	$8$			$\mathrm{SU}(2)[C_{12}]$
285.2.z.a	$285$	$2$	285.z	57.j	$18$	$156$	$26$	$2.276$		$_{}$	None	None		✓	✓	✓	285.2.z.a	$4$	$0$	$0$	$6$	$0$	$0$			$\mathrm{SU}(2)[C_{18}]$
285.2.be.a	$285$	$2$	285.be	95.p	$18$	$120$	$20$	$2.276$		$_{}$	None	None		✓	✓	✓	285.2.be.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{18}]$
285.2.bf.a	$285$	$2$	285.bf	285.af	$18$	$12$	$2$	$2.276$	12.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-15}) $	None		✓			285.2.bf.a	$4$	$0$	$-9$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{18}]$	$q+(-1+\beta _{4}-\beta _{5}-\beta _{6}+\beta _{11})q^{2}+\cdots$
285.2.bf.b	$285$	$2$	285.bf	285.af	$18$	$12$	$2$	$2.276$	12.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-15}) $	None		✓			285.2.bf.a	$4$	$0$	$9$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{18}]$	$q+(1-\beta _{4}-\beta _{5}-\beta _{6}-\beta _{8}-\beta _{10}+\beta _{11})q^{2}+\cdots$
285.2.bf.c	$285$	$2$	285.bf	285.af	$18$	$192$	$32$	$2.276$		$_{}$	None	None		✓	✓		285.2.bf.c	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{18}]$
285.2.bh.a	$285$	$2$	285.bh	95.r	$36$	$240$	$20$	$2.276$		$_{}$	None	None		✓	✓	✓	285.2.bh.a	$4$	$0$	$0$	$0$	$0$	$-12$			$\mathrm{SU}(2)[C_{36}]$
285.2.bi.a	$285$	$2$	285.bi	285.ai	$36$	$432$	$36$	$2.276$		$_{}$	None	None		✓	✓	✓	285.2.bi.a	$8$	$0$	$0$	$-12$	$0$	$-12$			$\mathrm{SU}(2)[C_{36}]$
285.3.d.a	$285$	$3$	285.d	3.b	$2$	$48$	$48$	$7.766$		$_{}$	None	None		✓	✓	✓	285.3.d.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

Next Download displayed columns for results to

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 124 matches)

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