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 69 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
3536.1.n.a	$3536$	$1$	3536.n	884.h	$2$	$1$	$1$	$1.765$	$\Q$	$D_{2}$	$\Q(\sqrt{-17}) $, $\Q(\sqrt{-221}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-2q^{3}+3q^{9}+q^{13}-q^{17}+2q^{23}+\cdots$
3536.1.n.b	$3536$	$1$	3536.n	884.h	$2$	$1$	$1$	$1.765$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-221}) $	$\Q(\sqrt{221}) $	✓	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-2q^{5}-q^{9}+q^{13}-q^{17}+3q^{25}+\cdots$
3536.1.n.c	$3536$	$1$	3536.n	884.h	$2$	$1$	$1$	$1.765$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-221}) $	$\Q(\sqrt{221}) $	✓	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+2q^{5}-q^{9}+q^{13}-q^{17}+3q^{25}+\cdots$
3536.1.n.d	$3536$	$1$	3536.n	884.h	$2$	$1$	$1$	$1.765$	$\Q$	$D_{2}$	$\Q(\sqrt{-17}) $, $\Q(\sqrt{-221}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+2q^{3}+3q^{9}+q^{13}-q^{17}-2q^{23}+\cdots$
3536.1.n.e	$3536$	$1$	3536.n	884.h	$2$	$2$	$2$	$1.765$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-13}) $, $\Q(\sqrt{-17}) $	$\Q(\sqrt{221}) $		$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q-iq^{7}-q^{9}+iq^{11}-q^{13}-q^{17}+\cdots$
3536.1.n.f	$3536$	$1$	3536.n	884.h	$2$	$2$	$2$	$1.765$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-221}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{3}+\beta q^{5}+q^{9}-q^{13}-2q^{15}+\cdots$
3536.1.n.g	$3536$	$1$	3536.n	884.h	$2$	$2$	$2$	$1.765$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-221}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{3}-\beta q^{5}+q^{9}-q^{13}+2q^{15}+\cdots$
3536.1.bh.a	$3536$	$1$	3536.bh	3536.ah	$4$	$2$	$1$	$1.765$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{17}) $		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+iq^{2}-q^{4}-iq^{8}+iq^{9}+q^{13}+\cdots$
3536.1.bh.b	$3536$	$1$	3536.bh	3536.ah	$4$	$2$	$1$	$1.765$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{17}) $		$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+q^{8}+iq^{9}-iq^{13}+q^{16}+\cdots$
3536.1.bp.a	$3536$	$1$	3536.bp	884.n	$4$	$2$	$1$	$1.765$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+(-1-i)q^{5}-iq^{9}-iq^{13}+q^{17}+\cdots$
3536.1.bp.b	$3536$	$1$	3536.bp	884.n	$4$	$2$	$1$	$1.765$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+(-1-i)q^{7}-iq^{9}+(1+i)q^{11}+\cdots$
3536.1.bp.c	$3536$	$1$	3536.bp	884.n	$4$	$2$	$1$	$1.765$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+(1+i)q^{7}-iq^{9}+(-1-i)q^{11}+\cdots$
3536.1.bp.d	$3536$	$1$	3536.bp	884.n	$4$	$2$	$1$	$1.765$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+(1+i)q^{5}-iq^{9}+iq^{13}+q^{17}+\cdots$
3536.1.ce.a	$3536$	$1$	3536.ce	3536.be	$4$	$2$	$1$	$1.765$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{17}) $		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{2}-q^{4}+iq^{8}+iq^{9}-q^{13}+\cdots$
3536.1.ce.b	$3536$	$1$	3536.ce	3536.be	$4$	$2$	$1$	$1.765$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{17}) $		$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+q^{8}+iq^{9}+iq^{13}+q^{16}+\cdots$
3536.1.cv.a	$3536$	$1$	3536.cv	884.v	$6$	$8$	$4$	$1.765$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-17}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{24}^{7}+\zeta_{24}^{9})q^{3}+(\zeta_{24}^{3}+\zeta_{24}^{5}+\cdots)q^{7}+\cdots$
3536.1.db.a	$3536$	$1$	3536.db	884.x	$6$	$2$	$1$	$1.765$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-17}) $	None		$4$	$0$	$0$	$-1$	$0$	$3$		$1$		$q+\zeta_{6}^{2}q^{3}+(1-\zeta_{6}^{2})q^{7}+q^{13}+\zeta_{6}q^{17}+\cdots$
3536.1.db.b	$3536$	$1$	3536.db	884.x	$6$	$2$	$1$	$1.765$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-q^{5}+\zeta_{6}q^{9}+\zeta_{6}^{2}q^{13}-q^{17}+(-1+\cdots)q^{29}+\cdots$
3536.1.db.c	$3536$	$1$	3536.db	884.x	$6$	$2$	$1$	$1.765$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+q^{5}+\zeta_{6}q^{9}+\zeta_{6}^{2}q^{13}-\zeta_{6}^{2}q^{17}+\cdots$
3536.1.db.d	$3536$	$1$	3536.db	884.x	$6$	$2$	$1$	$1.765$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-17}) $	None		$4$	$0$	$0$	$1$	$0$	$-3$		$1$		$q-\zeta_{6}^{2}q^{3}+(-1+\zeta_{6}^{2})q^{7}+q^{13}+\cdots$
3536.1.db.e	$3536$	$1$	3536.db	884.x	$6$	$4$	$2$	$1.765$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-17}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}q^{7}+(-1+\cdots)q^{9}+\cdots$
3536.1.ea.a	$3536$	$1$	3536.ea	884.ag	$8$	$4$	$1$	$1.765$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$0$	$0$	$0$	$-4$		$1$		$q+(-1+\zeta_{8})q^{7}-\zeta_{8}^{3}q^{9}+(-1-\zeta_{8}+\cdots)q^{11}+\cdots$
3536.1.ea.b	$3536$	$1$	3536.ea	884.ag	$8$	$4$	$1$	$1.765$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$0$	$0$	$0$	$4$		$1$		$q+(1-\zeta_{8})q^{7}-\zeta_{8}^{3}q^{9}+(1+\zeta_{8})q^{11}+\cdots$
3536.1.fu.a	$3536$	$1$	3536.fu	884.aq	$12$	$4$	$1$	$1.765$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+(-\zeta_{12}-\zeta_{12}^{2})q^{5}+\zeta_{12}^{5}q^{9}-\zeta_{12}q^{13}+\cdots$
3536.1.fu.b	$3536$	$1$	3536.fu	884.aq	$12$	$4$	$1$	$1.765$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+(-\zeta_{12}^{4}+\zeta_{12}^{5})q^{5}+\zeta_{12}^{5}q^{9}+\cdots$
3536.1.gw.a	$3536$	$1$	3536.gw	884.aw	$16$	$8$	$1$	$1.765$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{16}^{2}-\zeta_{16}^{3})q^{5}+\zeta_{16}^{5}q^{9}+\zeta_{16}^{7}q^{13}+\cdots$
3536.1.hu.a	$3536$	$1$	3536.hu	884.bc	$16$	$8$	$1$	$1.765$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{16}^{3}+\zeta_{16}^{6})q^{5}+\zeta_{16}q^{9}-\zeta_{16}q^{13}+\cdots$
3536.1.in.a	$3536$	$1$	3536.in	884.bh	$24$	$8$	$1$	$1.765$	$\Q(\zeta_{24})$	$D_{24}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{24}^{2}+\zeta_{24}^{7})q^{5}-\zeta_{24}q^{9}+\zeta_{24}^{11}q^{13}+\cdots$
3536.1.in.b	$3536$	$1$	3536.in	884.bh	$24$	$8$	$1$	$1.765$	$\Q(\zeta_{24})$	$D_{24}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{24}^{10}-\zeta_{24}^{11})q^{5}-\zeta_{24}q^{9}-\zeta_{24}^{5}q^{13}+\cdots$
3536.1.jl.a	$3536$	$1$	3536.jl	884.bn	$48$	$16$	$1$	$1.765$	$\Q(\zeta_{48})$	$D_{48}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{48}^{5}-\zeta_{48}^{22})q^{5}-\zeta_{48}^{11}q^{9}+\cdots$
3536.1.kj.a	$3536$	$1$	3536.kj	884.bt	$48$	$16$	$1$	$1.765$	$\Q(\zeta_{48})$	$D_{48}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{48}^{10}-\zeta_{48}^{17})q^{5}-\zeta_{48}^{19}q^{9}+\cdots$
3536.2.a.a	$3536$	$2$	3536.a	1.a	$1$	$1$	$1$	$28.235$	$\Q$	$_{}$	None	None	✓	$1$	$2$	$0$	$-2$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots$
3536.2.a.b	$3536$	$2$	3536.a	1.a	$1$	$1$	$1$	$28.235$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{5}-2q^{7}+q^{9}-2q^{11}+\cdots$
3536.2.a.c	$3536$	$2$	3536.a	1.a	$1$	$1$	$1$	$28.235$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{5}-2q^{7}+q^{9}+6q^{11}+\cdots$
3536.2.a.d	$3536$	$2$	3536.a	1.a	$1$	$1$	$1$	$28.235$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+4q^{5}+4q^{7}+q^{9}+2q^{11}+\cdots$
3536.2.a.e	$3536$	$2$	3536.a	1.a	$1$	$1$	$1$	$28.235$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-4$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}+2q^{7}-3q^{9}+2q^{11}-q^{13}+\cdots$
3536.2.a.f	$3536$	$2$	3536.a	1.a	$1$	$1$	$1$	$28.235$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-3q^{9}-6q^{11}-q^{13}+q^{17}+\cdots$
3536.2.a.g	$3536$	$2$	3536.a	1.a	$1$	$1$	$1$	$28.235$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{7}-3q^{9}+2q^{11}-q^{13}+\cdots$
3536.2.a.h	$3536$	$2$	3536.a	1.a	$1$	$1$	$1$	$28.235$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-3q^{9}-4q^{11}+q^{13}+q^{17}+\cdots$
3536.2.a.i	$3536$	$2$	3536.a	1.a	$1$	$1$	$1$	$28.235$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}-2q^{7}-3q^{9}+2q^{11}-q^{13}+\cdots$
3536.2.a.j	$3536$	$2$	3536.a	1.a	$1$	$1$	$1$	$28.235$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$4$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}+2q^{7}-3q^{9}-6q^{11}-q^{13}+\cdots$
3536.2.a.k	$3536$	$2$	3536.a	1.a	$1$	$1$	$1$	$28.235$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+2q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots$
3536.2.a.l	$3536$	$2$	3536.a	1.a	$1$	$1$	$1$	$28.235$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+2q^{5}-2q^{7}+q^{9}+2q^{11}+\cdots$
3536.2.a.m	$3536$	$2$	3536.a	1.a	$1$	$2$	$2$	$28.235$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-2$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+(-1-\beta )q^{5}-2q^{7}+\cdots$
3536.2.a.n	$3536$	$2$	3536.a	1.a	$1$	$2$	$2$	$28.235$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-2$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+(-1+\beta )q^{5}+(3+2\beta )q^{9}+\cdots$
3536.2.a.o	$3536$	$2$	3536.a	1.a	$1$	$2$	$2$	$28.235$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$2$	$-8$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+(1+\beta )q^{5}-4q^{7}+(1+\cdots)q^{9}+\cdots$
3536.2.a.p	$3536$	$2$	3536.a	1.a	$1$	$2$	$2$	$28.235$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$2$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+(1+\beta )q^{5}+2q^{7}+(3+\cdots)q^{9}+\cdots$
3536.2.a.q	$3536$	$2$	3536.a	1.a	$1$	$2$	$2$	$28.235$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$4$	$2$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+2q^{5}+(1+\beta )q^{7}+(3+\cdots)q^{9}+\cdots$
3536.2.a.r	$3536$	$2$	3536.a	1.a	$1$	$2$	$2$	$28.235$	$\Q(\sqrt{21}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-2$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}-q^{5}+(2+\beta )q^{7}+(2+\beta )q^{9}+\cdots$
3536.2.a.s	$3536$	$2$	3536.a	1.a	$1$	$2$	$2$	$28.235$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$4$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(1+2\beta )q^{5}+(2-3\beta )q^{7}+(-2+\cdots)q^{9}+\cdots$

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 69 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.