LMFDB - Newform search results

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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is twist minimal	Is self-dual

$Nk^2$	Coefficient ring index	Coefficient ring gens.	Projective image	Projective image type

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Results (1-50 of 58 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	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	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	3	61	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8784.2.a.a	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	$\Q$	None	✓		1464.2.a.d	$1$	$2$	$0$	$0$	$-3$	$-2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}-2q^{7}-6q^{11}+4q^{13}-5q^{17}+\cdots$
8784.2.a.b	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	$\Q$	None	✓		1098.2.a.f	$1$	$1$	$0$	$0$	$-3$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+2q^{11}-2q^{13}-q^{17}-2q^{19}+\cdots$
8784.2.a.c	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	$\Q$	None	✓		732.2.a.b	$1$	$1$	$0$	$0$	$-2$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-2q^{7}+2q^{11}-2q^{13}+2q^{17}+\cdots$
8784.2.a.d	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	$\Q$	None	✓		1098.2.a.d	$1$	$2$	$0$	$0$	$-1$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-4q^{7}-6q^{11}-6q^{13}+3q^{17}+\cdots$
8784.2.a.e	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	$\Q$	None	✓		1464.2.a.c	$1$	$1$	$0$	$0$	$-1$	$-3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{7}-3q^{11}-5q^{13}+6q^{17}+\cdots$
8784.2.a.f	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	$\Q$	None	✓		366.2.a.g	$1$	$0$	$0$	$0$	$-1$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-q^{7}-q^{11}-5q^{13}-2q^{17}+\cdots$
8784.2.a.g	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	$\Q$	None	✓		366.2.a.f	$1$	$0$	$0$	$0$	$-1$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}+2q^{11}+4q^{13}+7q^{17}+\cdots$
8784.2.a.h	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	$\Q$	None	✓		366.2.a.c	$1$	$1$	$0$	$0$	$-1$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}+6q^{11}-3q^{17}-q^{23}+\cdots$
8784.2.a.i	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	$\Q$	None	✓		1464.2.a.f	$1$	$1$	$0$	$0$	$-1$	$3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+3q^{7}-5q^{11}-q^{13}-2q^{17}+\cdots$
8784.2.a.j	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	$\Q$	None	✓		122.2.a.a	$1$	$1$	$0$	$0$	$-1$	$5$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+5q^{7}-3q^{11}-3q^{13}+5q^{23}+\cdots$
8784.2.a.k	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	$\Q$	None	✓		732.2.a.a	$1$	$0$	$0$	$0$	$-1$	$5$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+5q^{7}+5q^{11}+q^{13}+6q^{17}+\cdots$
8784.2.a.l	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	$\Q$	None	✓		2196.2.a.c	$1$	$1$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{11}-2q^{13}-2q^{17}+4q^{19}+\cdots$
8784.2.a.m	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	$\Q$	None	✓		2196.2.a.c	$1$	$1$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{11}-2q^{13}+2q^{17}+4q^{19}+\cdots$
8784.2.a.n	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	$\Q$	None	✓		549.2.a.a	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-4q^{11}-2q^{13}-2q^{17}+4q^{19}+\cdots$
8784.2.a.o	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	$\Q$	None	✓		549.2.a.a	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}+4q^{11}-2q^{13}+2q^{17}+4q^{19}+\cdots$
8784.2.a.p	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	$\Q$	None	✓		1098.2.a.d	$1$	$0$	$0$	$0$	$1$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-4q^{7}+6q^{11}-6q^{13}-3q^{17}+\cdots$
8784.2.a.q	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	$\Q$	None	✓		366.2.a.e	$1$	$1$	$0$	$0$	$1$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}+2q^{11}+4q^{13}-q^{17}+\cdots$
8784.2.a.r	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	$\Q$	None	✓		366.2.a.a	$1$	$0$	$0$	$0$	$2$	$-4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{7}-4q^{11}-2q^{13}-6q^{17}+\cdots$
8784.2.a.s	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	$\Q$	None	✓		1464.2.a.b	$1$	$1$	$0$	$0$	$2$	$-4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{7}-2q^{11}+2q^{13}-4q^{17}+\cdots$
8784.2.a.t	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	$\Q$	None	✓		1464.2.a.e	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-2q^{11}+2q^{13}+4q^{17}+4q^{19}+\cdots$
8784.2.a.u	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	$\Q$	None	✓		1464.2.a.a	$1$	$1$	$0$	$0$	$2$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-2q^{13}-6q^{17}-4q^{19}+4q^{23}+\cdots$
8784.2.a.v	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	$\Q$	None	✓		732.2.a.c	$1$	$1$	$0$	$0$	$2$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+2q^{7}-6q^{13}-4q^{23}-q^{25}+\cdots$
8784.2.a.w	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	$\Q$	None	✓		61.2.a.a	$1$	$1$	$0$	$0$	$3$	$-1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-q^{7}-5q^{11}+q^{13}-4q^{17}+\cdots$
8784.2.a.x	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	$\Q$	None	✓		1098.2.a.f	$1$	$1$	$0$	$0$	$3$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-2q^{11}-2q^{13}+q^{17}-2q^{19}+\cdots$
8784.2.a.y	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	$\Q$	None	✓		366.2.a.b	$1$	$0$	$0$	$0$	$3$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+q^{7}-3q^{11}-q^{13}+6q^{17}+\cdots$
8784.2.a.z	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	$\Q$	None	✓		366.2.a.d	$1$	$0$	$0$	$0$	$3$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+3q^{7}-q^{11}-5q^{13}-2q^{17}+\cdots$
8784.2.a.ba	$8784$	$2$	8784.a	1.a	$1$	$1$	$1$	$70.141$	$\Q$	None	✓		244.2.a.a	$1$	$0$	$0$	$0$	$3$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+3q^{7}-q^{11}+q^{13}+2q^{17}+\cdots$
8784.2.a.bb	$8784$	$2$	8784.a	1.a	$1$	$2$	$2$	$70.141$	$\Q(\sqrt{6}) $	None	✓		1464.2.a.h	$1$	$0$	$0$	$0$	$-6$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+(1-\beta )q^{7}+(3+\beta )q^{11}+(1+\cdots)q^{13}+\cdots$
8784.2.a.bc	$8784$	$2$	8784.a	1.a	$1$	$2$	$2$	$70.141$	$\Q(\sqrt{3}) $	None	✓		732.2.a.e	$1$	$0$	$0$	$0$	$-2$	$-2$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{5}+(-1+\beta )q^{7}+(-1+\beta )q^{11}+\cdots$
8784.2.a.bd	$8784$	$2$	8784.a	1.a	$1$	$2$	$2$	$70.141$	$\Q(\sqrt{13}) $	None	✓		122.2.a.b	$1$	$0$	$0$	$0$	$0$	$-5$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-3+\beta )q^{7}+(2-2\beta )q^{11}+(4-2\beta )q^{13}+\cdots$
8784.2.a.be	$8784$	$2$	8784.a	1.a	$1$	$2$	$2$	$70.141$	$\Q(\sqrt{3}) $	None	✓		732.2.a.d	$1$	$0$	$0$	$0$	$0$	$-4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{5}-2q^{7}+(3-\beta )q^{11}+(2+2\beta )q^{13}+\cdots$
8784.2.a.bf	$8784$	$2$	8784.a	1.a	$1$	$2$	$2$	$70.141$	$\Q(\sqrt{3}) $	None	✓		549.2.a.d	$2$	$1$	$0$	$0$	$0$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+q^{7}-3\beta q^{11}+5q^{13}+2\beta q^{17}+\cdots$
8784.2.a.bg	$8784$	$2$	8784.a	1.a	$1$	$2$	$2$	$70.141$	$\Q(\sqrt{17}) $	None	✓		366.2.a.h	$1$	$0$	$0$	$0$	$0$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-2\beta )q^{5}+(2-\beta )q^{7}+(2-\beta )q^{11}+\cdots$
8784.2.a.bh	$8784$	$2$	8784.a	1.a	$1$	$2$	$2$	$70.141$	$\Q(\sqrt{2}) $	None	✓		488.2.a.a	$1$	$0$	$0$	$0$	$2$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+(1+\beta )q^{7}+(-1+3\beta )q^{11}+\cdots$
8784.2.a.bi	$8784$	$2$	8784.a	1.a	$1$	$2$	$2$	$70.141$	$\Q(\sqrt{2}) $	None	✓		183.2.a.a	$1$	$1$	$0$	$0$	$2$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+(1+\beta )q^{7}+(-1-\beta )q^{11}-3q^{13}+\cdots$
8784.2.a.bj	$8784$	$2$	8784.a	1.a	$1$	$2$	$2$	$70.141$	$\Q(\sqrt{6}) $	None	✓		1464.2.a.g	$1$	$0$	$0$	$0$	$4$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+2\beta q^{7}+(-2-\beta )q^{11}+4q^{13}+\cdots$
8784.2.a.bk	$8784$	$2$	8784.a	1.a	$1$	$3$	$3$	$70.141$	3.3.148.1	None	✓		183.2.a.b	$1$	$0$	$0$	$0$	$-6$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-2q^{5}+(\beta _{1}-\beta _{2})q^{7}+(1-\beta _{1})q^{11}+\cdots$
8784.2.a.bl	$8784$	$2$	8784.a	1.a	$1$	$3$	$3$	$70.141$	3.3.892.1	None	✓		1098.2.a.o	$1$	$0$	$0$	$0$	$-4$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{5}+(1-\beta _{1})q^{7}+(1-\beta _{1}+\cdots)q^{11}+\cdots$
8784.2.a.bm	$8784$	$2$	8784.a	1.a	$1$	$3$	$3$	$70.141$	3.3.229.1	None	✓		122.2.a.c	$1$	$1$	$0$	$0$	$-1$	$-4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{2})q^{5}+(-1-2\beta _{1}+\beta _{2})q^{7}+\cdots$
8784.2.a.bn	$8784$	$2$	8784.a	1.a	$1$	$3$	$3$	$70.141$	3.3.148.1	None	✓		61.2.a.b	$1$	$0$	$0$	$0$	$1$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}-\beta _{2})q^{5}+(1-\beta _{2})q^{7}+(4+\beta _{1}+\cdots)q^{11}+\cdots$
8784.2.a.bo	$8784$	$2$	8784.a	1.a	$1$	$3$	$3$	$70.141$	3.3.148.1	None	✓		488.2.a.b	$1$	$1$	$0$	$0$	$1$	$7$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{2})q^{5}+(2+\beta _{1})q^{7}+(-1-\beta _{2})q^{11}+\cdots$
8784.2.a.bp	$8784$	$2$	8784.a	1.a	$1$	$3$	$3$	$70.141$	3.3.961.1	None	✓		1464.2.a.i	$1$	$1$	$0$	$0$	$2$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{5}-\beta _{2}q^{7}+(2\beta _{1}-\beta _{2})q^{11}+\cdots$
8784.2.a.bq	$8784$	$2$	8784.a	1.a	$1$	$3$	$3$	$70.141$	3.3.1304.1	None	✓		732.2.a.f	$1$	$0$	$0$	$0$	$3$	$-3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{5}+(-1+\beta _{1})q^{7}+(-2+\cdots)q^{11}+\cdots$
8784.2.a.br	$8784$	$2$	8784.a	1.a	$1$	$3$	$3$	$70.141$	3.3.892.1	None	✓		1098.2.a.o	$1$	$0$	$0$	$0$	$4$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{5}+(1-\beta _{1})q^{7}+(-1+\beta _{1}+\cdots)q^{11}+\cdots$
8784.2.a.bs	$8784$	$2$	8784.a	1.a	$1$	$4$	$4$	$70.141$	4.4.15317.1	None	✓		1464.2.a.l	$1$	$1$	$0$	$0$	$-6$	$-1$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-2-\beta _{2})q^{5}+\beta _{1}q^{7}+(1-\beta _{3})q^{11}+\cdots$
8784.2.a.bt	$8784$	$2$	8784.a	1.a	$1$	$4$	$4$	$70.141$	4.4.20308.1	None	✓		244.2.a.b	$1$	$1$	$0$	$0$	$-5$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{5}-\beta _{3}q^{7}+(\beta _{2}+\beta _{3})q^{11}+\cdots$
8784.2.a.bu	$8784$	$2$	8784.a	1.a	$1$	$4$	$4$	$70.141$	4.4.7232.1	None	✓		1464.2.a.j	$1$	$0$	$0$	$0$	$-2$	$6$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}+\beta _{2})q^{5}+(1+\beta _{1}-\beta _{3})q^{7}+\cdots$
8784.2.a.bv	$8784$	$2$	8784.a	1.a	$1$	$4$	$4$	$70.141$	4.4.13676.1	None	✓		488.2.a.c	$1$	$0$	$0$	$0$	$2$	$-7$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{2}-\beta _{3})q^{5}+(-2+\beta _{1})q^{7}+\cdots$
8784.2.a.bw	$8784$	$2$	8784.a	1.a	$1$	$4$	$4$	$70.141$	4.4.9248.1	None	✓		1464.2.a.k	$1$	$0$	$0$	$0$	$6$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(2+\beta _{2})q^{5}+(\beta _{1}-\beta _{2}+\beta _{3})q^{7}+(-1+\cdots)q^{11}+\cdots$
8784.2.a.bx	$8784$	$2$	8784.a	1.a	$1$	$5$	$5$	$70.141$	5.5.4383968.1	None	✓		1464.2.a.m	$1$	$0$	$0$	$0$	$1$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{5}+(-\beta _{2}-\beta _{3})q^{7}+(1+\beta _{1}+\cdots)q^{11}+\cdots$

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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.