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 187 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
351.1.d.a	$351$	$1$	351.d	39.d	$2$	$1$	$1$	$0.175$	$\Q$	$D_{3}$	$\Q(\sqrt{-39}) $	None	✓	✓			351.1.d.a	$2$	$0$	$-1$	$0$	$-1$	$0$		$1$		$q-q^{2}-q^{5}+q^{8}+q^{10}+2q^{11}+q^{13}+\cdots$
351.1.d.b	$351$	$1$	351.d	39.d	$2$	$1$	$1$	$0.175$	$\Q$	$D_{3}$	$\Q(\sqrt{-39}) $	None	✓	✓			351.1.d.a	$2$	$0$	$1$	$0$	$1$	$0$		$1$		$q+q^{2}+q^{5}-q^{8}+q^{10}-2q^{11}+q^{13}+\cdots$
351.1.d.c	$351$	$1$	351.d	39.d	$2$	$2$	$2$	$0.175$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-39}) $	None	✓	✓	✓		351.1.d.c	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{2}+2q^{4}+\beta q^{5}-\beta q^{8}-3q^{10}+\cdots$
351.1.o.a	$351$	$1$	351.o	39.h	$6$	$2$	$1$	$0.175$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	351.1.o.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{6}q^{4}-q^{13}+\zeta_{6}^{2}q^{16}+(1-\zeta_{6}^{2}+\cdots)q^{19}+\cdots$
351.1.p.a	$351$	$1$	351.p	39.i	$6$	$2$	$1$	$0.175$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	351.1.p.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\zeta_{6}q^{4}-\zeta_{6}q^{7}+q^{13}+\zeta_{6}^{2}q^{16}+\cdots$
351.1.bg.a	$351$	$1$	351.bg	13.f	$12$	$4$	$1$	$0.175$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		✓	✓	✓	351.1.bg.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+\zeta_{12}^{5}q^{4}+(\zeta_{12}^{2}-\zeta_{12}^{5})q^{7}+\zeta_{12}^{3}q^{13}+\cdots$
351.2.a.a	$351$	$2$	351.a	1.a	$1$	$2$	$2$	$2.803$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓	✓	✓	351.2.a.a	$1$	$1$	$-1$	$0$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+(-1-\beta )q^{5}+\cdots$
351.2.a.b	$351$	$2$	351.a	1.a	$1$	$2$	$2$	$2.803$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	✓	✓	✓	351.2.a.b	$1$	$1$	$-1$	$0$	$-5$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(1+\beta )q^{4}+(-3+\beta )q^{5}-q^{7}+\cdots$
351.2.a.c	$351$	$2$	351.a	1.a	$1$	$2$	$2$	$2.803$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	✓			351.2.a.a	$1$	$0$	$1$	$0$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+(1+\beta )q^{5}+(-1+\cdots)q^{7}+\cdots$
351.2.a.d	$351$	$2$	351.a	1.a	$1$	$2$	$2$	$2.803$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	✓			351.2.a.b	$1$	$0$	$1$	$0$	$5$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{4}+(3-\beta )q^{5}-q^{7}+\cdots$
351.2.a.e	$351$	$2$	351.a	1.a	$1$	$4$	$4$	$2.803$	4.4.65712.1	$_{}$	None	None	✓	✓	✓		351.2.a.e	$2$	$0$	$0$	$0$	$0$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{3}q^{5}+2q^{7}+\cdots$
351.2.a.f	$351$	$2$	351.a	1.a	$1$	$4$	$4$	$2.803$	4.4.7600.1	$_{}$	None	None	✓	✓	✓		351.2.a.f	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots$
351.2.b.a	$351$	$2$	351.b	13.b	$2$	$2$	$2$	$2.803$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			351.2.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+2 q^{4}+(2\beta-1)q^{7}+(\beta-3)q^{13}+\cdots$
351.2.b.b	$351$	$2$	351.b	13.b	$2$	$4$	$4$	$2.803$	4.0.8112.1	$_{}$	$\Q(\sqrt{-39}) $	None		✓			351.2.b.b	$4$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+(-4+\beta _{3})q^{4}+\beta _{2}q^{5}+(-2\beta _{1}+\cdots)q^{8}+\cdots$
351.2.b.c	$351$	$2$	351.b	13.b	$2$	$4$	$4$	$2.803$	4.0.8112.1	$_{}$	$\Q(\sqrt{-39}) $	None		✓			351.2.b.c	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-\beta _{3}q^{5}+\beta _{3}q^{8}+\cdots$
351.2.b.d	$351$	$2$	351.b	13.b	$2$	$4$	$4$	$2.803$	4.0.8112.1	$_{}$	None	None		✓			351.2.b.d	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots$
351.2.b.e	$351$	$2$	351.b	13.b	$2$	$4$	$4$	$2.803$	4.0.8112.1	$_{}$	None	None		✓			351.2.b.d	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots$
351.2.e.a	$351$	$2$	351.e	9.c	$3$	$2$	$1$	$2.803$	$\Q(\sqrt{-3}) $	$_{}$	None	None					117.2.e.a	$2$	$0$	$2$	$0$	$4$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+4\zeta_{6}q^{5}+\cdots$
351.2.e.b	$351$	$2$	351.e	9.c	$3$	$10$	$5$	$2.803$	10.0.$\cdots$.1	$_{}$	None	None					117.2.e.b	$2$	$0$	$2$	$0$	$1$	$2$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{9}q^{2}+(-\beta _{1}+\beta _{6}-\beta _{9})q^{4}+(\beta _{4}+\cdots)q^{5}+\cdots$
351.2.e.c	$351$	$2$	351.e	9.c	$3$	$12$	$6$	$2.803$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None			✓		117.2.e.c	$2$	$0$	$-2$	$0$	$-3$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}+(-1+\beta _{1}-\beta _{5}+\beta _{7}-\beta _{8}+\cdots)q^{4}+\cdots$
351.2.f.a	$351$	$2$	351.f	117.f	$3$	$24$	$12$	$2.803$		$_{}$	None	None			✓	✓	117.2.f.a	$2$	$0$	$-1$	$0$	$2$	$-6$			$\mathrm{SU}(2)[C_{3}]$
351.2.g.a	$351$	$2$	351.g	13.c	$3$	$2$	$1$	$2.803$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			351.2.g.a	$2$	$1$	$-2$	$0$	$-4$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-2q^{5}+\cdots$
351.2.g.b	$351$	$2$	351.g	13.c	$3$	$2$	$1$	$2.803$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			351.2.g.b	$4$	$0$	$0$	$0$	$0$	$1$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+2\zeta_{6}q^{4}+\zeta_{6}q^{7}+(1+3\zeta_{6})q^{13}+\cdots$
351.2.g.c	$351$	$2$	351.g	13.c	$3$	$2$	$1$	$2.803$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			351.2.g.a	$2$	$0$	$2$	$0$	$4$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+2q^{5}+\zeta_{6}q^{7}+\cdots$
351.2.g.d	$351$	$2$	351.g	13.c	$3$	$10$	$5$	$2.803$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		✓			351.2.g.d	$2$	$0$	$0$	$0$	$-2$	$-3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-1+\beta _{6}+\beta _{8})q^{4}+\beta _{3}q^{5}+\cdots$
351.2.g.e	$351$	$2$	351.g	13.c	$3$	$10$	$5$	$2.803$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		✓			351.2.g.d	$2$	$0$	$0$	$0$	$2$	$-3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-1+\beta _{6}+\beta _{8})q^{4}-\beta _{3}q^{5}+\cdots$
351.2.g.f	$351$	$2$	351.g	13.c	$3$	$12$	$6$	$2.803$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓	✓		351.2.g.f	$4$	$0$	$0$	$0$	$0$	$-4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-\beta _{2}+\beta _{5}+\beta _{6})q^{4}+(-\beta _{8}+\cdots)q^{5}+\cdots$
351.2.h.a	$351$	$2$	351.h	117.h	$3$	$24$	$12$	$2.803$		$_{}$	None	None			✓	✓	117.2.f.a	$2$	$0$	$2$	$0$	$2$	$3$			$\mathrm{SU}(2)[C_{3}]$
351.2.i.a	$351$	$2$	351.i	39.f	$4$	$4$	$2$	$2.803$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-3}) $	None		✓			351.2.i.a	$4$	$0$	$0$	$0$	$0$	$2$		$3^{2}$	$\mathrm{U}(1)[D_{4}]$	$q+2\beta_1 q^{4}+(\beta_{3}-\beta_{2}-\beta_1+1)q^{7}+\cdots$
351.2.i.b	$351$	$2$	351.i	39.f	$4$	$16$	$8$	$2.803$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓			351.2.i.b	$4$	$0$	$0$	$0$	$0$	$-8$		$2^{12}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{7}q^{2}+(-\beta _{2}-\beta _{3}-2\beta _{9})q^{4}-\beta _{13}q^{5}+\cdots$
351.2.i.c	$351$	$2$	351.i	39.f	$4$	$16$	$8$	$2.803$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			351.2.i.c	$4$	$0$	$0$	$0$	$0$	$4$		$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{6}q^{2}-\beta _{14}q^{4}-\beta _{15}q^{5}+\beta _{13}q^{7}+\cdots$
351.2.l.a	$351$	$2$	351.l	117.l	$6$	$2$	$1$	$2.803$	$\Q(\sqrt{-3}) $	$_{}$	None	None					117.2.l.a	$2$	$0$	$0$	$0$	$-3$	$3$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+2\zeta_{6})q^{2}-q^{4}+(-1-\zeta_{6})q^{5}+\cdots$
351.2.l.b	$351$	$2$	351.l	117.l	$6$	$22$	$11$	$2.803$		$_{}$	None	None			✓		117.2.l.b	$2$	$0$	$0$	$0$	$3$	$-6$			$\mathrm{SU}(2)[C_{6}]$
351.2.q.a	$351$	$2$	351.q	13.e	$6$	$2$	$1$	$2.803$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			351.2.q.a	$2$	$1$	$-3$	$0$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+(2-4\zeta_{6})q^{5}+\cdots$
351.2.q.b	$351$	$2$	351.q	13.e	$6$	$2$	$1$	$2.803$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			351.2.q.b	$2$	$1$	$-3$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+(-2+4\zeta_{6})q^{5}+\cdots$
351.2.q.c	$351$	$2$	351.q	13.e	$6$	$2$	$1$	$2.803$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		✓			351.2.q.c	$4$	$1$	$0$	$0$	$0$	$-9$		$1$	$\mathrm{U}(1)[D_{6}]$	$q-2\zeta_{6}q^{4}+(-6+3\zeta_{6})q^{7}+(-1-3\zeta_{6})q^{13}+\cdots$
351.2.q.d	$351$	$2$	351.q	13.e	$6$	$2$	$1$	$2.803$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			351.2.q.a	$2$	$0$	$3$	$0$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+(-2+4\zeta_{6})q^{5}+\cdots$
351.2.q.e	$351$	$2$	351.q	13.e	$6$	$2$	$1$	$2.803$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			351.2.q.b	$2$	$0$	$3$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+(2-4\zeta_{6})q^{5}+\cdots$
351.2.q.f	$351$	$2$	351.q	13.e	$6$	$4$	$2$	$2.803$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		✓			351.2.q.f	$4$	$0$	$0$	$0$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}-\beta _{3}q^{5}+(2-\beta _{2})q^{7}-2\beta _{3}q^{8}+\cdots$
351.2.q.g	$351$	$2$	351.q	13.e	$6$	$8$	$4$	$2.803$	8.0.142635249.1	$_{}$	None	None		✓			351.2.q.g	$2$	$0$	$-3$	$0$	$0$	$3$		$3$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{5}+\beta _{7})q^{2}+(1-\beta _{1}+2\beta _{2}-2\beta _{4}+\cdots)q^{4}+\cdots$
351.2.q.h	$351$	$2$	351.q	13.e	$6$	$8$	$4$	$2.803$	8.0.$\cdots$.51	$_{}$	None	None		✓			351.2.q.h	$4$	$0$	$0$	$0$	$0$	$12$		$3$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}-\beta _{3})q^{2}+(-2\beta _{5}-\beta _{6})q^{4}+\beta _{3}q^{5}+\cdots$
351.2.q.i	$351$	$2$	351.q	13.e	$6$	$8$	$4$	$2.803$	8.0.142635249.1	$_{}$	None	None		✓			351.2.q.g	$2$	$0$	$3$	$0$	$0$	$3$		$3$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{5}-\beta _{7})q^{2}+(1-\beta _{1}+2\beta _{2}-2\beta _{4}+\cdots)q^{4}+\cdots$
351.2.r.a	$351$	$2$	351.r	117.r	$6$	$2$	$1$	$2.803$	$\Q(\sqrt{-3}) $	$_{}$	None	None					117.2.l.a	$2$	$0$	$3$	$0$	$3$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(2-\zeta_{6})q^{2}+(1-\zeta_{6})q^{4}+(2-\zeta_{6})q^{5}+\cdots$
351.2.r.b	$351$	$2$	351.r	117.r	$6$	$22$	$11$	$2.803$		$_{}$	None	None			✓		117.2.l.b	$2$	$0$	$0$	$0$	$-3$	$0$			$\mathrm{SU}(2)[C_{6}]$
351.2.t.a	$351$	$2$	351.t	117.t	$6$	$2$	$1$	$2.803$	$\Q(\sqrt{-3}) $	$_{}$	None	None					117.2.t.a	$2$	$0$	$0$	$0$	$-6$	$6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-2+2\zeta_{6})q^{4}+(-2-2\zeta_{6})q^{5}+\cdots$
351.2.t.b	$351$	$2$	351.t	117.t	$6$	$2$	$1$	$2.803$	$\Q(\sqrt{-3}) $	$_{}$	None	None					117.2.t.a	$2$	$0$	$0$	$0$	$6$	$-6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-2+2\zeta_{6})q^{4}+(2+2\zeta_{6})q^{5}+(-4+\cdots)q^{7}+\cdots$
351.2.t.c	$351$	$2$	351.t	117.t	$6$	$20$	$10$	$2.803$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None			✓		117.2.t.c	$4$	$0$	$0$	$0$	$0$	$0$		$3^{9}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{15}q^{2}+(\beta _{5}+\beta _{8})q^{4}-\beta _{4}q^{5}+(\beta _{12}+\cdots)q^{7}+\cdots$
351.2.w.a	$351$	$2$	351.w	27.e	$9$	$6$	$1$	$2.803$	$\Q(\zeta_{18})$	$_{}$	None	None		✓			351.2.w.a	$2$	$0$	$3$	$0$	$6$	$-6$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(1+\zeta_{18}^{2}-\zeta_{18}^{3}-\zeta_{18}^{5})q^{2}+(1+\cdots)q^{3}+\cdots$
351.2.w.b	$351$	$2$	351.w	27.e	$9$	$102$	$17$	$2.803$		$_{}$	None	None		✓			351.2.w.b	$2$	$0$	$-3$	$0$	$-9$	$6$			$\mathrm{SU}(2)[C_{9}]$
351.2.w.c	$351$	$2$	351.w	27.e	$9$	$108$	$18$	$2.803$		$_{}$	None	None		✓	✓		351.2.w.c	$2$	$0$	$0$	$0$	$-3$	$0$			$\mathrm{SU}(2)[C_{9}]$

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 187 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.