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 146 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
612.1.e.a	$612$	$1$	612.e	68.d	$2$	$1$	$1$	$0.305$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-17}) $	$\Q(\sqrt{17}) $	✓		✓	✓	68.1.d.a	$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+q^{8}-2q^{13}+q^{16}-q^{17}+\cdots$
612.1.j.a	$612$	$1$	612.j	51.f	$4$	$4$	$2$	$0.305$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓	✓	✓	612.1.j.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{5}-\zeta_{8}^{3}q^{11}+q^{13}-\zeta_{8}^{3}q^{17}+\cdots$
612.1.l.a	$612$	$1$	612.l	68.f	$4$	$2$	$1$	$0.305$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None			✓	✓	68.1.f.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+iq^{2}-q^{4}+(1-i)q^{5}-iq^{8}+(1+\cdots)q^{10}+\cdots$
612.1.q.a	$612$	$1$	612.q	612.q	$6$	$2$	$1$	$0.305$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-17}) $	None		✓			612.1.q.a	$4$	$0$	$-1$	$-1$	$0$	$-2$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+q^{6}+\zeta_{6}^{2}q^{7}+\cdots$
612.1.q.b	$612$	$1$	612.q	612.q	$6$	$2$	$1$	$0.305$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-17}) $	None		✓			612.1.q.a	$4$	$0$	$-1$	$1$	$0$	$2$		$1$		$q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-q^{6}-\zeta_{6}^{2}q^{7}+\cdots$
612.1.q.c	$612$	$1$	612.q	612.q	$6$	$4$	$2$	$0.305$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-17}) $	None		✓	✓		612.1.q.c	$8$	$0$	$2$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{2}q^{2}-\zeta_{12}q^{3}+\zeta_{12}^{4}q^{4}-\zeta_{12}^{3}q^{6}+\cdots$
612.1.v.a	$612$	$1$	612.v	68.g	$8$	$4$	$1$	$0.305$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		✓			612.1.v.a	$4$	$0$	$0$	$0$	$-4$	$0$		$1$		$q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(-1+\zeta_{8})q^{5}+\cdots$
612.1.v.b	$612$	$1$	612.v	68.g	$8$	$4$	$1$	$0.305$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		✓			612.1.v.a	$4$	$0$	$0$	$0$	$4$	$0$		$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(1-\zeta_{8})q^{5}-\zeta_{8}q^{8}+\cdots$
612.1.bf.a	$612$	$1$	612.bf	204.t	$16$	$8$	$1$	$0.305$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-1}) $	None		✓			612.1.bf.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{16}^{3}q^{2}+\zeta_{16}^{6}q^{4}+(-\zeta_{16}-\zeta_{16}^{4}+\cdots)q^{5}+\cdots$
612.1.bf.b	$612$	$1$	612.bf	204.t	$16$	$8$	$1$	$0.305$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-1}) $	None		✓			612.1.bf.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}^{3}q^{2}+\zeta_{16}^{6}q^{4}+(\zeta_{16}+\zeta_{16}^{4}+\cdots)q^{5}+\cdots$
612.2.a.a	$612$	$2$	612.a	1.a	$1$	$1$	$1$	$4.887$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	612.2.a.a	$1$	$1$	$0$	$0$	$-3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+2q^{7}-3q^{11}-q^{13}+q^{17}+\cdots$
612.2.a.b	$612$	$2$	612.a	1.a	$1$	$1$	$1$	$4.887$	$\Q$	$_{}$	None	None	✓		✓	✓	204.2.a.b	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-5q^{11}-5q^{13}-q^{17}+q^{19}+\cdots$
612.2.a.c	$612$	$2$	612.a	1.a	$1$	$1$	$1$	$4.887$	$\Q$	$_{}$	None	None	✓				204.2.a.a	$1$	$0$	$0$	$0$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+4q^{7}-3q^{11}+3q^{13}+q^{17}+\cdots$
612.2.a.d	$612$	$2$	612.a	1.a	$1$	$1$	$1$	$4.887$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	612.2.a.a	$1$	$0$	$0$	$0$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+2q^{7}+3q^{11}-q^{13}-q^{17}+\cdots$
612.2.a.e	$612$	$2$	612.a	1.a	$1$	$2$	$2$	$4.887$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓		✓		68.2.a.a	$1$	$0$	$0$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{5}+(-1-\beta )q^{7}+(3-\beta )q^{11}+\cdots$
612.2.b.a	$612$	$2$	612.b	17.b	$2$	$2$	$2$	$4.887$	$\Q(\sqrt{-2}) $	$_{}$	None	None					68.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta q^{5}+3\beta q^{7}-\beta q^{11}-4q^{13}+\cdots$
612.2.b.b	$612$	$2$	612.b	17.b	$2$	$2$	$2$	$4.887$	$\Q(\sqrt{-1}) $	$_{}$	None	None					204.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{5}-2iq^{7}+3iq^{11}+3q^{13}+\cdots$
612.2.b.c	$612$	$2$	612.b	17.b	$2$	$4$	$4$	$4.887$	$\Q(i, \sqrt{17})$	$_{}$	$\Q(\sqrt{-51}) $	None		✓	✓		612.2.b.c	$4$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{5}+(\beta _{1}+2\beta _{2})q^{11}+(1-\beta _{3})q^{13}+\cdots$
612.2.c.a	$612$	$2$	612.c	12.b	$2$	$32$	$32$	$4.887$		$_{}$	None	None		✓	✓	✓	612.2.c.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
612.2.h.a	$612$	$2$	612.h	204.h	$2$	$4$	$4$	$4.887$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			612.2.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\zeta_{8}^{2}q^{2}-2q^{4}+(\zeta_{8}^{2}-2\zeta_{8}^{3})q^{5}+\cdots$
612.2.h.b	$612$	$2$	612.h	204.h	$2$	$32$	$32$	$4.887$		$_{}$	None	None		✓	✓		612.2.h.b	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
612.2.i.a	$612$	$2$	612.i	9.c	$3$	$2$	$1$	$4.887$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			612.2.i.a	$2$	$0$	$0$	$0$	$-1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots$
612.2.i.b	$612$	$2$	612.i	9.c	$3$	$2$	$1$	$4.887$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			612.2.i.b	$2$	$0$	$0$	$3$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(3-3\zeta_{6})q^{9}+\cdots$
612.2.i.c	$612$	$2$	612.i	9.c	$3$	$4$	$2$	$4.887$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None		✓			612.2.i.c	$2$	$0$	$0$	$-1$	$-3$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}+(1-2\beta _{1}-2\beta _{2}+\beta _{3})q^{5}+\cdots$
612.2.i.d	$612$	$2$	612.i	9.c	$3$	$10$	$5$	$4.887$	10.0.$\cdots$.1	$_{}$	None	None		✓			612.2.i.d	$2$	$0$	$0$	$-1$	$4$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{3}+(1+\beta _{2}-\beta _{7})q^{5}+(\beta _{1}-\beta _{5}+\cdots)q^{7}+\cdots$
612.2.i.e	$612$	$2$	612.i	9.c	$3$	$14$	$7$	$4.887$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		✓	✓		612.2.i.e	$2$	$0$	$0$	$-3$	$8$	$0$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{3}+(1+\beta _{4}-\beta _{7})q^{5}+(-\beta _{10}+\cdots)q^{7}+\cdots$
612.2.k.a	$612$	$2$	612.k	17.c	$4$	$2$	$1$	$4.887$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			612.2.k.a	$2$	$0$	$0$	$0$	$-2$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-i)q^{5}+(-2+2i)q^{7}+(4-4i)q^{11}+\cdots$
612.2.k.b	$612$	$2$	612.k	17.c	$4$	$2$	$1$	$4.887$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			612.2.k.a	$2$	$0$	$0$	$0$	$2$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+i)q^{5}+(-2+2i)q^{7}+(-4+4i)q^{11}+\cdots$
612.2.k.c	$612$	$2$	612.k	17.c	$4$	$4$	$2$	$4.887$	$\Q(\zeta_{8})$	$_{}$	None	None					204.2.j.a	$2$	$0$	$0$	$0$	$-8$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2+2\zeta_{8}^{2}-\zeta_{8}^{3})q^{5}+(-1+2\zeta_{8}+\cdots)q^{7}+\cdots$
612.2.k.d	$612$	$2$	612.k	17.c	$4$	$4$	$2$	$4.887$	$\Q(i, \sqrt{34})$	$_{}$	None	None		✓			612.2.k.d	$4$	$0$	$0$	$0$	$0$	$12$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{5}+(3-3\beta _{2})q^{7}-\beta _{3}q^{11}-5q^{13}+\cdots$
612.2.k.e	$612$	$2$	612.k	17.c	$4$	$4$	$2$	$4.887$	$\Q(i, \sqrt{13})$	$_{}$	None	None					68.2.e.a	$2$	$0$	$0$	$0$	$4$	$2$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{1})q^{5}-\beta _{3}q^{7}+(-2+2\beta _{1}+\cdots)q^{11}+\cdots$
612.2.m.a	$612$	$2$	612.m	204.l	$4$	$4$	$2$	$4.887$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			612.2.m.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+2q^{4}-2\zeta_{8}^{3}q^{5}+\cdots$
612.2.m.b	$612$	$2$	612.m	204.l	$4$	$4$	$2$	$4.887$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			612.2.m.b	$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+2q^{4}+4\zeta_{8}^{3}q^{5}+\cdots$
612.2.m.c	$612$	$2$	612.m	204.l	$4$	$64$	$32$	$4.887$		$_{}$	None	None		✓	✓		612.2.m.c	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
612.2.n.a	$612$	$2$	612.n	612.n	$6$	$16$	$8$	$4.887$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	$\Q(\sqrt{-17}) $	None		✓			612.2.n.a	$8$	$0$	$0$	$0$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{6}]$	$q+(\beta _{3}-\beta _{10})q^{2}+(-\beta _{8}+\beta _{14})q^{3}+\cdots$
612.2.n.b	$612$	$2$	612.n	612.n	$6$	$192$	$96$	$4.887$		$_{}$	None	None		✓	✓		612.2.n.b	$8$	$0$	$-6$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
612.2.s.a	$612$	$2$	612.s	36.h	$6$	$192$	$96$	$4.887$		$_{}$	None	None		✓	✓	✓	612.2.s.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
612.2.t.a	$612$	$2$	612.t	153.h	$6$	$16$	$8$	$4.887$	16.0.$\cdots$.3	$_{}$	None	None		✓			612.2.t.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{8}+\beta _{15})q^{3}+(\beta _{8}+\beta _{10}+\beta _{12}+\cdots)q^{5}+\cdots$
612.2.t.b	$612$	$2$	612.t	153.h	$6$	$20$	$10$	$4.887$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		✓	✓		612.2.t.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}+\beta _{16})q^{3}+(\beta _{2}+\beta _{5}-\beta _{16})q^{5}+\cdots$
612.2.w.a	$612$	$2$	612.w	17.d	$8$	$4$	$1$	$4.887$	$\Q(\zeta_{8})$	$_{}$	None	None					68.2.h.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(-1+\zeta_{8})q^{5}+(\zeta_{8}+\zeta_{8}^{2})q^{7}+(2+\cdots)q^{11}+\cdots$
612.2.w.b	$612$	$2$	612.w	17.d	$8$	$8$	$2$	$4.887$	8.0.$\cdots$.13	$_{}$	None	None		✓			612.2.w.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q-\beta _{5}q^{5}+(\beta _{2}+\beta _{4})q^{7}+(\beta _{1}-\beta _{5}+\beta _{7})q^{11}+\cdots$
612.2.w.c	$612$	$2$	612.w	17.d	$8$	$16$	$4$	$4.887$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None			✓		204.2.o.a	$2$	$0$	$0$	$0$	$8$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{8}]$	$q+(-1-2\beta _{2}-\beta _{4}+\beta _{5}+\beta _{9}+\beta _{10}+\cdots)q^{5}+\cdots$
612.2.x.a	$612$	$2$	612.x	204.p	$8$	$4$	$1$	$4.887$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			612.2.x.a	$4$	$0$	$-4$	$0$	$-4$	$0$		$1$	$\mathrm{U}(1)[D_{8}]$	$q+(-1-\zeta_{8}^{2})q^{2}+2\zeta_{8}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots$
612.2.x.b	$612$	$2$	612.x	204.p	$8$	$4$	$1$	$4.887$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			612.2.x.b	$4$	$0$	$-4$	$0$	$8$	$0$		$1$	$\mathrm{U}(1)[D_{8}]$	$q+(-1-\zeta_{8}^{2})q^{2}+2\zeta_{8}^{2}q^{4}+(2+2\zeta_{8}+\cdots)q^{5}+\cdots$
612.2.x.c	$612$	$2$	612.x	204.p	$8$	$4$	$1$	$4.887$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			612.2.x.b	$4$	$0$	$4$	$0$	$-8$	$0$		$1$	$\mathrm{U}(1)[D_{8}]$	$q+(1+\zeta_{8}^{2})q^{2}+2\zeta_{8}^{2}q^{4}+(-2-2\zeta_{8}+\cdots)q^{5}+\cdots$
612.2.x.d	$612$	$2$	612.x	204.p	$8$	$4$	$1$	$4.887$	$\Q(\zeta_{8})$	$_{}$	$\Q(\sqrt{-1}) $	None		✓			612.2.x.a	$4$	$0$	$4$	$0$	$4$	$0$		$1$	$\mathrm{U}(1)[D_{8}]$	$q+(1+\zeta_{8}^{2})q^{2}+2\zeta_{8}^{2}q^{4}+(1+\zeta_{8}+\cdots)q^{5}+\cdots$
612.2.x.e	$612$	$2$	612.x	204.p	$8$	$8$	$2$	$4.887$	8.0.157351936.1	$_{}$	None	None		✓			612.2.x.e	$4$	$0$	$0$	$0$	$-16$	$0$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+\beta _{1}q^{2}+(\beta _{3}+\beta _{5})q^{4}+(-2-2\beta _{4}+\cdots)q^{5}+\cdots$
612.2.x.f	$612$	$2$	612.x	204.p	$8$	$8$	$2$	$4.887$	8.0.157351936.1	$_{}$	None	None		✓			612.2.x.e	$4$	$0$	$0$	$0$	$16$	$0$		$1$	$\mathrm{SU}(2)[C_{8}]$	$q+(\beta _{2}+\beta _{4})q^{2}+(\beta _{3}+\beta _{5})q^{4}+(2+2\beta _{4}+\cdots)q^{5}+\cdots$
612.2.x.g	$612$	$2$	612.x	204.p	$8$	$56$	$14$	$4.887$		$_{}$	None	None		✓			612.2.x.g	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
612.2.x.h	$612$	$2$	612.x	204.p	$8$	$56$	$14$	$4.887$		$_{}$	None	None		✓			612.2.x.g	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$

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 146 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.