LMFDB - Newform search results

Refine search

Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is twist minimal	Is self-dual

$Nk^2$	Coefficient ring index	Coefficient ring gens.	Projective image	Projective image type

				Sort order	Select

Results (1-50 of 89 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	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	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
2925.1.o.a	$2925$	$1$	2925.o	65.h	$4$	$4$	$2$	$1.460$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-195}) $	$\Q(\sqrt{65}) $		✓	2925.1.o.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{7}+\zeta_{8}^{3}q^{13}-q^{16}+\cdots$
2925.1.o.b	$2925$	$1$	2925.o	65.h	$4$	$8$	$4$	$1.460$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-39}) $	None			585.1.o.a	$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q+(\zeta_{16}-\zeta_{16}^{3})q^{2}+(\zeta_{16}^{2}-\zeta_{16}^{4}+\cdots)q^{4}+\cdots$
2925.1.s.a	$2925$	$1$	2925.s	13.d	$4$	$2$	$1$	$1.460$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None			117.1.j.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-iq^{4}+(1-i)q^{7}-iq^{13}-q^{16}+\cdots$
2925.1.t.a	$2925$	$1$	2925.t	65.g	$4$	$2$	$1$	$1.460$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None			117.1.j.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-iq^{4}+(-1+i)q^{7}+q^{13}-q^{16}+\cdots$
2925.1.t.b	$2925$	$1$	2925.t	65.g	$4$	$2$	$1$	$1.460$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None			117.1.j.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-iq^{4}+(1-i)q^{7}-q^{13}-q^{16}+(1+\cdots)q^{19}+\cdots$
2925.1.bi.a	$2925$	$1$	2925.bi	117.n	$6$	$2$	$1$	$1.460$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{13}) $		✓	2925.1.bi.a	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-q^{3}+\zeta_{6}q^{4}+q^{9}-\zeta_{6}q^{12}+\zeta_{6}q^{13}+\cdots$
2925.1.bi.b	$2925$	$1$	2925.bi	117.n	$6$	$2$	$1$	$1.460$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{13}) $		✓	2925.1.bi.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+q^{3}+\zeta_{6}q^{4}+q^{9}+\zeta_{6}q^{12}-\zeta_{6}q^{13}+\cdots$
2925.1.bp.a	$2925$	$1$	2925.bp	585.ao	$6$	$4$	$2$	$1.460$	$\Q(\zeta_{12})$	$D_{6}$	None	$\Q(\sqrt{13}) $		✓	2925.1.bi.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{3}q^{3}+\zeta_{12}^{4}q^{4}-q^{9}+\zeta_{12}q^{12}+\cdots$
2925.1.cy.a	$2925$	$1$	2925.cy	65.q	$12$	$8$	$2$	$1.460$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓	2925.1.cy.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}^{10}q^{4}+(\zeta_{24}^{5}+\zeta_{24}^{9})q^{7}+\zeta_{24}^{3}q^{13}+\cdots$
2925.1.cy.b	$2925$	$1$	2925.cy	65.q	$12$	$8$	$2$	$1.460$	$\Q(\zeta_{24})$	$A_{4}$	None	None			325.1.u.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{11}q^{2}+\zeta_{24}^{7}q^{7}+\zeta_{24}^{9}q^{8}+\cdots$
2925.1.dg.a	$2925$	$1$	2925.dg	117.y	$12$	$4$	$1$	$1.460$	$\Q(\zeta_{12})$	$S_{4}$	None	None		✓	2925.1.dg.a	$4$	$0$	$0$	$-4$	$0$	$0$		$1$		$q-q^{3}+\zeta_{12}^{5}q^{4}+q^{9}+(-\zeta_{12}-\zeta_{12}^{4}+\cdots)q^{11}+\cdots$
2925.1.dg.b	$2925$	$1$	2925.dg	117.y	$12$	$4$	$1$	$1.460$	$\Q(\zeta_{12})$	$S_{4}$	None	None		✓	2925.1.dg.a	$4$	$0$	$0$	$4$	$0$	$0$		$1$		$q+q^{3}+\zeta_{12}^{5}q^{4}+q^{9}+(-\zeta_{12}-\zeta_{12}^{4}+\cdots)q^{11}+\cdots$
2925.1.dj.a	$2925$	$1$	2925.dj	585.cb	$12$	$4$	$1$	$1.460$	$\Q(\zeta_{12})$	$S_{4}$	None	None		✓	2925.1.dg.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{3}q^{3}-\zeta_{12}^{5}q^{4}-q^{9}+(-\zeta_{12}+\cdots)q^{11}+\cdots$
2925.1.dj.b	$2925$	$1$	2925.dj	585.cb	$12$	$4$	$1$	$1.460$	$\Q(\zeta_{12})$	$S_{4}$	None	None		✓	2925.1.dg.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{3}q^{3}-\zeta_{12}^{5}q^{4}-q^{9}+(-\zeta_{12}+\cdots)q^{11}+\cdots$
2925.1.do.a	$2925$	$1$	2925.do	65.s	$12$	$4$	$1$	$1.460$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		✓	2925.1.dp.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+\zeta_{12}^{5}q^{4}+(-\zeta_{12}^{3}+\zeta_{12}^{4})q^{7}+\cdots$
2925.1.do.b	$2925$	$1$	2925.do	65.s	$12$	$4$	$1$	$1.460$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		✓	2925.1.dp.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+\zeta_{12}^{5}q^{4}+(\zeta_{12}^{3}-\zeta_{12}^{4})q^{7}+q^{13}+\cdots$
2925.1.dp.a	$2925$	$1$	2925.dp	13.f	$12$	$4$	$1$	$1.460$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		✓	2925.1.dp.a	$4$	$0$	$0$	$0$	$0$	$-4$		$1$		$q-\zeta_{12}^{5}q^{4}+(-1+\zeta_{12})q^{7}-\zeta_{12}^{3}q^{13}+\cdots$
2925.1.dp.b	$2925$	$1$	2925.dp	13.f	$12$	$4$	$1$	$1.460$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		✓	2925.1.dp.a	$4$	$0$	$0$	$0$	$0$	$4$		$1$		$q-\zeta_{12}^{5}q^{4}+(1-\zeta_{12})q^{7}+\zeta_{12}^{3}q^{13}+\cdots$
2925.1.dq.a	$2925$	$1$	2925.dq	65.r	$12$	$8$	$2$	$1.460$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓	2925.1.dq.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}^{10}q^{4}-\zeta_{24}^{7}q^{7}+\zeta_{24}^{9}q^{13}+\cdots$
2925.1.er.a	$2925$	$1$	2925.er	325.ac	$20$	$32$	$4$	$1.460$	$\Q(\zeta_{80})$	$D_{40}$	$\Q(\sqrt{-39}) $	None		✓	2925.1.er.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{80}^{17}-\zeta_{80}^{35})q^{2}+(\zeta_{80}^{12}-\zeta_{80}^{30}+\cdots)q^{4}+\cdots$
2925.2.a.a	$2925$	$2$	2925.a	1.a	$1$	$1$	$1$	$23.356$	$\Q$	$_{}$	None	None	✓		325.2.a.a	$1$	$1$	$-2$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+2q^{7}-2q^{11}-q^{13}+\cdots$
2925.2.a.b	$2925$	$2$	2925.a	1.a	$1$	$1$	$1$	$23.356$	$\Q$	$_{}$	None	None	✓		975.2.a.d	$1$	$1$	$-1$	$0$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-3q^{7}+3q^{8}+q^{11}+q^{13}+\cdots$
2925.2.a.c	$2925$	$2$	2925.a	1.a	$1$	$1$	$1$	$23.356$	$\Q$	$_{}$	None	None	✓		585.2.a.d	$1$	$0$	$-1$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-2q^{7}+3q^{8}+4q^{11}+\cdots$
2925.2.a.d	$2925$	$2$	2925.a	1.a	$1$	$1$	$1$	$23.356$	$\Q$	$_{}$	None	None	✓		195.2.a.a	$1$	$0$	$-1$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+3q^{8}-4q^{11}-q^{13}+\cdots$
2925.2.a.e	$2925$	$2$	2925.a	1.a	$1$	$1$	$1$	$23.356$	$\Q$	$_{}$	None	None	✓		975.2.a.e	$1$	$1$	$-1$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{7}+3q^{8}+q^{11}+q^{13}+\cdots$
2925.2.a.f	$2925$	$2$	2925.a	1.a	$1$	$1$	$1$	$23.356$	$\Q$	$_{}$	None	None	✓		65.2.a.a	$1$	$1$	$-1$	$0$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+4q^{7}+3q^{8}-2q^{11}+\cdots$
2925.2.a.g	$2925$	$2$	2925.a	1.a	$1$	$1$	$1$	$23.356$	$\Q$	$_{}$	None	None	✓		325.2.a.b	$1$	$0$	$0$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-4q^{7}+6q^{11}+q^{13}+4q^{16}+\cdots$
2925.2.a.h	$2925$	$2$	2925.a	1.a	$1$	$1$	$1$	$23.356$	$\Q$	$_{}$	None	None	✓		195.2.c.a	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{7}+q^{11}-q^{13}+4q^{16}+\cdots$
2925.2.a.i	$2925$	$2$	2925.a	1.a	$1$	$1$	$1$	$23.356$	$\Q$	$_{}$	None	None	✓		585.2.a.e	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{7}-3q^{11}-q^{13}+4q^{16}+\cdots$
2925.2.a.j	$2925$	$2$	2925.a	1.a	$1$	$1$	$1$	$23.356$	$\Q$	$_{}$	None	None	✓		195.2.c.a	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{7}+q^{11}+q^{13}+4q^{16}+\cdots$
2925.2.a.k	$2925$	$2$	2925.a	1.a	$1$	$1$	$1$	$23.356$	$\Q$	$_{}$	None	None	✓		585.2.a.e	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{7}+3q^{11}-q^{13}+4q^{16}+\cdots$
2925.2.a.l	$2925$	$2$	2925.a	1.a	$1$	$1$	$1$	$23.356$	$\Q$	$_{}$	None	None	✓		325.2.a.b	$1$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+4q^{7}+6q^{11}-q^{13}+4q^{16}+\cdots$
2925.2.a.m	$2925$	$2$	2925.a	1.a	$1$	$1$	$1$	$23.356$	$\Q$	$_{}$	None	None	✓		585.2.a.d	$1$	$0$	$1$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-2q^{7}-3q^{8}-4q^{11}+\cdots$
2925.2.a.n	$2925$	$2$	2925.a	1.a	$1$	$1$	$1$	$23.356$	$\Q$	$_{}$	None	None	✓		975.2.a.e	$1$	$1$	$1$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{7}-3q^{8}+q^{11}-q^{13}+\cdots$
2925.2.a.o	$2925$	$2$	2925.a	1.a	$1$	$1$	$1$	$23.356$	$\Q$	$_{}$	None	None	✓		975.2.a.d	$1$	$1$	$1$	$0$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+3q^{7}-3q^{8}+q^{11}-q^{13}+\cdots$
2925.2.a.p	$2925$	$2$	2925.a	1.a	$1$	$1$	$1$	$23.356$	$\Q$	$_{}$	None	None	✓		39.2.a.a	$1$	$0$	$1$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+4q^{7}-3q^{8}-4q^{11}+\cdots$
2925.2.a.q	$2925$	$2$	2925.a	1.a	$1$	$1$	$1$	$23.356$	$\Q$	$_{}$	None	None	✓		195.2.a.b	$1$	$1$	$2$	$0$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-3q^{7}+q^{11}+q^{13}+\cdots$
2925.2.a.r	$2925$	$2$	2925.a	1.a	$1$	$1$	$1$	$23.356$	$\Q$	$_{}$	None	None	✓		325.2.a.a	$1$	$1$	$2$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-2q^{7}-2q^{11}+q^{13}+\cdots$
2925.2.a.s	$2925$	$2$	2925.a	1.a	$1$	$1$	$1$	$23.356$	$\Q$	$_{}$	None	None	✓		195.2.a.c	$1$	$1$	$2$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+q^{7}-5q^{11}+q^{13}+\cdots$
2925.2.a.t	$2925$	$2$	2925.a	1.a	$1$	$1$	$1$	$23.356$	$\Q$	$_{}$	None	None	✓		195.2.a.d	$1$	$0$	$2$	$0$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+3q^{7}+5q^{11}-q^{13}+\cdots$
2925.2.a.u	$2925$	$2$	2925.a	1.a	$1$	$2$	$2$	$23.356$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓		65.2.a.b	$1$	$1$	$-2$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+(-2+2\beta )q^{7}+\cdots$
2925.2.a.v	$2925$	$2$	2925.a	1.a	$1$	$2$	$2$	$23.356$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓		39.2.a.b	$1$	$1$	$-2$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-2\beta q^{7}+\cdots$
2925.2.a.w	$2925$	$2$	2925.a	1.a	$1$	$2$	$2$	$23.356$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓		325.2.a.f	$1$	$1$	$-2$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+(1-\beta )q^{7}+\cdots$
2925.2.a.x	$2925$	$2$	2925.a	1.a	$1$	$2$	$2$	$23.356$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓		585.2.a.j	$1$	$0$	$-1$	$0$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(2+\beta )q^{4}+(3-\beta )q^{7}+(-4+\cdots)q^{8}+\cdots$
2925.2.a.y	$2925$	$2$	2925.a	1.a	$1$	$2$	$2$	$23.356$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓		117.2.a.b	$2$	$1$	$0$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}-2q^{7}-\beta q^{8}+2\beta q^{11}+\cdots$
2925.2.a.z	$2925$	$2$	2925.a	1.a	$1$	$2$	$2$	$23.356$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓		65.2.a.c	$1$	$0$	$0$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}-2q^{7}-\beta q^{8}+(3-\beta )q^{11}+\cdots$
2925.2.a.ba	$2925$	$2$	2925.a	1.a	$1$	$2$	$2$	$23.356$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓	2925.2.a.ba	$2$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}-q^{7}-\beta q^{8}+\beta q^{11}+\cdots$
2925.2.a.bb	$2925$	$2$	2925.a	1.a	$1$	$2$	$2$	$23.356$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	✓	2925.2.a.ba	$2$	$1$	$0$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}+q^{7}-\beta q^{8}-\beta q^{11}+\cdots$
2925.2.a.bc	$2925$	$2$	2925.a	1.a	$1$	$2$	$2$	$23.356$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓		585.2.a.j	$1$	$0$	$1$	$0$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(2+\beta )q^{4}+(3-\beta )q^{7}+(4+\beta )q^{8}+\cdots$
2925.2.a.bd	$2925$	$2$	2925.a	1.a	$1$	$2$	$2$	$23.356$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓		325.2.a.f	$1$	$1$	$2$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(-1-\beta )q^{7}+\cdots$

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 89 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.