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 66 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	3	5	41	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
9840.2.a.a	$9840$	$2$	9840.a	1.a	$1$	$1$	$1$	$78.573$	$\Q$	None	✓				2460.2.a.b	$1$	$1$	$0$	$-1$	$-1$	$-4$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-4q^{7}+q^{9}+4q^{11}+q^{15}+\cdots$
9840.2.a.b	$9840$	$2$	9840.a	1.a	$1$	$1$	$1$	$78.573$	$\Q$	None	✓				4920.2.a.g	$1$	$1$	$0$	$-1$	$-1$	$-4$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-4q^{7}+q^{9}+6q^{11}+q^{15}+\cdots$
9840.2.a.c	$9840$	$2$	9840.a	1.a	$1$	$1$	$1$	$78.573$	$\Q$	None	✓				1230.2.a.j	$1$	$1$	$0$	$-1$	$-1$	$-3$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-3q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots$
9840.2.a.d	$9840$	$2$	9840.a	1.a	$1$	$1$	$1$	$78.573$	$\Q$	None	✓				4920.2.a.f	$1$	$2$	$0$	$-1$	$-1$	$-2$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots$
9840.2.a.e	$9840$	$2$	9840.a	1.a	$1$	$1$	$1$	$78.573$	$\Q$	None	✓				615.2.a.b	$1$	$1$	$0$	$-1$	$-1$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}+q^{11}-4q^{13}+q^{15}+\cdots$
9840.2.a.f	$9840$	$2$	9840.a	1.a	$1$	$1$	$1$	$78.573$	$\Q$	None	✓				1230.2.a.c	$1$	$1$	$0$	$-1$	$-1$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots$
9840.2.a.g	$9840$	$2$	9840.a	1.a	$1$	$1$	$1$	$78.573$	$\Q$	None	✓				1230.2.a.b	$1$	$0$	$0$	$-1$	$-1$	$1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{7}+q^{9}-6q^{11}-4q^{13}+\cdots$
9840.2.a.h	$9840$	$2$	9840.a	1.a	$1$	$1$	$1$	$78.573$	$\Q$	None	✓				1230.2.a.i	$1$	$1$	$0$	$-1$	$-1$	$2$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+2q^{7}+q^{9}-2q^{11}+6q^{13}+\cdots$
9840.2.a.i	$9840$	$2$	9840.a	1.a	$1$	$1$	$1$	$78.573$	$\Q$	None	✓				4920.2.a.e	$1$	$1$	$0$	$-1$	$-1$	$4$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+4q^{7}+q^{9}-3q^{11}-4q^{13}+\cdots$
9840.2.a.j	$9840$	$2$	9840.a	1.a	$1$	$1$	$1$	$78.573$	$\Q$	None	✓				1230.2.a.h	$1$	$0$	$0$	$-1$	$-1$	$4$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+4q^{7}+q^{9}+6q^{11}-4q^{13}+\cdots$
9840.2.a.k	$9840$	$2$	9840.a	1.a	$1$	$1$	$1$	$78.573$	$\Q$	None	✓				2460.2.a.e	$1$	$1$	$0$	$-1$	$1$	$-4$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-4q^{7}+q^{9}-3q^{11}-4q^{13}+\cdots$
9840.2.a.l	$9840$	$2$	9840.a	1.a	$1$	$1$	$1$	$78.573$	$\Q$	None	✓				2460.2.a.d	$1$	$1$	$0$	$-1$	$1$	$-4$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-4q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots$
9840.2.a.m	$9840$	$2$	9840.a	1.a	$1$	$1$	$1$	$78.573$	$\Q$	None	✓				4920.2.a.j	$1$	$1$	$0$	$-1$	$1$	$-2$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots$
9840.2.a.n	$9840$	$2$	9840.a	1.a	$1$	$1$	$1$	$78.573$	$\Q$	None	✓				1230.2.a.k	$1$	$1$	$0$	$-1$	$1$	$-1$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-q^{7}+q^{9}+2q^{11}-q^{15}+\cdots$
9840.2.a.o	$9840$	$2$	9840.a	1.a	$1$	$1$	$1$	$78.573$	$\Q$	None	✓				4920.2.a.i	$1$	$1$	$0$	$-1$	$1$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots$
9840.2.a.p	$9840$	$2$	9840.a	1.a	$1$	$1$	$1$	$78.573$	$\Q$	None	✓				1230.2.a.d	$1$	$1$	$0$	$-1$	$1$	$2$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+2q^{7}+q^{9}-4q^{13}-q^{15}+\cdots$
9840.2.a.q	$9840$	$2$	9840.a	1.a	$1$	$1$	$1$	$78.573$	$\Q$	None	✓				2460.2.a.c	$1$	$1$	$0$	$-1$	$1$	$4$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+4q^{7}+q^{9}-6q^{11}+2q^{13}+\cdots$
9840.2.a.r	$9840$	$2$	9840.a	1.a	$1$	$1$	$1$	$78.573$	$\Q$	None	✓				4920.2.a.h	$1$	$1$	$0$	$-1$	$1$	$4$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+4q^{7}+q^{9}-2q^{13}-q^{15}+\cdots$
9840.2.a.s	$9840$	$2$	9840.a	1.a	$1$	$1$	$1$	$78.573$	$\Q$	None	✓				2460.2.a.a	$1$	$0$	$0$	$1$	$-1$	$-4$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-4q^{7}+q^{9}+4q^{11}+4q^{13}+\cdots$
9840.2.a.t	$9840$	$2$	9840.a	1.a	$1$	$1$	$1$	$78.573$	$\Q$	None	✓				615.2.a.a	$1$	$1$	$0$	$1$	$-1$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}-2q^{11}-q^{15}-2q^{19}+\cdots$
9840.2.a.u	$9840$	$2$	9840.a	1.a	$1$	$1$	$1$	$78.573$	$\Q$	None	✓				1230.2.a.e	$1$	$0$	$0$	$1$	$-1$	$2$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+2q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots$
9840.2.a.v	$9840$	$2$	9840.a	1.a	$1$	$1$	$1$	$78.573$	$\Q$	None	✓				4920.2.a.a	$1$	$0$	$0$	$1$	$-1$	$4$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+4q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots$
9840.2.a.w	$9840$	$2$	9840.a	1.a	$1$	$1$	$1$	$78.573$	$\Q$	None	✓				1230.2.a.g	$1$	$1$	$0$	$1$	$1$	$-3$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-3q^{7}+q^{9}+2q^{11}+4q^{13}+\cdots$
9840.2.a.x	$9840$	$2$	9840.a	1.a	$1$	$1$	$1$	$78.573$	$\Q$	None	✓				4920.2.a.d	$1$	$1$	$0$	$1$	$1$	$-2$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{7}+q^{9}-4q^{11}-4q^{13}+\cdots$
9840.2.a.y	$9840$	$2$	9840.a	1.a	$1$	$1$	$1$	$78.573$	$\Q$	None	✓				1230.2.a.f	$1$	$1$	$0$	$1$	$1$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots$
9840.2.a.z	$9840$	$2$	9840.a	1.a	$1$	$1$	$1$	$78.573$	$\Q$	None	✓				4920.2.a.c	$1$	$0$	$0$	$1$	$1$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}+2q^{13}+q^{15}+6q^{17}+\cdots$
9840.2.a.ba	$9840$	$2$	9840.a	1.a	$1$	$1$	$1$	$78.573$	$\Q$	None	✓				4920.2.a.b	$1$	$1$	$0$	$1$	$1$	$1$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{7}+q^{9}-2q^{11}+4q^{13}+\cdots$
9840.2.a.bb	$9840$	$2$	9840.a	1.a	$1$	$1$	$1$	$78.573$	$\Q$	None	✓				1230.2.a.a	$1$	$1$	$0$	$1$	$1$	$2$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots$
9840.2.a.bc	$9840$	$2$	9840.a	1.a	$1$	$2$	$2$	$78.573$	$\Q(\sqrt{13}) $	None	✓				4920.2.a.o	$1$	$0$	$0$	$-2$	$2$	$-5$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+(-2-\beta )q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots$
9840.2.a.bd	$9840$	$2$	9840.a	1.a	$1$	$2$	$2$	$78.573$	$\Q(\sqrt{17}) $	None	✓				1230.2.a.m	$1$	$0$	$0$	$-2$	$2$	$-3$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+(-1-\beta )q^{7}+q^{9}-2q^{11}+\cdots$
9840.2.a.be	$9840$	$2$	9840.a	1.a	$1$	$2$	$2$	$78.573$	$\Q(\sqrt{5}) $	None	✓				1230.2.a.p	$1$	$1$	$0$	$-2$	$2$	$-2$	$-$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+(-1-\beta )q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots$
9840.2.a.bf	$9840$	$2$	9840.a	1.a	$1$	$2$	$2$	$78.573$	$\Q(\sqrt{33}) $	None	✓				4920.2.a.n	$1$	$0$	$0$	$-2$	$2$	$-1$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-\beta q^{7}+q^{9}+(1+\beta )q^{11}+\cdots$
9840.2.a.bg	$9840$	$2$	9840.a	1.a	$1$	$2$	$2$	$78.573$	$\Q(\sqrt{13}) $	None	✓				4920.2.a.m	$1$	$1$	$0$	$-2$	$2$	$1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+\beta q^{7}+q^{9}+(1-\beta )q^{11}+\cdots$
9840.2.a.bh	$9840$	$2$	9840.a	1.a	$1$	$2$	$2$	$78.573$	$\Q(\sqrt{5}) $	None	✓				2460.2.a.h	$1$	$1$	$0$	$-2$	$2$	$1$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+\beta q^{7}+q^{9}+(1+\beta )q^{11}+\cdots$
9840.2.a.bi	$9840$	$2$	9840.a	1.a	$1$	$2$	$2$	$78.573$	$\Q(\sqrt{13}) $	None	✓				4920.2.a.l	$1$	$0$	$0$	$-2$	$2$	$2$	$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+(1+\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
9840.2.a.bj	$9840$	$2$	9840.a	1.a	$1$	$2$	$2$	$78.573$	$\Q(\sqrt{5}) $	None	✓				2460.2.a.g	$1$	$0$	$0$	$-2$	$2$	$3$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+(1+\beta )q^{7}+q^{9}+(4-3\beta )q^{11}+\cdots$
9840.2.a.bk	$9840$	$2$	9840.a	1.a	$1$	$2$	$2$	$78.573$	$\Q(\sqrt{65}) $	None	✓				1230.2.a.n	$1$	$1$	$0$	$2$	$-2$	$-1$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-\beta q^{7}+q^{9}-2q^{11}-q^{15}+\cdots$
9840.2.a.bl	$9840$	$2$	9840.a	1.a	$1$	$2$	$2$	$78.573$	$\Q(\sqrt{5}) $	None	✓				2460.2.a.f	$1$	$1$	$0$	$2$	$-2$	$-1$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-\beta q^{7}+q^{9}+(1-3\beta )q^{11}+\cdots$
9840.2.a.bm	$9840$	$2$	9840.a	1.a	$1$	$2$	$2$	$78.573$	$\Q(\sqrt{17}) $	None	✓				615.2.a.c	$1$	$1$	$0$	$2$	$-2$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}+(2+\beta )q^{11}-q^{15}+\cdots$
9840.2.a.bn	$9840$	$2$	9840.a	1.a	$1$	$2$	$2$	$78.573$	$\Q(\sqrt{17}) $	None	✓				1230.2.a.l	$1$	$0$	$0$	$2$	$2$	$-5$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+(-2-\beta )q^{7}+q^{9}-2\beta q^{11}+\cdots$
9840.2.a.bo	$9840$	$2$	9840.a	1.a	$1$	$2$	$2$	$78.573$	$\Q(\sqrt{21}) $	None	✓				4920.2.a.k	$1$	$1$	$0$	$2$	$2$	$-5$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+(-2-\beta )q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots$
9840.2.a.bp	$9840$	$2$	9840.a	1.a	$1$	$2$	$2$	$78.573$	$\Q(\sqrt{5}) $	None	✓				1230.2.a.o	$1$	$0$	$0$	$2$	$2$	$6$	$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+(3+\beta )q^{7}+q^{9}+(3-\beta )q^{11}+\cdots$
9840.2.a.bq	$9840$	$2$	9840.a	1.a	$1$	$3$	$3$	$78.573$	3.3.837.1	None	✓				4920.2.a.s	$1$	$0$	$0$	$-3$	$-3$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-\beta _{1}q^{7}+q^{9}+(1-\beta _{1}+\cdots)q^{11}+\cdots$
9840.2.a.br	$9840$	$2$	9840.a	1.a	$1$	$3$	$3$	$78.573$	3.3.1101.1	None	✓		✓		2460.2.a.k	$1$	$1$	$0$	$-3$	$-3$	$1$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+\beta _{1}q^{7}+q^{9}+(-3+\beta _{1}+\cdots)q^{11}+\cdots$
9840.2.a.bs	$9840$	$2$	9840.a	1.a	$1$	$3$	$3$	$78.573$	3.3.621.1	None	✓				2460.2.a.j	$1$	$0$	$0$	$-3$	$-3$	$3$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+(1-\beta _{1})q^{7}+q^{9}+\beta _{1}q^{11}+\cdots$
9840.2.a.bt	$9840$	$2$	9840.a	1.a	$1$	$3$	$3$	$78.573$	3.3.229.1	None	✓				4920.2.a.r	$1$	$0$	$0$	$-3$	$-3$	$3$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+(1-\beta _{1})q^{7}+q^{9}+(2+\beta _{2})q^{11}+\cdots$
9840.2.a.bu	$9840$	$2$	9840.a	1.a	$1$	$3$	$3$	$78.573$	3.3.1101.1	None	✓		✓		2460.2.a.i	$1$	$1$	$0$	$3$	$3$	$-1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-\beta _{1}q^{7}+q^{9}+(-1-\beta _{1}+\cdots)q^{11}+\cdots$
9840.2.a.bv	$9840$	$2$	9840.a	1.a	$1$	$3$	$3$	$78.573$	3.3.316.1	None	✓				4920.2.a.q	$1$	$0$	$0$	$3$	$3$	$0$	$+$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}+\beta _{1}q^{11}-\beta _{2}q^{13}+\cdots$
9840.2.a.bw	$9840$	$2$	9840.a	1.a	$1$	$3$	$3$	$78.573$	3.3.229.1	None	✓				4920.2.a.p	$1$	$0$	$0$	$3$	$3$	$7$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+(2+2\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots$
9840.2.a.bx	$9840$	$2$	9840.a	1.a	$1$	$4$	$4$	$78.573$	4.4.13676.1	None	✓				4920.2.a.w	$1$	$1$	$0$	$-4$	$-4$	$1$	$+$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+\beta _{3}q^{7}+q^{9}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots$

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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.