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 247 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
39.1.d.a	$39$	$1$	39.d	39.d	$2$	$1$	$1$	$0.019$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-q^{3}-q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\cdots$
39.2.a.a	$39$	$2$	39.a	1.a	$1$	$1$	$1$	$0.311$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$-1$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}+2q^{5}-q^{6}-4q^{7}+\cdots$
39.2.a.b	$39$	$2$	39.a	1.a	$1$	$2$	$2$	$0.311$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$-2$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}-2\beta q^{5}+\cdots$
39.2.b.a	$39$	$2$	39.b	13.b	$2$	$2$	$2$	$0.311$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{6}q^{2}-q^{3}-q^{4}+\zeta_{6}q^{6}+2\zeta_{6}q^{7}+\cdots$
39.2.e.a	$39$	$2$	39.e	13.c	$3$	$2$	$1$	$0.311$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-1$	$1$	$-2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
39.2.e.b	$39$	$2$	39.e	13.c	$3$	$4$	$2$	$0.311$	$\Q(\sqrt{-3}, \sqrt{17})$	$_{}$	None	None		$2$	$0$	$-1$	$-2$	$-6$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}-\beta _{2}q^{3}+(-2+\beta _{1}+2\beta _{2}+\cdots)q^{4}+\cdots$
39.2.f.a	$39$	$2$	39.f	39.f	$4$	$4$	$2$	$0.311$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$-4$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}+(-1+\zeta_{8}+\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots$
39.2.j.a	$39$	$2$	39.j	13.e	$6$	$2$	$1$	$0.311$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$0$	$-3$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{4}+(-2+4\zeta_{6})q^{5}+\cdots$
39.2.k.a	$39$	$2$	39.k	39.k	$12$	$4$	$1$	$0.311$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-10$		$1$	$\mathrm{U}(1)[D_{12}]$	$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+2\zeta_{12}q^{4}+(-2+\cdots)q^{7}+\cdots$
39.2.k.b	$39$	$2$	39.k	39.k	$12$	$8$	$2$	$0.311$	8.0.56070144.2	$_{}$	None	None		$4$	$0$	$0$	$-2$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+2\beta _{5}+\beta _{7})q^{2}+\cdots$
39.3.c.a	$39$	$3$	39.c	3.b	$2$	$8$	$8$	$1.063$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$8$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+\beta _{3}q^{3}+(-2-\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots$
39.3.d.a	$39$	$3$	39.d	39.d	$2$	$2$	$2$	$1.063$	$\Q(\sqrt{13}) $	$_{}$	$\Q(\sqrt{-39}) $	None	✓	$4$	$0$	$0$	$-6$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{2}-3q^{3}+9q^{4}+2\beta q^{5}+3\beta q^{6}+\cdots$
39.3.d.b	$39$	$3$	39.d	39.d	$2$	$2$	$2$	$1.063$	$\Q(\sqrt{3}) $	$_{}$	$\Q(\sqrt{-39}) $	None	✓	$4$	$0$	$0$	$6$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{2}+3q^{3}-q^{4}-4\beta q^{5}+3\beta q^{6}+\cdots$
39.3.d.c	$39$	$3$	39.d	39.d	$2$	$4$	$4$	$1.063$	$\Q(\sqrt{3}, \sqrt{-35})$	$_{}$	None	None		$4$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(-1+\beta _{1})q^{3}-q^{4}-3\beta _{2}q^{5}+\cdots$
39.3.g.a	$39$	$3$	39.g	13.d	$4$	$8$	$4$	$1.063$	8.0.$\cdots$.10	$_{}$	None	None		$2$	$0$	$4$	$0$	$-20$	$8$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{4}q^{2}-\beta _{2}q^{3}+(-1-\beta _{1}-\beta _{4}+\cdots)q^{4}+\cdots$
39.3.h.a	$39$	$3$	39.h	39.h	$6$	$2$	$1$	$1.063$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-3$	$0$	$9$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-3+3\zeta_{6})q^{3}+4\zeta_{6}q^{4}+(6-3\zeta_{6})q^{7}+\cdots$
39.3.h.b	$39$	$3$	39.h	39.h	$6$	$12$	$6$	$1.063$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$2$	$0$	$-36$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{5}q^{2}+\beta _{11}q^{3}+(-3+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
39.3.i.a	$39$	$3$	39.i	39.i	$6$	$2$	$1$	$1.063$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$3$	$0$	$13$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+3\zeta_{6}q^{3}+(-4+4\zeta_{6})q^{4}+(13-13\zeta_{6})q^{7}+\cdots$
39.3.i.b	$39$	$3$	39.i	39.i	$6$	$12$	$6$	$1.063$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$-4$	$0$	$-16$		$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{4}q^{2}+(-1+\beta _{1}+\beta _{3}-\beta _{5}-\beta _{7}+\cdots)q^{3}+\cdots$
39.3.l.a	$39$	$3$	39.l	13.f	$12$	$8$	$2$	$1.063$	8.0.$\cdots$.10	$_{}$	None	None		$2$	$0$	$-2$	$0$	$16$	$14$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-\beta _{1}-\beta _{5})q^{2}+(2\beta _{4}-\beta _{5})q^{3}+(1+\cdots)q^{4}+\cdots$
39.3.l.b	$39$	$3$	39.l	13.f	$12$	$12$	$3$	$1.063$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$-2$	$0$	$4$	$-32$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-\beta _{1}-\beta _{2})q^{2}+(\beta _{4}+\beta _{5})q^{3}+(-2+\cdots)q^{4}+\cdots$
39.4.a.a	$39$	$4$	39.a	1.a	$1$	$1$	$1$	$2.301$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-12$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-8q^{4}-12q^{5}+2q^{7}+9q^{9}+\cdots$
39.4.a.b	$39$	$4$	39.a	1.a	$1$	$2$	$2$	$2.301$	$\Q(\sqrt{14}) $	$_{}$	None	None	✓	$1$	$0$	$2$	$-6$	$24$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-3q^{3}+(7+2\beta )q^{4}+(12+\cdots)q^{5}+\cdots$
39.4.a.c	$39$	$4$	39.a	1.a	$1$	$3$	$3$	$2.301$	3.3.3144.1	$_{}$	None	None	✓	$1$	$0$	$2$	$9$	$4$	$30$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+3q^{3}+(3+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots$
39.4.b.a	$39$	$4$	39.b	13.b	$2$	$4$	$4$	$2.301$	4.0.5054412.1	$_{}$	None	None		$2$	$0$	$0$	$-12$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-3q^{3}+(-7+\beta _{3})q^{4}+\beta _{2}q^{5}+\cdots$
39.4.b.b	$39$	$4$	39.b	13.b	$2$	$4$	$4$	$2.301$	4.0.1362828.1	$_{}$	None	None		$2$	$0$	$0$	$12$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+3q^{3}+(-4+\beta _{3})q^{4}+(2\beta _{1}+\cdots)q^{5}+\cdots$
39.4.e.a	$39$	$4$	39.e	13.c	$3$	$2$	$1$	$2.301$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-3$	$-3$	$-18$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-3+3\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}+\cdots$
39.4.e.b	$39$	$4$	39.e	13.c	$3$	$2$	$1$	$2.301$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$1$	$-3$	$14$	$10$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}+7\zeta_{6}q^{4}+\cdots$
39.4.e.c	$39$	$4$	39.e	13.c	$3$	$8$	$4$	$2.301$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		$2$	$0$	$-2$	$12$	$-12$	$14$		$2^{4}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(3+3\beta _{2})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots$
39.4.f.a	$39$	$4$	39.f	39.f	$4$	$4$	$2$	$2.301$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-40$		$2^{2}\cdot 3^{2}$	$\mathrm{U}(1)[D_{4}]$	$q-\zeta_{12}^{3}q^{3}+8\zeta_{12}q^{4}+(-10+10\zeta_{12}+\cdots)q^{7}+\cdots$
39.4.f.b	$39$	$4$	39.f	39.f	$4$	$20$	$10$	$2.301$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$-4$	$0$	$44$		$2^{12}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{8}q^{2}-\beta _{5}q^{3}+(-6\beta _{4}-\beta _{14})q^{4}+\cdots$
39.4.j.a	$39$	$4$	39.j	13.e	$6$	$2$	$1$	$2.301$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$3$	$0$	$18$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(3-3\zeta_{6})q^{3}-8\zeta_{6}q^{4}+(3-6\zeta_{6})q^{5}+\cdots$
39.4.j.b	$39$	$4$	39.j	13.e	$6$	$4$	$2$	$2.301$	$\Q(\sqrt{-3}, \sqrt{-17})$	$_{}$	None	None		$2$	$0$	$0$	$6$	$0$	$-66$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{2}+(3-3\beta _{2})q^{3}+9\beta _{2}q^{4}+(3+\cdots)q^{5}+\cdots$
39.4.j.c	$39$	$4$	39.j	13.e	$6$	$10$	$5$	$2.301$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-15$	$0$	$30$		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{3}q^{2}-3\beta _{2}q^{3}+(6-6\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots$
39.4.k.a	$39$	$4$	39.k	39.k	$12$	$48$	$12$	$2.301$		$_{}$	None	None		$4$	$0$	$0$	$-2$	$0$	$20$			$\mathrm{SU}(2)[C_{12}]$
39.5.c.a	$39$	$5$	39.c	3.b	$2$	$16$	$16$	$4.031$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$-80$		$2^{10}\cdot 3^{5}\cdot 13^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{6}q^{3}+(-6+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
39.5.d.a	$39$	$5$	39.d	39.d	$2$	$1$	$1$	$4.031$	$\Q$	$_{}$	$\Q(\sqrt{-39}) $	None	✓	$2$	$0$	$-5$	$9$	$-2$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-5q^{2}+9q^{3}+9q^{4}-2q^{5}-45q^{6}+\cdots$
39.5.d.b	$39$	$5$	39.d	39.d	$2$	$1$	$1$	$4.031$	$\Q$	$_{}$	$\Q(\sqrt{-39}) $	None	✓	$2$	$0$	$5$	$9$	$2$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+5q^{2}+9q^{3}+9q^{4}+2q^{5}+45q^{6}+\cdots$
39.5.d.c	$39$	$5$	39.d	39.d	$2$	$2$	$2$	$4.031$	$\Q(\sqrt{39}) $	$_{}$	$\Q(\sqrt{-39}) $	None	✓	$4$	$0$	$0$	$-18$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{2}-9q^{3}+23q^{4}+8\beta q^{5}-9\beta q^{6}+\cdots$
39.5.d.d	$39$	$5$	39.d	39.d	$2$	$12$	$12$	$4.031$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$-2$	$0$	$0$		$2^{14}\cdot 3^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+\beta _{4}q^{3}+(2+\beta _{1})q^{4}+(2\beta _{3}+\cdots)q^{5}+\cdots$
39.5.g.a	$39$	$5$	39.g	13.d	$4$	$20$	$10$	$4.031$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$24$	$-24$		$2^{18}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{1}q^{2}+\beta _{6}q^{3}+(10\beta _{4}+\beta _{9}+\beta _{15}+\cdots)q^{4}+\cdots$
39.5.h.a	$39$	$5$	39.h	39.h	$6$	$2$	$1$	$4.031$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$9$	$0$	$117$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(9-9\zeta_{6})q^{3}+2^{4}\zeta_{6}q^{4}+(78-39\zeta_{6})q^{7}+\cdots$
39.5.h.b	$39$	$5$	39.h	39.h	$6$	$32$	$16$	$4.031$		$_{}$	None	None		$4$	$0$	$0$	$-10$	$0$	$-210$			$\mathrm{SU}(2)[C_{6}]$
39.5.i.a	$39$	$5$	39.i	39.i	$6$	$2$	$1$	$4.031$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-9$	$0$	$-71$		$1$	$\mathrm{U}(1)[D_{6}]$	$q-9\zeta_{6}q^{3}+(-2^{4}+2^{4}\zeta_{6})q^{4}+(-71+\cdots)q^{7}+\cdots$
39.5.i.b	$39$	$5$	39.i	39.i	$6$	$32$	$16$	$4.031$		$_{}$	None	None		$4$	$0$	$0$	$8$	$0$	$122$			$\mathrm{SU}(2)[C_{6}]$
39.5.l.a	$39$	$5$	39.l	13.f	$12$	$16$	$4$	$4.031$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-54$	$-44$		$3^{2}\cdot 13^{2}$	$\mathrm{SU}(2)[C_{12}]$	$q+\beta _{6}q^{2}+(-6\beta _{4}+3\beta _{5})q^{3}+(-5+\cdots)q^{4}+\cdots$
39.5.l.b	$39$	$5$	39.l	13.f	$12$	$20$	$5$	$4.031$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$30$	$-42$		$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{12}]$	$q+\beta _{5}q^{2}+(-3\beta _{4}-3\beta _{7})q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots$
39.6.a.a	$39$	$6$	39.a	1.a	$1$	$1$	$1$	$6.255$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$2$	$9$	$-74$	$-112$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+9q^{3}-28q^{4}-74q^{5}+18q^{6}+\cdots$
39.6.a.b	$39$	$6$	39.a	1.a	$1$	$2$	$2$	$6.255$	$\Q(\sqrt{14}) $	$_{}$	None	None	✓	$1$	$1$	$-4$	$-18$	$-48$	$72$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-2+\beta )q^{2}-9q^{3}+(28-4\beta )q^{4}+\cdots$
39.6.a.c	$39$	$6$	39.a	1.a	$1$	$3$	$3$	$6.255$	3.3.125308.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-27$	$54$	$84$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-9q^{3}+(5+2\beta _{1}+\beta _{2})q^{4}+\cdots$

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 247 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.