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 62 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	5	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8800.2.a.a	$8800$	$2$	8800.a	1.a	$1$	$1$	$1$	$70.268$	$\Q$	None	✓				352.2.a.a	$1$	$1$	$0$	$-3$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+6q^{9}-q^{11}+6q^{13}+4q^{17}+\cdots$
8800.2.a.b	$8800$	$2$	8800.a	1.a	$1$	$1$	$1$	$70.268$	$\Q$	None	✓				1760.2.b.a	$1$	$1$	$0$	$-3$	$0$	$3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+3q^{7}+6q^{9}-q^{11}-4q^{13}+\cdots$
8800.2.a.c	$8800$	$2$	8800.a	1.a	$1$	$1$	$1$	$70.268$	$\Q$	None	✓				1760.2.b.a	$1$	$1$	$0$	$-3$	$0$	$3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+3q^{7}+6q^{9}+q^{11}+4q^{13}+\cdots$
8800.2.a.d	$8800$	$2$	8800.a	1.a	$1$	$1$	$1$	$70.268$	$\Q$	None	✓				1760.2.a.b	$1$	$2$	$0$	$-2$	$0$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-4q^{7}+q^{9}-q^{11}-4q^{13}+\cdots$
8800.2.a.e	$8800$	$2$	8800.a	1.a	$1$	$1$	$1$	$70.268$	$\Q$	None	✓	✓			8800.2.a.e	$1$	$0$	$0$	$-2$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{9}-q^{11}-q^{13}-4q^{17}+\cdots$
8800.2.a.f	$8800$	$2$	8800.a	1.a	$1$	$1$	$1$	$70.268$	$\Q$	None	✓				1760.2.a.c	$1$	$0$	$0$	$-2$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{9}+q^{11}-4q^{13}+4q^{17}+\cdots$
8800.2.a.g	$8800$	$2$	8800.a	1.a	$1$	$1$	$1$	$70.268$	$\Q$	None	✓	✓			8800.2.a.e	$1$	$1$	$0$	$-2$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{9}+q^{11}+q^{13}+4q^{17}+\cdots$
8800.2.a.h	$8800$	$2$	8800.a	1.a	$1$	$1$	$1$	$70.268$	$\Q$	None	✓				1760.2.a.a	$1$	$0$	$0$	$-2$	$0$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{7}+q^{9}-q^{11}+2q^{13}+\cdots$
8800.2.a.i	$8800$	$2$	8800.a	1.a	$1$	$1$	$1$	$70.268$	$\Q$	None	✓				352.2.a.c	$1$	$1$	$0$	$-1$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{7}-2q^{9}+q^{11}+2q^{13}+\cdots$
8800.2.a.j	$8800$	$2$	8800.a	1.a	$1$	$1$	$1$	$70.268$	$\Q$	None	✓				1760.2.a.e	$1$	$1$	$0$	$-1$	$0$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}-2q^{9}+q^{11}+2q^{13}+\cdots$
8800.2.a.k	$8800$	$2$	8800.a	1.a	$1$	$1$	$1$	$70.268$	$\Q$	None	✓				1760.2.a.f	$1$	$1$	$0$	$-1$	$0$	$3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{7}-2q^{9}-q^{11}+2q^{13}+\cdots$
8800.2.a.l	$8800$	$2$	8800.a	1.a	$1$	$1$	$1$	$70.268$	$\Q$	None	✓				1760.2.a.d	$1$	$1$	$0$	$-1$	$0$	$3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{7}-2q^{9}+q^{11}+2q^{13}+\cdots$
8800.2.a.m	$8800$	$2$	8800.a	1.a	$1$	$1$	$1$	$70.268$	$\Q$	None	✓				352.2.a.b	$1$	$0$	$0$	$-1$	$0$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{7}-2q^{9}+q^{11}+2q^{13}+\cdots$
8800.2.a.n	$8800$	$2$	8800.a	1.a	$1$	$1$	$1$	$70.268$	$\Q$	None	✓				1760.2.a.g	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{9}-q^{11}+2q^{13}+2q^{17}+4q^{19}+\cdots$
8800.2.a.o	$8800$	$2$	8800.a	1.a	$1$	$1$	$1$	$70.268$	$\Q$	None	✓				1760.2.a.g	$1$	$1$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{9}+q^{11}+2q^{13}+2q^{17}-4q^{19}+\cdots$
8800.2.a.p	$8800$	$2$	8800.a	1.a	$1$	$1$	$1$	$70.268$	$\Q$	None	✓				352.2.a.b	$1$	$0$	$0$	$1$	$0$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{7}-2q^{9}-q^{11}+2q^{13}+\cdots$
8800.2.a.q	$8800$	$2$	8800.a	1.a	$1$	$1$	$1$	$70.268$	$\Q$	None	✓				1760.2.a.d	$1$	$0$	$0$	$1$	$0$	$-3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{7}-2q^{9}-q^{11}+2q^{13}+\cdots$
8800.2.a.r	$8800$	$2$	8800.a	1.a	$1$	$1$	$1$	$70.268$	$\Q$	None	✓				1760.2.a.f	$1$	$0$	$0$	$1$	$0$	$-3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{7}-2q^{9}+q^{11}+2q^{13}+\cdots$
8800.2.a.s	$8800$	$2$	8800.a	1.a	$1$	$1$	$1$	$70.268$	$\Q$	None	✓				1760.2.a.e	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}-2q^{9}-q^{11}+2q^{13}+\cdots$
8800.2.a.t	$8800$	$2$	8800.a	1.a	$1$	$1$	$1$	$70.268$	$\Q$	None	✓				352.2.a.c	$1$	$0$	$0$	$1$	$0$	$4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{7}-2q^{9}-q^{11}+2q^{13}+\cdots$
8800.2.a.u	$8800$	$2$	8800.a	1.a	$1$	$1$	$1$	$70.268$	$\Q$	None	✓				1760.2.a.a	$1$	$0$	$0$	$2$	$0$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{7}+q^{9}+q^{11}+2q^{13}+\cdots$
8800.2.a.v	$8800$	$2$	8800.a	1.a	$1$	$1$	$1$	$70.268$	$\Q$	None	✓				1760.2.a.c	$1$	$1$	$0$	$2$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{9}-q^{11}-4q^{13}+4q^{17}+\cdots$
8800.2.a.w	$8800$	$2$	8800.a	1.a	$1$	$1$	$1$	$70.268$	$\Q$	None	✓	✓			8800.2.a.e	$1$	$0$	$0$	$2$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{9}-q^{11}+q^{13}+4q^{17}+\cdots$
8800.2.a.x	$8800$	$2$	8800.a	1.a	$1$	$1$	$1$	$70.268$	$\Q$	None	✓	✓			8800.2.a.e	$1$	$1$	$0$	$2$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{9}+q^{11}-q^{13}-4q^{17}+\cdots$
8800.2.a.y	$8800$	$2$	8800.a	1.a	$1$	$1$	$1$	$70.268$	$\Q$	None	✓				1760.2.a.b	$1$	$1$	$0$	$2$	$0$	$4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+4q^{7}+q^{9}+q^{11}-4q^{13}+\cdots$
8800.2.a.z	$8800$	$2$	8800.a	1.a	$1$	$1$	$1$	$70.268$	$\Q$	None	✓				1760.2.b.a	$1$	$0$	$0$	$3$	$0$	$-3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-3q^{7}+6q^{9}-q^{11}+4q^{13}+\cdots$
8800.2.a.ba	$8800$	$2$	8800.a	1.a	$1$	$1$	$1$	$70.268$	$\Q$	None	✓				1760.2.b.a	$1$	$0$	$0$	$3$	$0$	$-3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-3q^{7}+6q^{9}+q^{11}-4q^{13}+\cdots$
8800.2.a.bb	$8800$	$2$	8800.a	1.a	$1$	$1$	$1$	$70.268$	$\Q$	None	✓				352.2.a.a	$1$	$0$	$0$	$3$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+6q^{9}+q^{11}+6q^{13}+4q^{17}+\cdots$
8800.2.a.bc	$8800$	$2$	8800.a	1.a	$1$	$2$	$2$	$70.268$	$\Q(\sqrt{5}) $	None	✓				1760.2.a.o	$1$	$1$	$0$	$-2$	$0$	$-4$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}-2q^{7}+(3+2\beta )q^{9}+\cdots$
8800.2.a.bd	$8800$	$2$	8800.a	1.a	$1$	$2$	$2$	$70.268$	$\Q(\sqrt{17}) $	None	✓				352.2.a.g	$1$	$1$	$0$	$-1$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(1+\beta )q^{9}+q^{11}-2q^{13}+\cdots$
8800.2.a.be	$8800$	$2$	8800.a	1.a	$1$	$2$	$2$	$70.268$	$\Q(\sqrt{17}) $	None	✓				352.2.a.g	$1$	$1$	$0$	$1$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(1+\beta )q^{9}-q^{11}-2q^{13}+\cdots$
8800.2.a.bf	$8800$	$2$	8800.a	1.a	$1$	$2$	$2$	$70.268$	$\Q(\sqrt{5}) $	None	✓				1760.2.a.o	$1$	$0$	$0$	$2$	$0$	$4$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+2q^{7}+(3+2\beta )q^{9}-q^{11}+\cdots$
8800.2.a.bg	$8800$	$2$	8800.a	1.a	$1$	$3$	$3$	$70.268$	3.3.229.1	None	✓				1760.2.a.q	$1$	$1$	$0$	$-2$	$0$	$4$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}+(1-\beta _{1})q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots$
8800.2.a.bh	$8800$	$2$	8800.a	1.a	$1$	$3$	$3$	$70.268$	3.3.229.1	None	✓				1760.2.a.r	$1$	$0$	$0$	$-1$	$0$	$7$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(2-\beta _{1})q^{7}+(1-\beta _{1})q^{9}+\cdots$
8800.2.a.bi	$8800$	$2$	8800.a	1.a	$1$	$3$	$3$	$70.268$	3.3.229.1	None	✓				1760.2.a.r	$1$	$1$	$0$	$1$	$0$	$-7$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+(-2+\beta _{1})q^{7}+(1-\beta _{1})q^{9}+\cdots$
8800.2.a.bj	$8800$	$2$	8800.a	1.a	$1$	$3$	$3$	$70.268$	3.3.229.1	None	✓				1760.2.a.q	$1$	$1$	$0$	$2$	$0$	$-4$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+(-1+\beta _{1})q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots$
8800.2.a.bk	$8800$	$2$	8800.a	1.a	$1$	$4$	$4$	$70.268$	4.4.8112.1	None	✓	✓			8800.2.a.bk	$1$	$0$	$0$	$-4$	$0$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(1-\beta _{1}+\beta _{3})q^{7}+\cdots$
8800.2.a.bl	$8800$	$2$	8800.a	1.a	$1$	$4$	$4$	$70.268$	4.4.8112.1	None	✓	✓			8800.2.a.bk	$1$	$1$	$0$	$-4$	$0$	$4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(1-\beta _{1}+\beta _{3})q^{7}+\cdots$
8800.2.a.bm	$8800$	$2$	8800.a	1.a	$1$	$4$	$4$	$70.268$	4.4.18736.1	None	✓	✓			8800.2.a.bm	$1$	$1$	$0$	$-2$	$0$	$4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(1-\beta _{3})q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots$
8800.2.a.bn	$8800$	$2$	8800.a	1.a	$1$	$4$	$4$	$70.268$	4.4.18736.1	None	✓	✓			8800.2.a.bm	$1$	$1$	$0$	$-2$	$0$	$4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(1-\beta _{3})q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots$
8800.2.a.bo	$8800$	$2$	8800.a	1.a	$1$	$4$	$4$	$70.268$	4.4.18736.1	None	✓	✓			8800.2.a.bm	$1$	$1$	$0$	$2$	$0$	$-4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(-1+\beta _{3})q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots$
8800.2.a.bp	$8800$	$2$	8800.a	1.a	$1$	$4$	$4$	$70.268$	4.4.18736.1	None	✓	✓			8800.2.a.bm	$1$	$1$	$0$	$2$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(-1+\beta _{3})q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots$
8800.2.a.bq	$8800$	$2$	8800.a	1.a	$1$	$4$	$4$	$70.268$	4.4.8112.1	None	✓	✓			8800.2.a.bk	$1$	$0$	$0$	$4$	$0$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{3}+(-1-\beta _{1}+\beta _{3})q^{7}+\cdots$
8800.2.a.br	$8800$	$2$	8800.a	1.a	$1$	$4$	$4$	$70.268$	4.4.8112.1	None	✓	✓			8800.2.a.bk	$1$	$1$	$0$	$4$	$0$	$-4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{3}+(-1-\beta _{1}+\beta _{3})q^{7}+\cdots$
8800.2.a.bs	$8800$	$2$	8800.a	1.a	$1$	$5$	$5$	$70.268$	5.5.5060976.1	None	✓	✓			8800.2.a.bs	$1$	$1$	$0$	$-2$	$0$	$4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1+\beta _{3})q^{7}+(1+\beta _{2})q^{9}+\cdots$
8800.2.a.bt	$8800$	$2$	8800.a	1.a	$1$	$5$	$5$	$70.268$	5.5.5060976.1	None	✓	✓			8800.2.a.bs	$1$	$0$	$0$	$-2$	$0$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1+\beta _{3})q^{7}+(1+\beta _{2})q^{9}+\cdots$
8800.2.a.bu	$8800$	$2$	8800.a	1.a	$1$	$5$	$5$	$70.268$	5.5.792644.1	None	✓				1760.2.a.u	$1$	$0$	$0$	$0$	$0$	$-2$	$+$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}-\beta _{4}q^{7}+(2-\beta _{1})q^{9}+q^{11}+\cdots$
8800.2.a.bv	$8800$	$2$	8800.a	1.a	$1$	$5$	$5$	$70.268$	5.5.792644.1	None	✓				1760.2.a.u	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$+$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}+\beta _{4}q^{7}+(2-\beta _{1})q^{9}-q^{11}+\cdots$
8800.2.a.bw	$8800$	$2$	8800.a	1.a	$1$	$5$	$5$	$70.268$	5.5.5060976.1	None	✓	✓	✓		8800.2.a.bs	$1$	$1$	$0$	$2$	$0$	$-4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1-\beta _{3})q^{7}+(1+\beta _{2})q^{9}+\cdots$
8800.2.a.bx	$8800$	$2$	8800.a	1.a	$1$	$5$	$5$	$70.268$	5.5.5060976.1	None	✓	✓			8800.2.a.bs	$1$	$0$	$0$	$2$	$0$	$-4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1-\beta _{3})q^{7}+(1+\beta _{2})q^{9}+\cdots$

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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.