LMFDB - Newform search results

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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

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Results (1-50 of 60 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	5	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4160.2.a.a	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	$\Q$	None	✓				520.2.a.b	$1$	$1$	$0$	$-2$	$-1$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}+q^{9}-2q^{11}-q^{13}+\cdots$
4160.2.a.b	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	$\Q$	None	✓				130.2.a.a	$1$	$0$	$0$	$-2$	$-1$	$4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}+4q^{7}+q^{9}-6q^{11}+\cdots$
4160.2.a.c	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	$\Q$	None	✓				130.2.a.c	$1$	$1$	$0$	$-2$	$1$	$-4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}-4q^{7}+q^{9}+2q^{11}+\cdots$
4160.2.a.d	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	$\Q$	None	✓				260.2.a.a	$1$	$1$	$0$	$-2$	$1$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+2q^{7}+q^{9}-4q^{11}+\cdots$
4160.2.a.e	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	$\Q$	None	✓				2080.2.a.a	$1$	$0$	$0$	$-2$	$1$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+4q^{7}+q^{9}-6q^{11}+\cdots$
4160.2.a.f	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	$\Q$	None	✓				65.2.a.a	$1$	$0$	$0$	$-2$	$1$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+4q^{7}+q^{9}+2q^{11}+\cdots$
4160.2.a.g	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	$\Q$	None	✓				2080.2.a.d	$1$	$0$	$0$	$0$	$-1$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-4q^{7}-3q^{9}+4q^{11}-q^{13}+\cdots$
4160.2.a.h	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	$\Q$	None	✓				130.2.a.b	$1$	$0$	$0$	$0$	$-1$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{9}-q^{13}+2q^{17}-8q^{19}+\cdots$
4160.2.a.i	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	$\Q$	None	✓				130.2.a.b	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{9}-q^{13}+2q^{17}+8q^{19}+\cdots$
4160.2.a.j	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	$\Q$	None	✓				2080.2.a.d	$1$	$0$	$0$	$0$	$-1$	$4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{7}-3q^{9}-4q^{11}-q^{13}+\cdots$
4160.2.a.k	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	$\Q$	None	✓				2080.2.a.b	$1$	$1$	$0$	$0$	$1$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}-3q^{9}+2q^{11}+q^{13}+\cdots$
4160.2.a.l	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	$\Q$	None	✓				520.2.a.a	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-3q^{9}-4q^{11}+q^{13}-6q^{17}+\cdots$
4160.2.a.m	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	$\Q$	None	✓				520.2.a.a	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-3q^{9}+4q^{11}+q^{13}-6q^{17}+\cdots$
4160.2.a.n	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	$\Q$	None	✓				2080.2.a.b	$1$	$1$	$0$	$0$	$1$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}-3q^{9}-2q^{11}+q^{13}+\cdots$
4160.2.a.o	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	$\Q$	None	✓				130.2.a.a	$1$	$1$	$0$	$2$	$-1$	$-4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{5}-4q^{7}+q^{9}+6q^{11}+\cdots$
4160.2.a.p	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	$\Q$	None	✓				520.2.a.b	$1$	$0$	$0$	$2$	$-1$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{5}+q^{9}+2q^{11}-q^{13}+\cdots$
4160.2.a.q	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	$\Q$	None	✓				65.2.a.a	$1$	$1$	$0$	$2$	$1$	$-4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}-4q^{7}+q^{9}-2q^{11}+\cdots$
4160.2.a.r	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	$\Q$	None	✓				2080.2.a.a	$1$	$0$	$0$	$2$	$1$	$-4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}-4q^{7}+q^{9}+6q^{11}+\cdots$
4160.2.a.s	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	$\Q$	None	✓				260.2.a.a	$1$	$0$	$0$	$2$	$1$	$-2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}-2q^{7}+q^{9}+4q^{11}+\cdots$
4160.2.a.t	$4160$	$2$	4160.a	1.a	$1$	$1$	$1$	$33.218$	$\Q$	None	✓				130.2.a.c	$1$	$0$	$0$	$2$	$1$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}+4q^{7}+q^{9}-2q^{11}+\cdots$
4160.2.a.u	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	$\Q(\sqrt{2}) $	None	✓				520.2.a.c	$1$	$1$	$0$	$-4$	$-2$	$4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-2+\beta )q^{3}-q^{5}+2q^{7}+(3-4\beta )q^{9}+\cdots$
4160.2.a.v	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	$\Q(\sqrt{3}) $	None	✓				520.2.a.d	$1$	$1$	$0$	$-2$	$2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+q^{5}+2\beta q^{7}+(1-2\beta )q^{9}+\cdots$
4160.2.a.w	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	$\Q(\sqrt{3}) $	None	✓				520.2.a.e	$1$	$1$	$0$	$-2$	$2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+q^{5}-2\beta q^{7}+(1-2\beta )q^{9}+\cdots$
4160.2.a.x	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	$\Q(\sqrt{5}) $	None	✓		✓		520.2.a.g	$1$	$1$	$0$	$-2$	$2$	$0$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+q^{5}+(3+2\beta )q^{9}+(-3+\cdots)q^{11}+\cdots$
4160.2.a.y	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	$\Q(\sqrt{3}) $	None	✓				65.2.a.c	$1$	$0$	$0$	$-2$	$2$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+q^{5}+2q^{7}+(1-2\beta )q^{9}+\cdots$
4160.2.a.z	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	$\Q(\sqrt{2}) $	None	✓				65.2.a.b	$1$	$1$	$0$	$0$	$-2$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}+(-2+2\beta )q^{7}-q^{9}+\cdots$
4160.2.a.ba	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	$\Q(\sqrt{6}) $	None	✓				520.2.a.f	$1$	$1$	$0$	$0$	$-2$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}-2q^{7}+3q^{9}+(-2+\beta )q^{11}+\cdots$
4160.2.a.bb	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	$\Q(\sqrt{2}) $	None	✓				2080.2.a.i	$2$	$0$	$0$	$0$	$-2$	$0$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{5}+\beta q^{7}-3q^{9}+\beta q^{11}-q^{13}+\cdots$
4160.2.a.bc	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	$\Q(\sqrt{2}) $	None	✓				2080.2.a.j	$2$	$1$	$0$	$0$	$-2$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}+2\beta q^{7}-q^{9}+\beta q^{11}+\cdots$
4160.2.a.bd	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	$\Q(\sqrt{2}) $	None	✓				2080.2.a.k	$2$	$1$	$0$	$0$	$-2$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}-2\beta q^{7}-q^{9}+\beta q^{11}+\cdots$
4160.2.a.be	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	$\Q(\sqrt{2}) $	None	✓				2080.2.a.l	$2$	$0$	$0$	$0$	$-2$	$0$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}+5q^{9}+\beta q^{11}-q^{13}+\cdots$
4160.2.a.bf	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	$\Q(\sqrt{2}) $	None	✓				65.2.a.b	$1$	$0$	$0$	$0$	$-2$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}+(2+2\beta )q^{7}-q^{9}+(-2+\cdots)q^{11}+\cdots$
4160.2.a.bg	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	$\Q(\sqrt{6}) $	None	✓				520.2.a.f	$1$	$0$	$0$	$0$	$-2$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}+2q^{7}+3q^{9}+(2+\beta )q^{11}+\cdots$
4160.2.a.bh	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	$\Q(\sqrt{2}) $	None	✓				2080.2.a.h	$2$	$1$	$0$	$0$	$2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+q^{5}-q^{9}+\beta q^{11}-q^{13}+\cdots$
4160.2.a.bi	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	$\Q(\sqrt{2}) $	None	✓				2080.2.a.g	$2$	$1$	$0$	$0$	$2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+q^{5}-q^{9}-3\beta q^{11}-q^{13}+\cdots$
4160.2.a.bj	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	$\Q(\sqrt{3}) $	None	✓				65.2.a.c	$1$	$1$	$0$	$2$	$2$	$-4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+q^{5}-2q^{7}+(1+2\beta )q^{9}+\cdots$
4160.2.a.bk	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	$\Q(\sqrt{3}) $	None	✓				520.2.a.e	$1$	$0$	$0$	$2$	$2$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+q^{5}-2\beta q^{7}+(1+2\beta )q^{9}+\cdots$
4160.2.a.bl	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	$\Q(\sqrt{3}) $	None	✓				520.2.a.d	$1$	$0$	$0$	$2$	$2$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+q^{5}+2\beta q^{7}+(1+2\beta )q^{9}+\cdots$
4160.2.a.bm	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	$\Q(\sqrt{5}) $	None	✓				520.2.a.g	$1$	$0$	$0$	$2$	$2$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+q^{5}+(3+2\beta )q^{9}+(3-\beta )q^{11}+\cdots$
4160.2.a.bn	$4160$	$2$	4160.a	1.a	$1$	$2$	$2$	$33.218$	$\Q(\sqrt{2}) $	None	✓				520.2.a.c	$1$	$0$	$0$	$4$	$-2$	$-4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{3}-q^{5}-2q^{7}+(3+4\beta )q^{9}+\cdots$
4160.2.a.bo	$4160$	$2$	4160.a	1.a	$1$	$3$	$3$	$33.218$	3.3.564.1	None	✓				260.2.a.b	$1$	$1$	$0$	$-2$	$-3$	$-2$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}-q^{5}+(-1-\beta _{1})q^{7}+\cdots$
4160.2.a.bp	$4160$	$2$	4160.a	1.a	$1$	$3$	$3$	$33.218$	3.3.148.1	None	✓				2080.2.a.m	$1$	$1$	$0$	$-2$	$-3$	$6$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}-q^{5}+2q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots$
4160.2.a.bq	$4160$	$2$	4160.a	1.a	$1$	$3$	$3$	$33.218$	3.3.148.1	None	✓				2080.2.a.m	$1$	$1$	$0$	$2$	$-3$	$-6$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}-q^{5}-2q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots$
4160.2.a.br	$4160$	$2$	4160.a	1.a	$1$	$3$	$3$	$33.218$	3.3.564.1	None	✓		✓		260.2.a.b	$1$	$0$	$0$	$2$	$-3$	$2$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}-q^{5}+(1+\beta _{1})q^{7}+(4+\cdots)q^{9}+\cdots$
4160.2.a.bs	$4160$	$2$	4160.a	1.a	$1$	$4$	$4$	$33.218$	4.4.4752.1	None	✓				2080.2.a.o	$1$	$0$	$0$	$-4$	$-4$	$4$	$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}-q^{5}+(1+\beta _{1})q^{7}+\cdots$
4160.2.a.bt	$4160$	$2$	4160.a	1.a	$1$	$4$	$4$	$33.218$	4.4.5744.1	None	✓				2080.2.a.p	$1$	$0$	$0$	$-2$	$4$	$0$	$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+q^{5}-\beta _{1}q^{7}+(1-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots$
4160.2.a.bu	$4160$	$2$	4160.a	1.a	$1$	$4$	$4$	$33.218$	$\Q(\zeta_{16})^+$	None	✓				2080.2.a.q	$2$	$0$	$0$	$0$	$4$	$0$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{5}+(\beta _{1}+\beta _{2})q^{7}+(1+\beta _{3})q^{9}+\cdots$
4160.2.a.bv	$4160$	$2$	4160.a	1.a	$1$	$4$	$4$	$33.218$	4.4.25088.1	None	✓				2080.2.a.r	$2$	$0$	$0$	$0$	$4$	$0$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+q^{5}+(-\beta _{1}+\beta _{2})q^{7}+(3+\cdots)q^{9}+\cdots$
4160.2.a.bw	$4160$	$2$	4160.a	1.a	$1$	$4$	$4$	$33.218$	4.4.5744.1	None	✓				2080.2.a.p	$1$	$0$	$0$	$2$	$4$	$0$	$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+q^{5}+\beta _{1}q^{7}+(1-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots$
4160.2.a.bx	$4160$	$2$	4160.a	1.a	$1$	$4$	$4$	$33.218$	4.4.4752.1	None	✓				2080.2.a.o	$1$	$0$	$0$	$4$	$-4$	$-4$	$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}-q^{5}+(-1+\beta _{1})q^{7}+\cdots$

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Elliptic curves over $\Q$
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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.