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 76 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	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8550.2.a.a	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				114.2.a.a	$1$	$1$	$-1$	$0$	$0$	$-4$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-4q^{7}-q^{8}-4q^{11}+4q^{14}+\cdots$
8550.2.a.b	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				570.2.a.d	$1$	$0$	$-1$	$0$	$0$	$-4$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-4q^{7}-q^{8}-2q^{13}+4q^{14}+\cdots$
8550.2.a.c	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				2850.2.a.f	$1$	$0$	$-1$	$0$	$0$	$-4$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-4q^{7}-q^{8}+q^{11}+4q^{14}+\cdots$
8550.2.a.d	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				2850.2.a.o	$1$	$1$	$-1$	$0$	$0$	$-2$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{7}-q^{8}-3q^{11}-2q^{13}+\cdots$
8550.2.a.e	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				570.2.a.f	$1$	$1$	$-1$	$0$	$0$	$-2$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{7}-q^{8}-2q^{13}+2q^{14}+\cdots$
8550.2.a.f	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				2850.2.a.d	$1$	$0$	$-1$	$0$	$0$	$-2$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{7}-q^{8}+3q^{11}-6q^{13}+\cdots$
8550.2.a.g	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				570.2.a.b	$1$	$0$	$-1$	$0$	$0$	$-2$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{7}-q^{8}+6q^{11}+2q^{14}+\cdots$
8550.2.a.h	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				2850.2.a.l	$1$	$1$	$-1$	$0$	$0$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{8}-q^{11}-4q^{13}+q^{16}+\cdots$
8550.2.a.i	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				342.2.a.a	$1$	$1$	$-1$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{8}+2q^{11}+4q^{13}+\cdots$
8550.2.a.j	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				570.2.d.b	$1$	$1$	$-1$	$0$	$0$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{8}+4q^{11}-4q^{13}+\cdots$
8550.2.a.k	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				570.2.d.a	$1$	$1$	$-1$	$0$	$0$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{8}+4q^{11}+2q^{13}+\cdots$
8550.2.a.l	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				190.2.a.a	$1$	$0$	$-1$	$0$	$0$	$1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{7}-q^{8}+3q^{13}-q^{14}+\cdots$
8550.2.a.m	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				38.2.a.a	$1$	$1$	$-1$	$0$	$0$	$1$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{7}-q^{8}+6q^{11}-5q^{13}+\cdots$
8550.2.a.n	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				570.2.a.a	$1$	$1$	$-1$	$0$	$0$	$2$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{7}-q^{8}-4q^{11}+6q^{13}+\cdots$
8550.2.a.o	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				570.2.a.c	$1$	$1$	$-1$	$0$	$0$	$2$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{7}-q^{8}+2q^{11}-2q^{14}+\cdots$
8550.2.a.p	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				1710.2.a.h	$1$	$0$	$-1$	$0$	$0$	$2$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{7}-q^{8}+2q^{11}+4q^{13}+\cdots$
8550.2.a.q	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				1710.2.a.a	$1$	$1$	$-1$	$0$	$0$	$4$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{7}-q^{8}-6q^{11}-4q^{14}+\cdots$
8550.2.a.r	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				570.2.a.e	$1$	$0$	$-1$	$0$	$0$	$4$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{7}-q^{8}+4q^{11}+6q^{13}+\cdots$
8550.2.a.s	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				570.2.a.i	$1$	$0$	$1$	$0$	$0$	$-4$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-4q^{7}+q^{8}+6q^{13}-4q^{14}+\cdots$
8550.2.a.t	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				570.2.a.m	$1$	$1$	$1$	$0$	$0$	$-4$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-4q^{7}+q^{8}+4q^{11}+2q^{13}+\cdots$
8550.2.a.u	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				38.2.a.b	$1$	$1$	$1$	$0$	$0$	$-3$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{7}+q^{8}-2q^{11}+q^{13}+\cdots$
8550.2.a.v	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				570.2.a.k	$1$	$0$	$1$	$0$	$0$	$-2$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{7}+q^{8}-6q^{11}+4q^{13}+\cdots$
8550.2.a.w	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				570.2.a.j	$1$	$0$	$1$	$0$	$0$	$-2$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{7}+q^{8}+4q^{11}-6q^{13}+\cdots$
8550.2.a.x	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				570.2.a.g	$1$	$1$	$1$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}-4q^{11}-2q^{13}+\cdots$
8550.2.a.y	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				342.2.a.a	$1$	$0$	$1$	$0$	$0$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}-2q^{11}+4q^{13}+\cdots$
8550.2.a.z	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				2850.2.a.l	$1$	$1$	$1$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}-q^{11}+4q^{13}+q^{16}+\cdots$
8550.2.a.ba	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				114.2.a.b	$1$	$1$	$1$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}+4q^{11}-2q^{13}+\cdots$
8550.2.a.bb	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				570.2.d.a	$1$	$0$	$1$	$0$	$0$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}+4q^{11}-2q^{13}+\cdots$
8550.2.a.bc	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				570.2.d.b	$1$	$0$	$1$	$0$	$0$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}+4q^{11}+4q^{13}+\cdots$
8550.2.a.bd	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				190.2.a.c	$1$	$0$	$1$	$0$	$0$	$1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{7}+q^{8}+q^{13}+q^{14}+\cdots$
8550.2.a.be	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				2850.2.a.o	$1$	$1$	$1$	$0$	$0$	$2$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{7}+q^{8}-3q^{11}+2q^{13}+\cdots$
8550.2.a.bf	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				570.2.a.l	$1$	$1$	$1$	$0$	$0$	$2$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{7}+q^{8}-2q^{11}-4q^{13}+\cdots$
8550.2.a.bg	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				1710.2.a.h	$1$	$1$	$1$	$0$	$0$	$2$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{7}+q^{8}-2q^{11}+4q^{13}+\cdots$
8550.2.a.bh	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				570.2.a.h	$1$	$0$	$1$	$0$	$0$	$2$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{7}+q^{8}-6q^{13}+2q^{14}+\cdots$
8550.2.a.bi	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				2850.2.a.d	$1$	$0$	$1$	$0$	$0$	$2$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{7}+q^{8}+3q^{11}+6q^{13}+\cdots$
8550.2.a.bj	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				114.2.a.c	$1$	$0$	$1$	$0$	$0$	$4$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{7}+q^{8}+4q^{13}+4q^{14}+\cdots$
8550.2.a.bk	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				2850.2.a.f	$1$	$0$	$1$	$0$	$0$	$4$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{7}+q^{8}+q^{11}+4q^{14}+\cdots$
8550.2.a.bl	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				1710.2.a.a	$1$	$0$	$1$	$0$	$0$	$4$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{7}+q^{8}+6q^{11}+4q^{14}+\cdots$
8550.2.a.bm	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓				190.2.a.b	$1$	$0$	$1$	$0$	$0$	$5$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+5q^{7}+q^{8}+4q^{11}+q^{13}+\cdots$
8550.2.a.bn	$8550$	$2$	8550.a	1.a	$1$	$2$	$2$	$68.272$	$\Q(\sqrt{2}) $	None	✓				190.2.b.a	$1$	$1$	$-2$	$0$	$0$	$-6$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-3+\beta )q^{7}-q^{8}-\beta q^{11}+\cdots$
8550.2.a.bo	$8550$	$2$	8550.a	1.a	$1$	$2$	$2$	$68.272$	$\Q(\sqrt{3}) $	None	✓				1710.2.a.u	$1$	$0$	$-2$	$0$	$0$	$-4$	$+$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{7}-q^{8}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
8550.2.a.bp	$8550$	$2$	8550.a	1.a	$1$	$2$	$2$	$68.272$	$\Q(\sqrt{17}) $	None	✓				1710.2.a.v	$1$	$1$	$-2$	$0$	$0$	$-2$	$+$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1-\beta )q^{7}-q^{8}+2q^{11}+\cdots$
8550.2.a.bq	$8550$	$2$	8550.a	1.a	$1$	$2$	$2$	$68.272$	$\Q(\sqrt{10}) $	None	✓				2850.2.a.bf	$1$	$0$	$-2$	$0$	$0$	$0$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{7}-q^{8}+(-1-\beta )q^{11}+\cdots$
8550.2.a.br	$8550$	$2$	8550.a	1.a	$1$	$2$	$2$	$68.272$	$\Q(\sqrt{17}) $	None	✓				190.2.a.d	$1$	$0$	$-2$	$0$	$0$	$1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{7}-q^{8}-4q^{11}+(2+\cdots)q^{13}+\cdots$
8550.2.a.bs	$8550$	$2$	8550.a	1.a	$1$	$2$	$2$	$68.272$	$\Q(\sqrt{3}) $	None	✓				2850.2.a.bd	$1$	$1$	$-2$	$0$	$0$	$2$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta )q^{7}-q^{8}+(-2+\cdots)q^{11}+\cdots$
8550.2.a.bt	$8550$	$2$	8550.a	1.a	$1$	$2$	$2$	$68.272$	$\Q(\sqrt{3}) $	None	✓				2850.2.a.be	$1$	$0$	$-2$	$0$	$0$	$2$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta )q^{7}-q^{8}-3\beta q^{11}+\cdots$
8550.2.a.bu	$8550$	$2$	8550.a	1.a	$1$	$2$	$2$	$68.272$	$\Q(\sqrt{6}) $	None	✓		✓		2850.2.a.bc	$1$	$1$	$-2$	$0$	$0$	$4$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(2+\beta )q^{7}-q^{8}+(-1+\cdots)q^{11}+\cdots$
8550.2.a.bv	$8550$	$2$	8550.a	1.a	$1$	$2$	$2$	$68.272$	$\Q(\sqrt{6}) $	None	✓				2850.2.a.bc	$1$	$1$	$2$	$0$	$0$	$-4$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-2+\beta )q^{7}+q^{8}+(-1+\cdots)q^{11}+\cdots$
8550.2.a.bw	$8550$	$2$	8550.a	1.a	$1$	$2$	$2$	$68.272$	$\Q(\sqrt{3}) $	None	✓				1710.2.a.u	$1$	$1$	$2$	$0$	$0$	$-4$	$-$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{7}+q^{8}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
8550.2.a.bx	$8550$	$2$	8550.a	1.a	$1$	$2$	$2$	$68.272$	$\Q(\sqrt{17}) $	None	✓				1710.2.a.v	$1$	$0$	$2$	$0$	$0$	$-2$	$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta )q^{7}+q^{8}-2q^{11}+\cdots$

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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.