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Level	Weight	Analytic conductor	$Nk^2$	Dim.

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

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

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 76 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	3	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
6534.2.a.a	$6534$	$2$	6534.a	1.a	$1$	$1$	$1$	$52.174$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-3$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-3q^{5}-q^{8}+3q^{10}-3q^{13}+\cdots$
6534.2.a.b	$6534$	$2$	6534.a	1.a	$1$	$1$	$1$	$52.174$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$-3$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-3q^{5}+q^{7}-q^{8}+3q^{10}+\cdots$
6534.2.a.c	$6534$	$2$	6534.a	1.a	$1$	$1$	$1$	$52.174$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-3$	$4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-3q^{5}+4q^{7}-q^{8}+3q^{10}+\cdots$
6534.2.a.d	$6534$	$2$	6534.a	1.a	$1$	$1$	$1$	$52.174$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-2$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}+q^{7}-q^{8}+2q^{10}+\cdots$
6534.2.a.e	$6534$	$2$	6534.a	1.a	$1$	$1$	$1$	$52.174$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-1$	$-4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-4q^{7}-q^{8}+q^{10}+\cdots$
6534.2.a.f	$6534$	$2$	6534.a	1.a	$1$	$1$	$1$	$52.174$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$-1$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-2q^{7}-q^{8}+q^{10}+\cdots$
6534.2.a.g	$6534$	$2$	6534.a	1.a	$1$	$1$	$1$	$52.174$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$-3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-3q^{7}-q^{8}+3q^{14}+q^{16}+\cdots$
6534.2.a.h	$6534$	$2$	6534.a	1.a	$1$	$1$	$1$	$52.174$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3q^{7}-q^{8}-3q^{14}+q^{16}+\cdots$
6534.2.a.i	$6534$	$2$	6534.a	1.a	$1$	$1$	$1$	$52.174$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$1$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots$
6534.2.a.j	$6534$	$2$	6534.a	1.a	$1$	$1$	$1$	$52.174$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$2$	$-1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-q^{7}-q^{8}-2q^{10}+\cdots$
6534.2.a.k	$6534$	$2$	6534.a	1.a	$1$	$1$	$1$	$52.174$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$2$	$-1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-q^{7}-q^{8}-2q^{10}+\cdots$
6534.2.a.l	$6534$	$2$	6534.a	1.a	$1$	$1$	$1$	$52.174$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$2$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-2q^{10}+\cdots$
6534.2.a.m	$6534$	$2$	6534.a	1.a	$1$	$1$	$1$	$52.174$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$3$	$-4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3q^{5}-4q^{7}-q^{8}-3q^{10}+\cdots$
6534.2.a.n	$6534$	$2$	6534.a	1.a	$1$	$1$	$1$	$52.174$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$3$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3q^{5}-q^{8}-3q^{10}+3q^{13}+\cdots$
6534.2.a.o	$6534$	$2$	6534.a	1.a	$1$	$1$	$1$	$52.174$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$3$	$4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3q^{5}+4q^{7}-q^{8}-3q^{10}+\cdots$
6534.2.a.p	$6534$	$2$	6534.a	1.a	$1$	$1$	$1$	$52.174$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$-3$	$-4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{5}-4q^{7}+q^{8}-3q^{10}+\cdots$
6534.2.a.q	$6534$	$2$	6534.a	1.a	$1$	$1$	$1$	$52.174$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$-3$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}+3q^{13}+\cdots$
6534.2.a.r	$6534$	$2$	6534.a	1.a	$1$	$1$	$1$	$52.174$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$-3$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{5}+4q^{7}+q^{8}-3q^{10}+\cdots$
6534.2.a.s	$6534$	$2$	6534.a	1.a	$1$	$1$	$1$	$52.174$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$-2$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}-q^{7}+q^{8}-2q^{10}+\cdots$
6534.2.a.t	$6534$	$2$	6534.a	1.a	$1$	$1$	$1$	$52.174$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-2$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}-q^{7}+q^{8}-2q^{10}+\cdots$
6534.2.a.u	$6534$	$2$	6534.a	1.a	$1$	$1$	$1$	$52.174$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$-2$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}+q^{7}+q^{8}-2q^{10}+\cdots$
6534.2.a.v	$6534$	$2$	6534.a	1.a	$1$	$1$	$1$	$52.174$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-1$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots$
6534.2.a.w	$6534$	$2$	6534.a	1.a	$1$	$1$	$1$	$52.174$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$-3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{7}+q^{8}-3q^{14}+q^{16}+\cdots$
6534.2.a.x	$6534$	$2$	6534.a	1.a	$1$	$1$	$1$	$52.174$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{7}+q^{8}+3q^{14}+q^{16}+\cdots$
6534.2.a.y	$6534$	$2$	6534.a	1.a	$1$	$1$	$1$	$52.174$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$1$	$-4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-4q^{7}+q^{8}+q^{10}+\cdots$
6534.2.a.z	$6534$	$2$	6534.a	1.a	$1$	$1$	$1$	$52.174$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$1$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-2q^{7}+q^{8}+q^{10}+\cdots$
6534.2.a.ba	$6534$	$2$	6534.a	1.a	$1$	$1$	$1$	$52.174$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$2$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}+q^{7}+q^{8}+2q^{10}+\cdots$
6534.2.a.bb	$6534$	$2$	6534.a	1.a	$1$	$1$	$1$	$52.174$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$3$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-3q^{13}+\cdots$
6534.2.a.bc	$6534$	$2$	6534.a	1.a	$1$	$1$	$1$	$52.174$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$3$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{5}+q^{7}+q^{8}+3q^{10}+\cdots$
6534.2.a.bd	$6534$	$2$	6534.a	1.a	$1$	$1$	$1$	$52.174$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$3$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{5}+4q^{7}+q^{8}+3q^{10}+\cdots$
6534.2.a.be	$6534$	$2$	6534.a	1.a	$1$	$2$	$2$	$52.174$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$0$	$-4$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1-2\beta )q^{5}-q^{7}-q^{8}+\cdots$
6534.2.a.bf	$6534$	$2$	6534.a	1.a	$1$	$2$	$2$	$52.174$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$0$	$-2$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2\beta q^{5}+(1-3\beta )q^{7}-q^{8}+\cdots$
6534.2.a.bg	$6534$	$2$	6534.a	1.a	$1$	$2$	$2$	$52.174$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$0$	$-2$	$4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+(1+2\beta )q^{7}-q^{8}+\cdots$
6534.2.a.bh	$6534$	$2$	6534.a	1.a	$1$	$2$	$2$	$52.174$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$0$	$-2$	$7$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2\beta q^{5}+(3+\beta )q^{7}-q^{8}+\cdots$
6534.2.a.bi	$6534$	$2$	6534.a	1.a	$1$	$2$	$2$	$52.174$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$0$	$-1$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-\beta q^{5}-q^{7}-q^{8}+\beta q^{10}+\cdots$
6534.2.a.bj	$6534$	$2$	6534.a	1.a	$1$	$2$	$2$	$52.174$	$\Q(\sqrt{13}) $	None	✓	$1$	$1$	$-2$	$0$	$-1$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-\beta q^{5}+(1-2\beta )q^{7}-q^{8}+\cdots$
6534.2.a.bk	$6534$	$2$	6534.a	1.a	$1$	$2$	$2$	$52.174$	$\Q(\sqrt{37}) $	None	✓	$1$	$0$	$-2$	$0$	$-1$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-\beta q^{5}+q^{7}-q^{8}+\beta q^{10}+\cdots$
6534.2.a.bl	$6534$	$2$	6534.a	1.a	$1$	$2$	$2$	$52.174$	$\Q(\sqrt{3}) $	None	✓	$2$	$1$	$-2$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}-2\beta q^{7}-q^{8}-\beta q^{10}+\cdots$
6534.2.a.bm	$6534$	$2$	6534.a	1.a	$1$	$2$	$2$	$52.174$	$\Q(\sqrt{3}) $	None	✓	$2$	$1$	$-2$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2\beta q^{5}-\beta q^{7}-q^{8}-2\beta q^{10}+\cdots$
6534.2.a.bn	$6534$	$2$	6534.a	1.a	$1$	$2$	$2$	$52.174$	$\Q(\sqrt{3}) $	None	✓	$2$	$0$	$-2$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}+2\beta q^{7}-q^{8}-\beta q^{10}+\cdots$
6534.2.a.bo	$6534$	$2$	6534.a	1.a	$1$	$2$	$2$	$52.174$	$\Q(\sqrt{3}) $	None	✓	$2$	$0$	$-2$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}+4\beta q^{13}+\cdots$
6534.2.a.bp	$6534$	$2$	6534.a	1.a	$1$	$2$	$2$	$52.174$	$\Q(\sqrt{37}) $	None	✓	$1$	$1$	$-2$	$0$	$1$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}-q^{7}-q^{8}-\beta q^{10}+\cdots$
6534.2.a.bq	$6534$	$2$	6534.a	1.a	$1$	$2$	$2$	$52.174$	$\Q(\sqrt{13}) $	None	✓	$1$	$0$	$-2$	$0$	$1$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}+(-1+2\beta )q^{7}+\cdots$
6534.2.a.br	$6534$	$2$	6534.a	1.a	$1$	$2$	$2$	$52.174$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$0$	$1$	$2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}+q^{7}-q^{8}-\beta q^{10}+\cdots$
6534.2.a.bs	$6534$	$2$	6534.a	1.a	$1$	$2$	$2$	$52.174$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$0$	$2$	$-7$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2\beta q^{5}+(-3-\beta )q^{7}+\cdots$
6534.2.a.bt	$6534$	$2$	6534.a	1.a	$1$	$2$	$2$	$52.174$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$0$	$2$	$-4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+(-1-2\beta )q^{7}-q^{8}+\cdots$
6534.2.a.bu	$6534$	$2$	6534.a	1.a	$1$	$2$	$2$	$52.174$	$\Q(\sqrt{10}) $	None	✓	$1$	$0$	$-2$	$0$	$2$	$-4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta )q^{5}-2q^{7}-q^{8}+\cdots$
6534.2.a.bv	$6534$	$2$	6534.a	1.a	$1$	$2$	$2$	$52.174$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$0$	$2$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2\beta q^{5}+(-1+3\beta )q^{7}+\cdots$
6534.2.a.bw	$6534$	$2$	6534.a	1.a	$1$	$2$	$2$	$52.174$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$0$	$4$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+2\beta )q^{5}+q^{7}-q^{8}+\cdots$
6534.2.a.bx	$6534$	$2$	6534.a	1.a	$1$	$2$	$2$	$52.174$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$0$	$-4$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-2\beta )q^{5}+q^{7}+q^{8}+\cdots$

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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.