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 90 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	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8400.2.a.a	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				1050.2.a.j	$1$	$1$	$0$	$-1$	$0$	$-1$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-6q^{11}-q^{13}+3q^{17}+\cdots$
8400.2.a.b	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				840.2.a.a	$1$	$1$	$0$	$-1$	$0$	$-1$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
8400.2.a.c	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				420.2.a.a	$1$	$0$	$0$	$-1$	$0$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots$
8400.2.a.d	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				1050.2.a.b	$1$	$0$	$0$	$-1$	$0$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-2q^{11}-q^{13}+3q^{17}+\cdots$
8400.2.a.e	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				84.2.a.a	$1$	$0$	$0$	$-1$	$0$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-2q^{11}+6q^{13}+\cdots$
8400.2.a.f	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				840.2.a.e	$1$	$1$	$0$	$-1$	$0$	$-1$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-2q^{13}-2q^{17}+\cdots$
8400.2.a.g	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				4200.2.a.b	$1$	$1$	$0$	$-1$	$0$	$-1$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+q^{11}-4q^{13}-2q^{17}+\cdots$
8400.2.a.h	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				2100.2.a.c	$1$	$0$	$0$	$-1$	$0$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+q^{11}+2q^{13}-6q^{19}+\cdots$
8400.2.a.i	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				2100.2.a.b	$1$	$1$	$0$	$-1$	$0$	$-1$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+3q^{11}-4q^{13}+\cdots$
8400.2.a.j	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				4200.2.a.a	$1$	$0$	$0$	$-1$	$0$	$-1$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+3q^{11}+2q^{13}+\cdots$
8400.2.a.k	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				42.2.a.a	$1$	$0$	$0$	$-1$	$0$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots$
8400.2.a.l	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				840.2.a.d	$1$	$1$	$0$	$-1$	$0$	$-1$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
8400.2.a.m	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				210.2.a.a	$1$	$0$	$0$	$-1$	$0$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
8400.2.a.n	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				4200.2.a.o	$1$	$0$	$0$	$-1$	$0$	$1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-5q^{11}-2q^{13}+\cdots$
8400.2.a.o	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				420.2.k.b	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots$
8400.2.a.p	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				210.2.a.c	$1$	$1$	$0$	$-1$	$0$	$1$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
8400.2.a.q	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				840.2.a.f	$1$	$0$	$0$	$-1$	$0$	$1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
8400.2.a.r	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				4200.2.a.m	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-3q^{11}-2q^{17}+\cdots$
8400.2.a.s	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				4200.2.a.l	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-2q^{11}-3q^{13}+\cdots$
8400.2.a.t	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				1050.2.a.e	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-2q^{11}+q^{13}-q^{17}+\cdots$
8400.2.a.u	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				840.2.t.a	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots$
8400.2.a.v	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				840.2.t.b	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots$
8400.2.a.w	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				210.2.g.b	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-2q^{11}+6q^{13}+\cdots$
8400.2.a.x	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				2100.2.a.g	$1$	$1$	$0$	$-1$	$0$	$1$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-q^{11}-4q^{13}-2q^{17}+\cdots$
8400.2.a.y	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				168.2.a.a	$1$	$0$	$0$	$-1$	$0$	$1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-6q^{13}+2q^{17}+\cdots$
8400.2.a.z	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				840.2.a.c	$1$	$0$	$0$	$-1$	$0$	$1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+2q^{13}-6q^{17}+\cdots$
8400.2.a.ba	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				2100.2.a.f	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+q^{11}-2q^{13}+8q^{17}+\cdots$
8400.2.a.bb	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				1050.2.a.f	$1$	$1$	$0$	$-1$	$0$	$1$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+2q^{11}-7q^{13}+\cdots$
8400.2.a.bc	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				420.2.a.b	$1$	$1$	$0$	$-1$	$0$	$1$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots$
8400.2.a.bd	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				210.2.g.a	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots$
8400.2.a.be	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				4200.2.a.g	$1$	$0$	$0$	$-1$	$0$	$1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+2q^{11}+5q^{13}+\cdots$
8400.2.a.bf	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				4200.2.a.f	$1$	$0$	$0$	$-1$	$0$	$1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+3q^{11}+2q^{13}+\cdots$
8400.2.a.bg	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				840.2.a.b	$1$	$0$	$0$	$-1$	$0$	$1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots$
8400.2.a.bh	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				420.2.k.a	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots$
8400.2.a.bi	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				4200.2.a.d	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+5q^{11}+4q^{13}+\cdots$
8400.2.a.bj	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				105.2.d.a	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots$
8400.2.a.bk	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				4200.2.a.o	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-5q^{11}+2q^{13}+\cdots$
8400.2.a.bl	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				840.2.a.j	$1$	$0$	$0$	$1$	$0$	$-1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
8400.2.a.bm	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				420.2.k.b	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
8400.2.a.bn	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				21.2.a.a	$1$	$1$	$0$	$1$	$0$	$-1$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
8400.2.a.bo	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				4200.2.a.m	$1$	$0$	$0$	$1$	$0$	$-1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-3q^{11}+2q^{17}+\cdots$
8400.2.a.bp	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				210.2.g.b	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots$
8400.2.a.bq	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				420.2.a.d	$1$	$1$	$0$	$1$	$0$	$-1$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots$
8400.2.a.br	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				840.2.t.a	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots$
8400.2.a.bs	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				840.2.t.b	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots$
8400.2.a.bt	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				1050.2.a.e	$1$	$1$	$0$	$1$	$0$	$-1$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-2q^{11}-q^{13}+q^{17}+\cdots$
8400.2.a.bu	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				4200.2.a.l	$1$	$0$	$0$	$1$	$0$	$-1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-2q^{11}+3q^{13}+\cdots$
8400.2.a.bv	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				2100.2.a.g	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-q^{11}+4q^{13}+2q^{17}+\cdots$
8400.2.a.bw	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				840.2.a.h	$1$	$0$	$0$	$1$	$0$	$-1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-6q^{13}+2q^{17}+\cdots$
8400.2.a.bx	$8400$	$2$	8400.a	1.a	$1$	$1$	$1$	$67.074$	$\Q$	None	✓				168.2.a.b	$1$	$0$	$0$	$1$	$0$	$-1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+2q^{13}-6q^{17}+\cdots$

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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.