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 245 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
84.1.p.a	$84$	$1$	84.p	21.h	$6$	$2$	$1$	$0.042$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-1$		$1$		$q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}-q^{13}+\cdots$
84.2.a.a	$84$	$2$	84.a	1.a	$1$	$1$	$1$	$0.671$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{5}-q^{7}+q^{9}+2q^{11}-6q^{13}+\cdots$
84.2.a.b	$84$	$2$	84.a	1.a	$1$	$1$	$1$	$0.671$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}-6q^{11}+2q^{13}+\cdots$
84.2.b.a	$84$	$2$	84.b	28.d	$2$	$4$	$4$	$0.671$	4.0.2312.1	$_{}$	None	None		$2$	$0$	$-1$	$-4$	$0$	$2$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots$
84.2.b.b	$84$	$2$	84.b	28.d	$2$	$4$	$4$	$0.671$	4.0.2312.1	$_{}$	None	None		$2$	$0$	$-1$	$4$	$0$	$-2$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots$
84.2.e.a	$84$	$2$	84.e	12.b	$2$	$12$	$12$	$0.671$	12.0.$\cdots$.2	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}-\beta _{9}q^{3}+(-\beta _{2}-\beta _{3})q^{4}+\cdots$
84.2.f.a	$84$	$2$	84.f	21.c	$2$	$2$	$2$	$0.671$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$4$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\zeta_{6}q^{3}+(2-\zeta_{6})q^{7}-3q^{9}+4\zeta_{6}q^{13}+\cdots$
84.2.i.a	$84$	$2$	84.i	7.c	$3$	$2$	$1$	$0.671$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$2$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{3}+(2-2\zeta_{6})q^{5}+(-1+3\zeta_{6})q^{7}+\cdots$
84.2.k.a	$84$	$2$	84.k	21.g	$6$	$2$	$1$	$0.671$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-3$	$3$	$4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-2+\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots$
84.2.k.b	$84$	$2$	84.k	21.g	$6$	$2$	$1$	$0.671$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-3$	$4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-2\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots$
84.2.k.c	$84$	$2$	84.k	21.g	$6$	$2$	$1$	$0.671$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$3$	$0$	$-5$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(1+\zeta_{6})q^{3}+(-2-\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots$
84.2.n.a	$84$	$2$	84.n	84.n	$6$	$24$	$12$	$0.671$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
84.2.o.a	$84$	$2$	84.o	28.f	$6$	$8$	$4$	$0.671$	8.0.562828176.1	$_{}$	None	None		$2$	$0$	$1$	$-4$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{4}q^{2}+(-1+\beta _{3})q^{3}+(\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots$
84.2.o.b	$84$	$2$	84.o	28.f	$6$	$8$	$4$	$0.671$	8.0.562828176.1	$_{}$	None	None		$2$	$0$	$1$	$4$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{6}q^{2}+\beta _{3}q^{3}+(\beta _{1}-\beta _{2})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots$
84.3.c.a	$84$	$3$	84.c	3.b	$2$	$4$	$4$	$2.289$	4.0.116032.1	$_{}$	None	None		$2$	$0$	$0$	$6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(2-\beta _{1})q^{3}+(-2+\beta _{1}-\beta _{2}-2\beta _{3})q^{5}+\cdots$
84.3.d.a	$84$	$3$	84.d	7.b	$2$	$2$	$2$	$2.289$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-14$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{6}q^{3}-4\zeta_{6}q^{5}-7q^{7}-3q^{9}+18q^{11}+\cdots$
84.3.g.a	$84$	$3$	84.g	4.b	$2$	$12$	$12$	$2.289$	12.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$2$	$0$	$8$	$0$		$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{9}q^{2}+\beta _{6}q^{3}+(\beta _{5}-\beta _{6})q^{4}+(1+\cdots)q^{5}+\cdots$
84.3.h.a	$84$	$3$	84.h	84.h	$2$	$1$	$1$	$2.289$	$\Q$	$_{}$	$\Q(\sqrt{-21}) $	None	✓	$2$	$0$	$-2$	$-3$	$-4$	$7$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}-3q^{3}+4q^{4}-4q^{5}+6q^{6}+\cdots$
84.3.h.b	$84$	$3$	84.h	84.h	$2$	$1$	$1$	$2.289$	$\Q$	$_{}$	$\Q(\sqrt{-21}) $	None	✓	$2$	$0$	$-2$	$3$	$4$	$-7$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}+3q^{3}+4q^{4}+4q^{5}-6q^{6}+\cdots$
84.3.h.c	$84$	$3$	84.h	84.h	$2$	$1$	$1$	$2.289$	$\Q$	$_{}$	$\Q(\sqrt{-21}) $	None	✓	$2$	$0$	$2$	$-3$	$4$	$7$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}-3q^{3}+4q^{4}+4q^{5}-6q^{6}+\cdots$
84.3.h.d	$84$	$3$	84.h	84.h	$2$	$1$	$1$	$2.289$	$\Q$	$_{}$	$\Q(\sqrt{-21}) $	None	✓	$2$	$0$	$2$	$3$	$-4$	$-7$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+3q^{3}+4q^{4}-4q^{5}+6q^{6}+\cdots$
84.3.h.e	$84$	$3$	84.h	84.h	$2$	$24$	$24$	$2.289$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
84.3.j.a	$84$	$3$	84.j	84.j	$6$	$56$	$28$	$2.289$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
84.3.l.a	$84$	$3$	84.l	28.g	$6$	$2$	$1$	$2.289$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-2$	$3$	$5$	$-7$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q-2\zeta_{6}q^{2}+(2-\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots$
84.3.l.b	$84$	$3$	84.l	28.g	$6$	$2$	$1$	$2.289$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$4$	$-3$	$5$	$7$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+2q^{2}+(-2+\zeta_{6})q^{3}+4q^{4}+(5-5\zeta_{6})q^{5}+\cdots$
84.3.l.c	$84$	$3$	84.l	28.g	$6$	$14$	$7$	$2.289$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		$2$	$0$	$-3$	$-21$	$-5$	$-19$		$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{1}-\beta _{4})q^{2}+(-1+\beta _{3})q^{3}+(1+\cdots)q^{4}+\cdots$
84.3.l.d	$84$	$3$	84.l	28.g	$6$	$14$	$7$	$2.289$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		$2$	$0$	$3$	$21$	$-5$	$19$		$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{4}+\beta _{9})q^{2}+(2-\beta _{2})q^{3}-\beta _{10}q^{4}+\cdots$
84.3.m.a	$84$	$3$	84.m	7.d	$6$	$2$	$1$	$2.289$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$3$	$3$	$13$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1+\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(5+3\zeta_{6})q^{7}+\cdots$
84.3.m.b	$84$	$3$	84.m	7.d	$6$	$4$	$2$	$2.289$	$\Q(\sqrt{-3}, \sqrt{65})$	$_{}$	None	None		$2$	$0$	$0$	$-6$	$-9$	$2$		$3$	$\mathrm{SU}(2)[C_{6}]$	$q+(-2+\beta _{1})q^{3}+(-2-\beta _{1}+\beta _{3})q^{5}+\cdots$
84.3.p.a	$84$	$3$	84.p	21.h	$6$	$2$	$1$	$2.289$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$3$	$0$	$11$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+3\zeta_{6}q^{3}+(3+5\zeta_{6})q^{7}+(-9+9\zeta_{6})q^{9}+\cdots$
84.3.p.b	$84$	$3$	84.p	21.h	$6$	$4$	$2$	$2.289$	$\Q(\sqrt{-3}, \sqrt{-5})$	$_{}$	None	None		$4$	$0$	$0$	$-4$	$0$	$22$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}-2\beta _{2}-\beta _{3})q^{3}-3\beta _{1}q^{5}+(8+\cdots)q^{7}+\cdots$
84.3.p.c	$84$	$3$	84.p	21.h	$6$	$4$	$2$	$2.289$	$\Q(\sqrt{-3}, \sqrt{-35})$	$_{}$	None	None		$4$	$0$	$0$	$1$	$0$	$-28$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{1}q^{3}+(\beta _{2}+2\beta _{3})q^{5}-7q^{7}+(9\beta _{2}+\cdots)q^{9}+\cdots$
84.4.a.a	$84$	$4$	84.a	1.a	$1$	$1$	$1$	$4.956$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$6$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+6q^{5}+7q^{7}+9q^{9}+6^{2}q^{11}+\cdots$
84.4.a.b	$84$	$4$	84.a	1.a	$1$	$1$	$1$	$4.956$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$14$	$-7$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+14q^{5}-7q^{7}+9q^{9}+4q^{11}+\cdots$
84.4.b.a	$84$	$4$	84.b	28.d	$2$	$12$	$12$	$4.956$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$1$	$-36$	$0$	$10$		$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-3q^{3}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{8}+\cdots)q^{5}+\cdots$
84.4.b.b	$84$	$4$	84.b	28.d	$2$	$12$	$12$	$4.956$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$1$	$36$	$0$	$-10$		$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+3q^{3}+\beta _{2}q^{4}+(\beta _{1}+\beta _{8}+\cdots)q^{5}+\cdots$
84.4.e.a	$84$	$4$	84.e	12.b	$2$	$36$	$36$	$4.956$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
84.4.f.a	$84$	$4$	84.f	21.c	$2$	$8$	$8$	$4.956$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-20$		$2^{7}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}-\beta _{5}q^{5}+(-3-\beta _{7})q^{7}+(-2+\cdots)q^{9}+\cdots$
84.4.i.a	$84$	$4$	84.i	7.c	$3$	$4$	$2$	$4.956$	$\Q(\sqrt{-3}, \sqrt{193})$	$_{}$	None	None		$2$	$0$	$0$	$-6$	$-11$	$6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-3+3\beta _{2})q^{3}+(\beta _{1}-6\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots$
84.4.i.b	$84$	$4$	84.i	7.c	$3$	$4$	$2$	$4.956$	$\Q(\sqrt{-3}, \sqrt{-19})$	$_{}$	None	None		$2$	$0$	$0$	$6$	$3$	$-20$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-3\beta _{2}q^{3}+(1+2\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+\cdots$
84.4.k.a	$84$	$4$	84.k	21.g	$6$	$2$	$1$	$4.956$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-9$	$0$	$-17$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-3-3\zeta_{6})q^{3}+(-18+19\zeta_{6})q^{7}+\cdots$
84.4.k.b	$84$	$4$	84.k	21.g	$6$	$2$	$1$	$4.956$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$9$	$0$	$37$		$1$	$\mathrm{U}(1)[D_{6}]$	$q+(3+3\zeta_{6})q^{3}+(18+\zeta_{6})q^{7}+3^{3}\zeta_{6}q^{9}+\cdots$
84.4.k.c	$84$	$4$	84.k	21.g	$6$	$12$	$6$	$4.956$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-42$		$2^{4}\cdot 3^{7}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{5}q^{3}-\beta _{9}q^{5}+(-1+2\beta _{1}-2\beta _{4}+\cdots)q^{7}+\cdots$
84.4.n.a	$84$	$4$	84.n	84.n	$6$	$88$	$44$	$4.956$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
84.4.o.a	$84$	$4$	84.o	28.f	$6$	$24$	$12$	$4.956$		$_{}$	None	None		$2$	$0$	$-1$	$-36$	$0$	$10$			$\mathrm{SU}(2)[C_{6}]$
84.4.o.b	$84$	$4$	84.o	28.f	$6$	$24$	$12$	$4.956$		$_{}$	None	None		$2$	$0$	$-1$	$36$	$0$	$-10$			$\mathrm{SU}(2)[C_{6}]$
84.5.c.a	$84$	$5$	84.c	3.b	$2$	$8$	$8$	$8.683$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-18$	$0$	$0$		$2^{2}\cdot 3^{3}\cdot 7^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2-\beta _{3})q^{3}+(\beta _{1}+\beta _{3})q^{5}+\beta _{2}q^{7}+\cdots$
84.5.d.a	$84$	$5$	84.d	7.b	$2$	$6$	$6$	$8.683$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$42$		$2^{4}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+(\beta _{2}-\beta _{5})q^{5}+(7-\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots$
84.5.g.a	$84$	$5$	84.g	4.b	$2$	$24$	$24$	$8.683$		$_{}$	None	None		$2$	$0$	$-6$	$0$	$-48$	$0$			$\mathrm{SU}(2)[C_{2}]$
84.5.h.a	$84$	$5$	84.h	84.h	$2$	$1$	$1$	$8.683$	$\Q$	$_{}$	$\Q(\sqrt{-21}) $	None	✓	$2$	$0$	$-4$	$-9$	$-34$	$-49$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-4q^{2}-9q^{3}+2^{4}q^{4}-34q^{5}+6^{2}q^{6}+\cdots$

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 245 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.