LMFDB - Newform search results

Refine search

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.		Projective image	Projective image type
		Only for weight 1:

				Sort order	Select

Results (1-50 of 354 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	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
63.1.d.a	$63$	$1$	63.d	7.b	$2$	$1$	$1$	$0.031$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-7}) $	$\Q(\sqrt{21}) $	✓	$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q-q^{4}-q^{7}+q^{16}+q^{25}+q^{28}-2q^{37}+\cdots$
63.2.a.a	$63$	$2$	63.a	1.a	$1$	$1$	$1$	$0.503$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+2q^{5}-q^{7}-3q^{8}+2q^{10}+\cdots$
63.2.a.b	$63$	$2$	63.a	1.a	$1$	$2$	$2$	$0.503$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}-2\beta q^{5}+q^{7}-\beta q^{8}+\cdots$
63.2.c.a	$63$	$2$	63.c	21.c	$2$	$4$	$4$	$0.503$	$\Q(\sqrt{-2}, \sqrt{7})$	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}-\beta _{2}q^{7}+(-2\beta _{1}+\cdots)q^{8}+\cdots$
63.2.e.a	$63$	$2$	63.e	7.c	$3$	$2$	$1$	$0.503$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-1$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+2\zeta_{6}q^{4}+(1-3\zeta_{6})q^{7}-7q^{13}+(-4+\cdots)q^{16}+\cdots$
63.2.e.b	$63$	$2$	63.e	7.c	$3$	$2$	$1$	$0.503$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$2$	$0$	$-2$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{5}+\cdots$
63.2.f.a	$63$	$2$	63.f	9.c	$3$	$6$	$3$	$0.503$	$\Q(\zeta_{18})$	$_{}$	None	None		$2$	$0$	$-3$	$0$	$-3$	$-3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{18}+\zeta_{18}^{5})q^{2}+(-\zeta_{18}^{3}+\cdots)q^{3}+\cdots$
63.2.f.b	$63$	$2$	63.f	9.c	$3$	$6$	$3$	$0.503$	6.0.309123.1	$_{}$	None	None		$2$	$0$	$1$	$-4$	$5$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}+(\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots$
63.2.g.a	$63$	$2$	63.g	63.g	$3$	$2$	$1$	$0.503$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-1$	$-3$	$-2$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$
63.2.g.b	$63$	$2$	63.g	63.g	$3$	$10$	$5$	$0.503$	10.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$2$	$2$	$-8$	$-1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(\beta _{2}-\beta _{7})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
63.2.h.a	$63$	$2$	63.h	63.h	$3$	$2$	$1$	$0.503$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$2$	$0$	$1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(1-2\zeta_{6})q^{3}-q^{4}+\zeta_{6}q^{5}+\cdots$
63.2.h.b	$63$	$2$	63.h	63.h	$3$	$10$	$5$	$0.503$	10.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$-4$	$-1$	$4$	$-4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{5})q^{2}-\beta _{8}q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots$
63.2.i.a	$63$	$2$	63.i	63.i	$6$	$2$	$1$	$0.503$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-3$	$4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-2\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-q^{4}+\cdots$
63.2.i.b	$63$	$2$	63.i	63.i	$6$	$10$	$5$	$0.503$	10.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$-3$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{3}-\beta _{5})q^{2}+(\beta _{1}-\beta _{7})q^{3}+(-1+\cdots)q^{4}+\cdots$
63.2.o.a	$63$	$2$	63.o	63.o	$6$	$12$	$6$	$0.503$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$4$	$0$	$-6$	$0$	$0$	$-2$		$3$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{1}q^{2}-\beta _{2}q^{3}+(\beta _{1}+\beta _{4}+\beta _{7})q^{4}+\cdots$
63.2.p.a	$63$	$2$	63.p	21.g	$6$	$4$	$2$	$0.503$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(-\beta _{1}+2\beta _{3})q^{5}+(1-3\beta _{2}+\cdots)q^{7}+\cdots$
63.2.s.a	$63$	$2$	63.s	63.s	$6$	$2$	$1$	$0.503$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$-3$	$-3$	$-6$	$-5$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1-\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
63.2.s.b	$63$	$2$	63.s	63.s	$6$	$10$	$5$	$0.503$	10.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$3$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{4}+\beta _{7}+\beta _{8})q^{2}+(-\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{3}+\cdots$
63.3.b.a	$63$	$3$	63.b	3.b	$2$	$4$	$4$	$1.717$	$\Q(\sqrt{-2}, \sqrt{7})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+2\beta _{1}q^{5}+\beta _{2}q^{7}+\cdots$
63.3.d.a	$63$	$3$	63.d	7.b	$2$	$1$	$1$	$1.717$	$\Q$	$_{}$	$\Q(\sqrt{-7}) $	None	✓	$2$	$0$	$3$	$0$	$0$	$-7$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+3q^{2}+5q^{4}-7q^{7}+3q^{8}+6q^{11}+\cdots$
63.3.d.b	$63$	$3$	63.d	7.b	$2$	$2$	$2$	$1.717$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$2$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-3q^{4}-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots$
63.3.d.c	$63$	$3$	63.d	7.b	$2$	$2$	$2$	$1.717$	$\Q(\sqrt{7}) $	$_{}$	$\Q(\sqrt{-7}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$14$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{2}+3q^{4}+7q^{7}-\beta q^{8}-8\beta q^{11}+\cdots$
63.3.j.a	$63$	$3$	63.j	63.j	$6$	$6$	$3$	$1.717$	6.0.63369648.1	$_{}$	None	None		$2$	$0$	$0$	$18$	$-15$	$-2$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1-\beta _{4}-\beta _{5})q^{2}+3q^{3}+(-4+\cdots)q^{4}+\cdots$
63.3.j.b	$63$	$3$	63.j	63.j	$6$	$22$	$11$	$1.717$		$_{}$	None	None		$2$	$0$	$0$	$-19$	$12$	$0$			$\mathrm{SU}(2)[C_{6}]$
63.3.k.a	$63$	$3$	63.k	63.k	$6$	$28$	$14$	$1.717$		$_{}$	None	None		$2$	$0$	$1$	$-3$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
63.3.l.a	$63$	$3$	63.l	63.l	$6$	$28$	$14$	$1.717$		$_{}$	None	None		$4$	$0$	$-2$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
63.3.m.a	$63$	$3$	63.m	7.d	$6$	$2$	$1$	$1.717$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-2$	$0$	$6$	$-7$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-2\zeta_{6}q^{2}+(4-2\zeta_{6})q^{5}-7\zeta_{6}q^{7}+\cdots$
63.3.m.b	$63$	$3$	63.m	7.d	$6$	$2$	$1$	$1.717$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$13$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(4-4\zeta_{6})q^{4}+(8-3\zeta_{6})q^{7}+(-7+\cdots)q^{13}+\cdots$
63.3.m.c	$63$	$3$	63.m	7.d	$6$	$2$	$1$	$1.717$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$1$	$0$	$9$	$-7$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{4}+(6-3\zeta_{6})q^{5}+\cdots$
63.3.m.d	$63$	$3$	63.m	7.d	$6$	$2$	$1$	$1.717$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$3$	$0$	$-9$	$13$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+3\zeta_{6}q^{2}+(-5+5\zeta_{6})q^{4}+(-6+3\zeta_{6})q^{5}+\cdots$
63.3.m.e	$63$	$3$	63.m	7.d	$6$	$4$	$2$	$1.717$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-26$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{2}q^{2}+(-9+9\beta _{1})q^{4}+(\beta _{2}+2\beta _{3})q^{5}+\cdots$
63.3.n.a	$63$	$3$	63.n	63.n	$6$	$6$	$3$	$1.717$	6.0.63369648.1	$_{}$	None	None		$2$	$0$	$3$	$-9$	$0$	$-5$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(1+\beta _{5})q^{2}+3\beta _{2}q^{3}+(\beta _{1}-4\beta _{2}+\cdots)q^{4}+\cdots$
63.3.n.b	$63$	$3$	63.n	63.n	$6$	$22$	$11$	$1.717$		$_{}$	None	None		$2$	$0$	$-6$	$8$	$0$	$3$			$\mathrm{SU}(2)[C_{6}]$
63.3.q.a	$63$	$3$	63.q	21.h	$6$	$12$	$6$	$1.717$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-2$		$2^{4}\cdot 3^{5}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(-3\beta _{8}+\beta _{9})q^{4}-\beta _{6}q^{5}+\cdots$
63.3.r.a	$63$	$3$	63.r	9.d	$6$	$24$	$12$	$1.717$		$_{}$	None	None		$2$	$0$	$0$	$2$	$-18$	$0$			$\mathrm{SU}(2)[C_{6}]$
63.3.t.a	$63$	$3$	63.t	63.t	$6$	$28$	$14$	$1.717$		$_{}$	None	None		$2$	$0$	$-2$	$-3$	$-3$	$0$			$\mathrm{SU}(2)[C_{6}]$
63.4.a.a	$63$	$4$	63.a	1.a	$1$	$1$	$1$	$3.717$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-4$	$0$	$4$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{2}+8q^{4}+4q^{5}-7q^{7}-2^{4}q^{10}+\cdots$
63.4.a.b	$63$	$4$	63.a	1.a	$1$	$1$	$1$	$3.717$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$-16$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-7q^{4}-2^{4}q^{5}-7q^{7}-15q^{8}+\cdots$
63.4.a.c	$63$	$4$	63.a	1.a	$1$	$1$	$1$	$3.717$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$3$	$0$	$18$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{2}+q^{4}+18q^{5}+7q^{7}-21q^{8}+\cdots$
63.4.a.d	$63$	$4$	63.a	1.a	$1$	$2$	$2$	$3.717$	$\Q(\sqrt{19}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$-14$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+11q^{4}+2\beta q^{5}-7q^{7}+3\beta q^{8}+\cdots$
63.4.a.e	$63$	$4$	63.a	1.a	$1$	$2$	$2$	$3.717$	$\Q(\sqrt{57}) $	$_{}$	None	None	✓	$1$	$0$	$3$	$0$	$-6$	$14$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(7+3\beta )q^{4}+(-2-2\beta )q^{5}+\cdots$
63.4.c.a	$63$	$4$	63.c	21.c	$2$	$4$	$4$	$3.717$	$\Q(\sqrt{-2}, \sqrt{7})$	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}+(-8-5\beta _{3})q^{4}-7\beta _{3}q^{7}+\cdots$
63.4.c.b	$63$	$4$	63.c	21.c	$2$	$4$	$4$	$3.717$	$\Q(\sqrt{-2}, \sqrt{111})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-44$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta _{1}q^{2}+\beta _{3}q^{5}+(-11-\beta _{2})q^{7}+\cdots$
63.4.e.a	$63$	$4$	63.e	7.c	$3$	$2$	$1$	$3.717$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-3$	$0$	$-3$	$-7$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-3+3\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-3+3\zeta_{6})q^{5}+\cdots$
63.4.e.b	$63$	$4$	63.e	7.c	$3$	$2$	$1$	$3.717$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$2$	$0$	$7$	$28$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}+4\zeta_{6}q^{4}+(7-7\zeta_{6})q^{5}+\cdots$
63.4.e.c	$63$	$4$	63.e	7.c	$3$	$6$	$3$	$3.717$	6.0.9924270768.1	$_{}$	None	None		$2$	$0$	$1$	$0$	$11$	$-13$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-8+\beta _{1}+\beta _{2}+8\beta _{4}+\beta _{5})q^{4}+\cdots$
63.4.e.d	$63$	$4$	63.e	7.c	$3$	$8$	$4$	$3.717$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-12$		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+\beta _{3})q^{2}+(-2-2\beta _{2}-\beta _{6})q^{4}+\cdots$
63.4.f.a	$63$	$4$	63.f	9.c	$3$	$2$	$1$	$3.717$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$1$	$-9$	$14$	$7$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-6+3\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots$
63.4.f.b	$63$	$4$	63.f	9.c	$3$	$16$	$8$	$3.717$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$2$	$0$	$-3$	$2$	$-30$	$56$		$2^{2}\cdot 3^{7}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-\beta _{3}-\beta _{7})q^{3}+(5\beta _{3}-\beta _{5}+\cdots)q^{4}+\cdots$
63.4.f.c	$63$	$4$	63.f	9.c	$3$	$18$	$9$	$3.717$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		$2$	$0$	$6$	$9$	$24$	$-63$		$3^{10}$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{2}-\beta _{3}-\beta _{5})q^{2}+(1+\beta _{8})q^{3}+\cdots$

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 354 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.