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 53 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
5880.2.a.a	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓				120.2.a.b	$1$	$1$	$0$	$-1$	$-1$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}-4q^{11}-6q^{13}+\cdots$
5880.2.a.b	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓	✓			5880.2.a.b	$1$	$0$	$0$	$-1$	$-1$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}-2q^{11}-6q^{13}+\cdots$
5880.2.a.c	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓				840.2.bg.e	$1$	$1$	$0$	$-1$	$-1$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}-2q^{11}+q^{13}+q^{15}+\cdots$
5880.2.a.d	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓	✓			5880.2.a.d	$1$	$1$	$0$	$-1$	$-1$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}+2q^{13}+q^{15}+2q^{17}+\cdots$
5880.2.a.e	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓				840.2.bg.f	$1$	$0$	$0$	$-1$	$-1$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}+2q^{11}+5q^{13}+\cdots$
5880.2.a.f	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓				840.2.bg.d	$1$	$1$	$0$	$-1$	$-1$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}+3q^{11}+q^{13}+q^{15}+\cdots$
5880.2.a.g	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓				840.2.a.j	$1$	$1$	$0$	$-1$	$-1$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots$
5880.2.a.h	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓	✓			5880.2.a.h	$1$	$0$	$0$	$-1$	$-1$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots$
5880.2.a.i	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓	✓			5880.2.a.i	$1$	$0$	$0$	$-1$	$1$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}-6q^{11}+2q^{13}+\cdots$
5880.2.a.j	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓				840.2.a.g	$1$	$0$	$0$	$-1$	$1$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}-4q^{11}+6q^{13}+\cdots$
5880.2.a.k	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓				840.2.bg.c	$1$	$1$	$0$	$-1$	$1$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}-q^{11}-5q^{13}-q^{15}+\cdots$
5880.2.a.l	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓				840.2.a.h	$1$	$1$	$0$	$-1$	$1$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}-6q^{13}-q^{15}+2q^{17}+\cdots$
5880.2.a.m	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓				840.2.a.i	$1$	$0$	$0$	$-1$	$1$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}-2q^{13}-q^{15}-2q^{17}+\cdots$
5880.2.a.n	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓	✓			5880.2.a.n	$1$	$1$	$0$	$-1$	$1$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}-2q^{13}-q^{15}-2q^{17}+\cdots$
5880.2.a.o	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓				840.2.bg.a	$1$	$0$	$0$	$-1$	$1$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}-q^{13}-q^{15}+2q^{17}+\cdots$
5880.2.a.p	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓				120.2.a.a	$1$	$1$	$0$	$-1$	$1$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}+6q^{13}-q^{15}+2q^{17}+\cdots$
5880.2.a.q	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓				840.2.bg.b	$1$	$1$	$0$	$-1$	$1$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}+4q^{11}-5q^{13}+\cdots$
5880.2.a.r	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓	✓			5880.2.a.r	$1$	$0$	$0$	$-1$	$1$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots$
5880.2.a.s	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓	✓			5880.2.a.i	$1$	$0$	$0$	$1$	$-1$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}-6q^{11}-2q^{13}+\cdots$
5880.2.a.t	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓				840.2.a.d	$1$	$0$	$0$	$1$	$-1$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots$
5880.2.a.u	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓				840.2.bg.c	$1$	$0$	$0$	$1$	$-1$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}-q^{11}+5q^{13}-q^{15}+\cdots$
5880.2.a.v	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓				840.2.a.e	$1$	$1$	$0$	$1$	$-1$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}-2q^{13}-q^{15}-2q^{17}+\cdots$
5880.2.a.w	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓				840.2.bg.a	$1$	$1$	$0$	$1$	$-1$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}+q^{13}-q^{15}-2q^{17}+\cdots$
5880.2.a.x	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓	✓			5880.2.a.n	$1$	$1$	$0$	$1$	$-1$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}+2q^{13}-q^{15}+2q^{17}+\cdots$
5880.2.a.y	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓	✓			5880.2.a.r	$1$	$0$	$0$	$1$	$-1$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots$
5880.2.a.z	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓				840.2.a.f	$1$	$0$	$0$	$1$	$-1$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots$
5880.2.a.ba	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓				840.2.bg.b	$1$	$0$	$0$	$1$	$-1$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}+4q^{11}+5q^{13}+\cdots$
5880.2.a.bb	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓				840.2.a.b	$1$	$1$	$0$	$1$	$1$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots$
5880.2.a.bc	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓				840.2.bg.e	$1$	$0$	$0$	$1$	$1$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}-2q^{11}-q^{13}+q^{15}+\cdots$
5880.2.a.bd	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓	✓			5880.2.a.b	$1$	$0$	$0$	$1$	$1$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}-2q^{11}+6q^{13}+\cdots$
5880.2.a.be	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓	✓			5880.2.a.d	$1$	$1$	$0$	$1$	$1$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}-2q^{13}+q^{15}-2q^{17}+\cdots$
5880.2.a.bf	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓				840.2.a.c	$1$	$0$	$0$	$1$	$1$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}+2q^{13}+q^{15}-6q^{17}+\cdots$
5880.2.a.bg	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓				840.2.bg.f	$1$	$1$	$0$	$1$	$1$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}+2q^{11}-5q^{13}+\cdots$
5880.2.a.bh	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓				840.2.bg.d	$1$	$0$	$0$	$1$	$1$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}+3q^{11}-q^{13}+q^{15}+\cdots$
5880.2.a.bi	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓	✓			5880.2.a.h	$1$	$0$	$0$	$1$	$1$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}+4q^{11}-6q^{13}+\cdots$
5880.2.a.bj	$5880$	$2$	5880.a	1.a	$1$	$1$	$1$	$46.952$	$\Q$	None	✓				840.2.a.a	$1$	$0$	$0$	$1$	$1$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots$
5880.2.a.bk	$5880$	$2$	5880.a	1.a	$1$	$2$	$2$	$46.952$	$\Q(\sqrt{2}) $	None	✓	✓	✓		5880.2.a.bk	$1$	$1$	$0$	$-2$	$-2$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}-4q^{11}+(2-2\beta )q^{13}+\cdots$
5880.2.a.bl	$5880$	$2$	5880.a	1.a	$1$	$2$	$2$	$46.952$	$\Q(\sqrt{2}) $	None	✓				840.2.a.k	$1$	$0$	$0$	$-2$	$-2$	$0$	$+$	$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}+\beta q^{11}-2q^{13}+\cdots$
5880.2.a.bm	$5880$	$2$	5880.a	1.a	$1$	$2$	$2$	$46.952$	$\Q(\sqrt{2}) $	None	✓				840.2.bg.g	$1$	$0$	$0$	$-2$	$-2$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}+\beta q^{11}+(1+3\beta )q^{13}+\cdots$
5880.2.a.bn	$5880$	$2$	5880.a	1.a	$1$	$2$	$2$	$46.952$	$\Q(\sqrt{2}) $	None	✓	✓	✓		5880.2.a.bn	$1$	$1$	$0$	$-2$	$2$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}+2\beta q^{11}+2q^{13}+\cdots$
5880.2.a.bo	$5880$	$2$	5880.a	1.a	$1$	$2$	$2$	$46.952$	$\Q(\sqrt{7}) $	None	✓		✓		840.2.bg.h	$1$	$0$	$0$	$-2$	$2$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}+(1+\beta )q^{11}+(2+\beta )q^{13}+\cdots$
5880.2.a.bp	$5880$	$2$	5880.a	1.a	$1$	$2$	$2$	$46.952$	$\Q(\sqrt{2}) $	None	✓	✓			5880.2.a.bn	$1$	$1$	$0$	$2$	$-2$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}+2\beta q^{11}-2q^{13}+\cdots$
5880.2.a.bq	$5880$	$2$	5880.a	1.a	$1$	$2$	$2$	$46.952$	$\Q(\sqrt{7}) $	None	✓				840.2.bg.h	$1$	$1$	$0$	$2$	$-2$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}+(1+\beta )q^{11}+(-2+\cdots)q^{13}+\cdots$
5880.2.a.br	$5880$	$2$	5880.a	1.a	$1$	$2$	$2$	$46.952$	$\Q(\sqrt{2}) $	None	✓	✓			5880.2.a.bk	$1$	$1$	$0$	$2$	$2$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}-4q^{11}+(-2+2\beta )q^{13}+\cdots$
5880.2.a.bs	$5880$	$2$	5880.a	1.a	$1$	$2$	$2$	$46.952$	$\Q(\sqrt{2}) $	None	✓				840.2.bg.g	$1$	$1$	$0$	$2$	$2$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}+\beta q^{11}+(-1-3\beta )q^{13}+\cdots$
5880.2.a.bt	$5880$	$2$	5880.a	1.a	$1$	$3$	$3$	$46.952$	3.3.3576.1	None	✓		✓		840.2.bg.i	$1$	$1$	$0$	$-3$	$-3$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}+\beta _{2}q^{11}-\beta _{1}q^{13}+\cdots$
5880.2.a.bu	$5880$	$2$	5880.a	1.a	$1$	$3$	$3$	$46.952$	3.3.3132.1	None	✓		✓		840.2.bg.j	$1$	$1$	$0$	$-3$	$3$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}+(-1-\beta _{1}+\beta _{2})q^{11}+\cdots$
5880.2.a.bv	$5880$	$2$	5880.a	1.a	$1$	$3$	$3$	$46.952$	3.3.3132.1	None	✓				840.2.bg.j	$1$	$0$	$0$	$3$	$-3$	$0$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}+(-1-\beta _{1}+\beta _{2})q^{11}+\cdots$
5880.2.a.bw	$5880$	$2$	5880.a	1.a	$1$	$3$	$3$	$46.952$	3.3.3576.1	None	✓				840.2.bg.i	$1$	$0$	$0$	$3$	$3$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}+\beta _{2}q^{11}+\beta _{1}q^{13}+\cdots$
5880.2.a.bx	$5880$	$2$	5880.a	1.a	$1$	$4$	$4$	$46.952$	4.4.22592.1	None	✓	✓	✓		5880.2.a.bx	$1$	$0$	$0$	$-4$	$-4$	$0$	$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}+(1+\beta _{1}-\beta _{3})q^{11}+\cdots$

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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.