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 54 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	7	17	Fricke sign	Coefficient ring index	Sato-Tate	$q$ -expansion
5712.2.a.a	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	$\Q$	None	✓				714.2.a.i	$1$	$0$	$0$	$-1$	$-3$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}-q^{7}+q^{9}-3q^{11}+5q^{13}+\cdots$
5712.2.a.b	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	$\Q$	None	✓				1428.2.a.d	$1$	$1$	$0$	$-1$	$-3$	$-1$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}-q^{7}+q^{9}+3q^{11}-q^{13}+\cdots$
5712.2.a.c	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	$\Q$	None	✓				357.2.a.a	$1$	$0$	$0$	$-1$	$-3$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}-q^{7}+q^{9}+3q^{11}+q^{13}+\cdots$
5712.2.a.d	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	$\Q$	None	✓				2856.2.a.e	$1$	$2$	$0$	$-1$	$-2$	$-1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}-q^{7}+q^{9}-6q^{11}-4q^{13}+\cdots$
5712.2.a.e	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	$\Q$	None	✓				2856.2.a.d	$1$	$0$	$0$	$-1$	$-2$	$-1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}-q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots$
5712.2.a.f	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	$\Q$	None	✓				2856.2.a.c	$1$	$1$	$0$	$-1$	$-2$	$1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+q^{7}+q^{9}+2q^{13}+2q^{15}+\cdots$
5712.2.a.g	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	$\Q$	None	✓				2856.2.a.g	$1$	$0$	$0$	$-1$	$-1$	$-1$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-q^{7}+q^{9}-q^{11}-3q^{13}+\cdots$
5712.2.a.h	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	$\Q$	None	✓				2856.2.a.f	$1$	$1$	$0$	$-1$	$-1$	$1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{7}+q^{9}+3q^{11}+q^{13}+\cdots$
5712.2.a.i	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	$\Q$	None	✓				357.2.a.d	$1$	$1$	$0$	$-1$	$1$	$1$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{7}+q^{9}-q^{11}+q^{13}+\cdots$
5712.2.a.j	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	$\Q$	None	✓				2856.2.a.h	$1$	$1$	$0$	$-1$	$1$	$1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{7}+q^{9}+3q^{11}-q^{13}+\cdots$
5712.2.a.k	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	$\Q$	None	✓				1428.2.a.e	$1$	$0$	$0$	$-1$	$2$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}-q^{7}+q^{9}-2q^{13}-2q^{15}+\cdots$
5712.2.a.l	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	$\Q$	None	✓				2856.2.a.i	$1$	$0$	$0$	$-1$	$2$	$1$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+q^{7}+q^{9}-6q^{11}+4q^{13}+\cdots$
5712.2.a.m	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	$\Q$	None	✓				2856.2.a.j	$1$	$1$	$0$	$-1$	$3$	$1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}+q^{7}+q^{9}-5q^{11}-3q^{13}+\cdots$
5712.2.a.n	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	$\Q$	None	✓				1428.2.a.a	$1$	$0$	$0$	$1$	$-3$	$1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}+q^{7}+q^{9}+5q^{11}+q^{13}+\cdots$
5712.2.a.o	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	$\Q$	None	✓				714.2.a.f	$1$	$0$	$0$	$1$	$-2$	$-1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots$
5712.2.a.p	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	$\Q$	None	✓				714.2.a.a	$1$	$0$	$0$	$1$	$-2$	$-1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-q^{7}+q^{9}+2q^{11}+4q^{13}+\cdots$
5712.2.a.q	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	$\Q$	None	✓				714.2.a.e	$1$	$1$	$0$	$1$	$-2$	$1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{7}+q^{9}-6q^{13}-2q^{15}+\cdots$
5712.2.a.r	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	$\Q$	None	✓				2856.2.a.a	$1$	$0$	$0$	$1$	$-1$	$-1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-q^{7}+q^{9}+q^{11}-q^{13}+\cdots$
5712.2.a.s	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	$\Q$	None	✓				714.2.a.c	$1$	$1$	$0$	$1$	$1$	$-1$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-q^{7}+q^{9}-5q^{11}-q^{13}+\cdots$
5712.2.a.t	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	$\Q$	None	✓				1428.2.a.b	$1$	$1$	$0$	$1$	$1$	$-1$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-q^{7}+q^{9}+q^{11}-7q^{13}+\cdots$
5712.2.a.u	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	$\Q$	None	✓				357.2.a.c	$1$	$0$	$0$	$1$	$1$	$-1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-q^{7}+q^{9}+5q^{11}-5q^{13}+\cdots$
5712.2.a.v	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	$\Q$	None	✓				714.2.a.b	$1$	$1$	$0$	$1$	$1$	$1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{7}+q^{9}-3q^{11}-3q^{13}+\cdots$
5712.2.a.w	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	$\Q$	None	✓				357.2.a.b	$1$	$1$	$0$	$1$	$1$	$1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{7}+q^{9}-3q^{11}+3q^{13}+\cdots$
5712.2.a.x	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	$\Q$	None	✓				2856.2.a.b	$1$	$0$	$0$	$1$	$2$	$-1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
5712.2.a.y	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	$\Q$	None	✓				1428.2.a.c	$1$	$0$	$0$	$1$	$2$	$1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{7}+q^{9}+6q^{13}+2q^{15}+\cdots$
5712.2.a.z	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	$\Q$	None	✓				714.2.a.d	$1$	$0$	$0$	$1$	$2$	$1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{7}+q^{9}+6q^{11}+2q^{15}+\cdots$
5712.2.a.ba	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	$\Q$	None	✓				714.2.a.h	$1$	$0$	$0$	$1$	$3$	$-1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}-q^{7}+q^{9}+q^{11}+3q^{13}+\cdots$
5712.2.a.bb	$5712$	$2$	5712.a	1.a	$1$	$1$	$1$	$45.611$	$\Q$	None	✓				714.2.a.g	$1$	$0$	$0$	$1$	$3$	$1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}+q^{7}+q^{9}-q^{11}+q^{13}+\cdots$
5712.2.a.bc	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	$\Q(\sqrt{3})$	None	✓				357.2.a.e	$1$	$0$	$0$	$-2$	$-4$	$2$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-2+\beta )q^{5}+q^{7}+q^{9}+5q^{11}+\cdots$
5712.2.a.bd	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	$\Q(\sqrt{33})$	None	✓				714.2.a.j	$1$	$1$	$0$	$-2$	$-3$	$-2$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta )q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
5712.2.a.be	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	$\Q(\sqrt{17})$	None	✓				2856.2.a.m	$1$	$0$	$0$	$-2$	$-3$	$2$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta )q^{5}+q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots$
5712.2.a.bf	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	$\Q(\sqrt{2})$	None	✓				1428.2.a.g	$1$	$1$	$0$	$-2$	$-2$	$2$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1+\beta )q^{5}+q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots$
5712.2.a.bg	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	$\Q(\sqrt{3})$	None	✓				2856.2.a.o	$1$	$1$	$0$	$-2$	$0$	$-2$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}-q^{7}+q^{9}+(3+2\beta )q^{11}+\cdots$
5712.2.a.bh	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	$\Q(\sqrt{15})$	None	✓				2856.2.a.n	$1$	$0$	$0$	$-2$	$0$	$2$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}+q^{7}+q^{9}+5q^{11}+(2+\cdots)q^{13}+\cdots$
5712.2.a.bi	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	$\Q(\sqrt{41})$	None	✓				714.2.a.k	$1$	$1$	$0$	$-2$	$1$	$2$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}+q^{7}+q^{9}-\beta q^{11}+(2+\cdots)q^{13}+\cdots$
5712.2.a.bj	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	$\Q(\sqrt{10})$	None	✓				1428.2.a.h	$1$	$0$	$0$	$-2$	$2$	$-2$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta )q^{5}-q^{7}+q^{9}-3q^{11}+\cdots$
5712.2.a.bk	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	$\Q(\sqrt{17})$	None	✓				1428.2.a.i	$1$	$0$	$0$	$-2$	$3$	$2$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta )q^{5}+q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
5712.2.a.bl	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	$\Q(\sqrt{17})$	None	✓				714.2.a.l	$1$	$0$	$0$	$-2$	$3$	$2$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta )q^{5}+q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
5712.2.a.bm	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	$\Q(\sqrt{6})$	None	✓				714.2.a.m	$1$	$0$	$0$	$-2$	$4$	$-2$	$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}-q^{7}+q^{9}-\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
5712.2.a.bn	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	$\Q(\sqrt{201})$	None	✓		✓		2856.2.a.p	$1$	$0$	$0$	$-2$	$6$	$-2$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}-q^{7}+q^{9}-q^{11}+q^{13}+\cdots$
5712.2.a.bo	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	$\Q(\sqrt{3})$	None	✓		✓		1428.2.a.f	$1$	$1$	$0$	$2$	$-4$	$2$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-2+\beta )q^{5}+q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots$
5712.2.a.bp	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	$\Q(\sqrt{17})$	None	✓				2856.2.a.k	$1$	$1$	$0$	$2$	$-3$	$2$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta )q^{5}+q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots$
5712.2.a.bq	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	$\Q(\sqrt{2})$	None	✓		✓		357.2.a.f	$1$	$0$	$0$	$2$	$-2$	$2$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1+\beta )q^{5}+q^{7}+q^{9}-q^{11}+\cdots$
5712.2.a.br	$5712$	$2$	5712.a	1.a	$1$	$2$	$2$	$45.611$	$\Q(\sqrt{17})$	None	✓				2856.2.a.l	$1$	$1$	$0$	$2$	$-2$	$2$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{7}+q^{9}+(1-2\beta )q^{11}+\cdots$
5712.2.a.bs	$5712$	$2$	5712.a	1.a	$1$	$3$	$3$	$45.611$	3.3.316.1	None	✓		✓		2856.2.a.s	$1$	$0$	$0$	$-3$	$-2$	$3$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1+\beta _{1})q^{5}+q^{7}+q^{9}+(2\beta _{1}+\cdots)q^{11}+\cdots$
5712.2.a.bt	$5712$	$2$	5712.a	1.a	$1$	$3$	$3$	$45.611$	3.3.316.1	None	✓		✓		357.2.a.g	$1$	$1$	$0$	$-3$	$2$	$-3$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1-\beta _{1})q^{5}-q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots$
5712.2.a.bu	$5712$	$2$	5712.a	1.a	$1$	$3$	$3$	$45.611$	3.3.568.1	None	✓				2856.2.a.q	$1$	$1$	$0$	$3$	$-4$	$-3$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta _{1})q^{5}-q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots$
5712.2.a.bv	$5712$	$2$	5712.a	1.a	$1$	$3$	$3$	$45.611$	3.3.961.1	None	✓		✓		2856.2.a.r	$1$	$0$	$0$	$3$	$2$	$-3$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1-\beta _{1})q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
5712.2.a.bw	$5712$	$2$	5712.a	1.a	$1$	$3$	$3$	$45.611$	3.3.4764.1	None	✓		✓		1428.2.a.j	$1$	$0$	$0$	$3$	$2$	$-3$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1-\beta _{1})q^{5}-q^{7}+q^{9}+(1+\beta _{2})q^{11}+\cdots$
5712.2.a.bx	$5712$	$2$	5712.a	1.a	$1$	$4$	$4$	$45.611$	4.4.7232.1	None	✓		✓		357.2.a.h	$1$	$1$	$0$	$4$	$-2$	$-4$	$-$	$-$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{3}q^{5}-q^{7}+q^{9}+\beta _{1}q^{11}+\cdots$

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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.