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 764 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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
219.1.o.a	$219$	$1$	219.o	219.o	$12$	$4$	$1$	$0.109$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+\zeta_{12}^{3}q^{3}-\zeta_{12}^{2}q^{4}+(\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{7}+\cdots$
260.1.be.a	$260$	$1$	260.be	260.ae	$12$	$4$	$1$	$0.130$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}-\zeta_{12}^{5}q^{5}+\cdots$
260.1.bl.a	$260$	$1$	260.bl	260.al	$12$	$4$	$1$	$0.130$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{2}q^{5}+\zeta_{12}^{3}q^{8}+\cdots$
273.1.bs.a	$273$	$1$	273.bs	273.as	$12$	$4$	$1$	$0.136$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{12}q^{3}-\zeta_{12}^{3}q^{4}-\zeta_{12}q^{7}+\zeta_{12}^{2}q^{9}+\cdots$
273.1.ch.a	$273$	$1$	273.ch	273.bh	$12$	$4$	$1$	$0.136$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-\zeta_{12}^{3}q^{3}-\zeta_{12}^{5}q^{4}+\zeta_{12}^{4}q^{7}+\cdots$
333.1.bb.a	$333$	$1$	333.bb	37.g	$12$	$4$	$1$	$0.166$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{12}^{5}q^{4}+(\zeta_{12}+\zeta_{12}^{3})q^{7}+(-\zeta_{12}^{3}+\cdots)q^{13}+\cdots$
351.1.bg.a	$351$	$1$	351.bg	13.f	$12$	$4$	$1$	$0.175$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+\zeta_{12}^{5}q^{4}+(\zeta_{12}^{2}-\zeta_{12}^{5})q^{7}+\zeta_{12}^{3}q^{13}+\cdots$
368.1.k.b	$368$	$1$	368.k	368.k	$4$	$4$	$2$	$0.184$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q+\zeta_{12}^{5}q^{2}+(\zeta_{12}-\zeta_{12}^{2})q^{3}-\zeta_{12}^{4}q^{4}+\cdots$
388.1.m.a	$388$	$1$	388.m	388.m	$12$	$4$	$1$	$0.194$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-\zeta_{12}^{2}-\zeta_{12}^{3}+\cdots)q^{5}+\cdots$
416.1.bl.a	$416$	$1$	416.bl	13.f	$12$	$4$	$1$	$0.208$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+(\zeta_{12}^{4}+\zeta_{12}^{5})q^{5}+\zeta_{12}^{2}q^{9}+\zeta_{12}q^{13}+\cdots$
468.1.bx.a	$468$	$1$	468.bx	156.v	$12$	$8$	$2$	$0.234$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-\zeta_{24}-\zeta_{24}^{5}+\cdots)q^{5}+\cdots$
468.1.cd.a	$468$	$1$	468.cd	13.f	$12$	$4$	$1$	$0.234$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+(\zeta_{12}^{2}+\zeta_{12}^{3})q^{7}-\zeta_{12}q^{13}+(\zeta_{12}+\cdots)q^{19}+\cdots$
495.1.bd.a	$495$	$1$	495.bd	495.ad	$12$	$4$	$1$	$0.247$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{12}q^{3}-\zeta_{12}q^{4}-\zeta_{12}^{3}q^{5}+\zeta_{12}^{2}q^{9}+\cdots$
495.1.bd.b	$495$	$1$	495.bd	495.ad	$12$	$4$	$1$	$0.247$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q-\zeta_{12}^{4}q^{3}-\zeta_{12}q^{4}-\zeta_{12}^{5}q^{5}-\zeta_{12}^{2}q^{9}+\cdots$
496.1.j.b	$496$	$1$	496.j	496.j	$4$	$4$	$2$	$0.248$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$2$	$0$	$-2$	$0$	$1$		$q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+(\zeta_{12}^{4}-\zeta_{12}^{5}+\cdots)q^{5}+\cdots$
584.1.z.a	$584$	$1$	584.z	584.z	$12$	$4$	$1$	$0.291$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q-\zeta_{12}^{4}q^{2}+\zeta_{12}^{3}q^{3}-\zeta_{12}^{2}q^{4}+\cdots$
620.1.m.c	$620$	$1$	620.m	620.m	$4$	$4$	$2$	$0.309$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{5}q^{5}+\cdots$
620.1.m.d	$620$	$1$	620.m	620.m	$4$	$4$	$2$	$0.309$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$2$	$0$	$0$	$-2$	$1$		$q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}-\zeta_{12}q^{5}+(\zeta_{12}^{4}+\cdots)q^{7}+\cdots$
624.1.cp.a	$624$	$1$	624.cp	156.v	$12$	$4$	$1$	$0.311$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+\zeta_{12}q^{3}+(-\zeta_{12}^{3}+\zeta_{12}^{4})q^{7}+\zeta_{12}^{2}q^{9}+\cdots$
624.1.cp.b	$624$	$1$	624.cp	156.v	$12$	$4$	$1$	$0.311$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q-\zeta_{12}q^{3}+(\zeta_{12}^{3}-\zeta_{12}^{4})q^{7}+\zeta_{12}^{2}q^{9}+\cdots$
660.1.v.a	$660$	$1$	660.v	165.l	$4$	$4$	$2$	$0.329$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{3}-\zeta_{12}^{5}q^{5}+\zeta_{12}^{2}q^{9}-\zeta_{12}^{3}q^{11}+\cdots$
660.1.v.b	$660$	$1$	660.v	165.l	$4$	$4$	$2$	$0.329$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+\zeta_{12}^{2}q^{3}+\zeta_{12}^{5}q^{5}+\zeta_{12}^{4}q^{9}+\cdots$
665.1.ca.a	$665$	$1$	665.ca	665.ba	$12$	$4$	$1$	$0.332$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-4$	$2$	$1$		$q-\zeta_{12}^{5}q^{4}-q^{5}-\zeta_{12}^{4}q^{7}-\zeta_{12}q^{9}+\cdots$
665.1.ca.b	$665$	$1$	665.ca	665.ba	$12$	$4$	$1$	$0.332$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-\zeta_{12}^{5}q^{4}-\zeta_{12}^{2}q^{5}+\zeta_{12}q^{7}-\zeta_{12}q^{9}+\cdots$
695.1.d.g	$695$	$1$	695.d	695.d	$2$	$4$	$4$	$0.347$	$\Q(\zeta_{24})^+$	$D_{12}$	$\Q(\sqrt{-695}) $	None	✓	$4$	$0$	$0$	$0$	$-4$	$0$	$1$		$q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
715.1.bb.a	$715$	$1$	715.bb	715.ab	$6$	$8$	$4$	$0.357$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{24}^{7}-\zeta_{24}^{9})q^{2}+(-\zeta_{24}^{2}+\zeta_{24}^{4}+\cdots)q^{4}+\cdots$
728.1.bl.a	$728$	$1$	728.bl	728.al	$6$	$8$	$4$	$0.363$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-14}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{24}^{2}q^{2}+(\zeta_{24}^{7}+\zeta_{24}^{9})q^{3}+\zeta_{24}^{4}q^{4}+\cdots$
740.1.bj.a	$740$	$1$	740.bj	740.aj	$12$	$4$	$1$	$0.369$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$2$	$0$	$2$	$0$	$1$		$q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+\zeta_{12}^{2}q^{5}+\cdots$
740.1.bm.a	$740$	$1$	740.bm	740.am	$12$	$4$	$1$	$0.369$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{3}q^{5}+\cdots$
741.1.cc.a	$741$	$1$	741.cc	741.bc	$12$	$4$	$1$	$0.370$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-\zeta_{12}q^{3}-\zeta_{12}^{5}q^{4}+(\zeta_{12}^{4}-\zeta_{12}^{5}+\cdots)q^{7}+\cdots$
741.1.cc.b	$741$	$1$	741.cc	741.bc	$12$	$4$	$1$	$0.370$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+\zeta_{12}q^{3}-\zeta_{12}^{5}q^{4}+(-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{7}+\cdots$
772.1.m.a	$772$	$1$	772.m	772.m	$12$	$4$	$1$	$0.385$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-\zeta_{12}-\zeta_{12}^{4}+\cdots)q^{5}+\cdots$
776.1.ba.a	$776$	$1$	776.ba	776.aa	$12$	$4$	$1$	$0.387$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-6$	$0$	$0$	$1$		$q+\zeta_{12}q^{2}+(-1-\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
777.1.w.d	$777$	$1$	777.w	777.w	$6$	$8$	$4$	$0.388$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-111}) $	None		$8$	$0$	$0$	$4$	$0$	$0$	$1$		$q+(\zeta_{24}^{7}+\zeta_{24}^{9})q^{2}+\zeta_{24}^{4}q^{3}+(-\zeta_{24}^{2}+\cdots)q^{4}+\cdots$
777.1.ca.a	$777$	$1$	777.ca	777.ba	$12$	$4$	$1$	$0.388$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q+\zeta_{12}^{4}q^{3}+\zeta_{12}q^{4}+\zeta_{12}^{5}q^{7}-\zeta_{12}^{2}q^{9}+\cdots$
777.1.ca.b	$777$	$1$	777.ca	777.ba	$12$	$4$	$1$	$0.388$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q-\zeta_{12}^{4}q^{3}+\zeta_{12}q^{4}+\zeta_{12}^{3}q^{7}-\zeta_{12}^{2}q^{9}+\cdots$
793.1.bn.a	$793$	$1$	793.bn	793.an	$12$	$4$	$1$	$0.396$	$\Q(\zeta_{12})$	$D_{12}$	None	$\Q(\sqrt{61}) $		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}q^{4}+(\zeta_{12}^{4}+\cdots)q^{5}+\cdots$
819.1.eu.a	$819$	$1$	819.eu	91.x	$12$	$4$	$1$	$0.409$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}^{3}q^{4}-\zeta_{12}q^{7}-\zeta_{12}^{5}q^{13}+\cdots$
819.1.ff.a	$819$	$1$	819.ff	91.ad	$12$	$4$	$1$	$0.409$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q-\zeta_{12}q^{4}+\zeta_{12}^{2}q^{7}+\zeta_{12}q^{13}+\zeta_{12}^{2}q^{16}+\cdots$
832.1.bl.a	$832$	$1$	832.bl	13.f	$12$	$4$	$1$	$0.415$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+(-\zeta_{12}+\zeta_{12}^{2})q^{5}-\zeta_{12}^{4}q^{9}-\zeta_{12}^{5}q^{13}+\cdots$
840.1.dh.a	$840$	$1$	840.dh	840.ch	$12$	$8$	$2$	$0.419$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-6}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{24}^{5}q^{2}+\zeta_{24}q^{3}+\zeta_{24}^{10}q^{4}+\cdots$
840.1.dh.b	$840$	$1$	840.dh	840.ch	$12$	$8$	$2$	$0.419$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-6}) $	None		$8$	$0$	$0$	$0$	$0$	$4$	$1$		$q+\zeta_{24}^{5}q^{2}+\zeta_{24}q^{3}+\zeta_{24}^{10}q^{4}+\cdots$
855.1.z.d	$855$	$1$	855.z	855.z	$6$	$8$	$4$	$0.427$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-95}) $	None		$8$	$0$	$0$	$0$	$4$	$0$	$1$		$q+(\zeta_{24}^{7}+\zeta_{24}^{9})q^{2}+\zeta_{24}^{11}q^{3}+(-\zeta_{24}^{2}+\cdots)q^{4}+\cdots$
880.1.y.c	$880$	$1$	880.y	220.i	$4$	$4$	$2$	$0.439$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q+(-\zeta_{12}-\zeta_{12}^{2})q^{3}+\zeta_{12}^{5}q^{5}+(\zeta_{12}^{2}+\cdots)q^{9}+\cdots$
880.1.y.d	$880$	$1$	880.y	220.i	$4$	$4$	$2$	$0.439$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+(-\zeta_{12}+\zeta_{12}^{2})q^{3}-\zeta_{12}^{5}q^{5}+(\zeta_{12}^{2}+\cdots)q^{9}+\cdots$
884.1.x.a	$884$	$1$	884.x	884.x	$6$	$8$	$4$	$0.441$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-17}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{24}^{10}q^{2}+(-\zeta_{24}^{9}+\zeta_{24}^{11})q^{3}+\cdots$
884.1.bp.a	$884$	$1$	884.bp	884.ap	$12$	$4$	$1$	$0.441$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+(-\zeta_{12}^{4}-\zeta_{12}^{5}+\cdots)q^{5}+\cdots$
884.1.bp.b	$884$	$1$	884.bp	884.ap	$12$	$4$	$1$	$0.441$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+(-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
885.1.k.c	$885$	$1$	885.k	885.k	$4$	$4$	$2$	$0.442$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$0$	$-2$	$-2$	$1$		$q-\zeta_{12}q^{3}-\zeta_{12}^{3}q^{4}+\zeta_{12}^{4}q^{5}+(-\zeta_{12}+\cdots)q^{7}+\cdots$
885.1.k.d	$885$	$1$	885.k	885.k	$4$	$4$	$2$	$0.442$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$2$	$2$	$-2$	$1$		$q+\zeta_{12}^{2}q^{3}-\zeta_{12}^{3}q^{4}-\zeta_{12}^{4}q^{5}+\cdots$

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 764 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.