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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 74 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	5	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
6400.2.a.a	$6400$	$2$	6400.a	1.a	$1$	$1$	$1$	$51.104$	$\Q$	$\Q(\sqrt{-2}) $	✓	$2$	$0$	$0$	$-2$	$0$	$0$	$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{3}+q^{9}+6q^{11}+6q^{17}+2q^{19}+\cdots$
6400.2.a.b	$6400$	$2$	6400.a	1.a	$1$	$1$	$1$	$51.104$	$\Q$	None	✓	$1$	$2$	$0$	$-1$	$0$	$-4$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{7}-2q^{9}-3q^{11}-q^{17}+\cdots$
6400.2.a.c	$6400$	$2$	6400.a	1.a	$1$	$1$	$1$	$51.104$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$-4$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{7}-2q^{9}+3q^{11}+q^{17}+\cdots$
6400.2.a.d	$6400$	$2$	6400.a	1.a	$1$	$1$	$1$	$51.104$	$\Q$	None	✓	$1$	$2$	$0$	$-1$	$0$	$-2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}-2q^{9}-5q^{11}-6q^{13}+\cdots$
6400.2.a.e	$6400$	$2$	6400.a	1.a	$1$	$1$	$1$	$51.104$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$0$	$-2$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}-2q^{9}+5q^{11}+6q^{13}+\cdots$
6400.2.a.f	$6400$	$2$	6400.a	1.a	$1$	$1$	$1$	$51.104$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}-2q^{9}-5q^{11}+6q^{13}+\cdots$
6400.2.a.g	$6400$	$2$	6400.a	1.a	$1$	$1$	$1$	$51.104$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$2$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}-2q^{9}+5q^{11}-6q^{13}+\cdots$
6400.2.a.h	$6400$	$2$	6400.a	1.a	$1$	$1$	$1$	$51.104$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$4$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{7}-2q^{9}-3q^{11}-q^{17}+\cdots$
6400.2.a.i	$6400$	$2$	6400.a	1.a	$1$	$1$	$1$	$51.104$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$0$	$4$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{7}-2q^{9}+3q^{11}+q^{17}+\cdots$
6400.2.a.j	$6400$	$2$	6400.a	1.a	$1$	$1$	$1$	$51.104$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	$q-3q^{9}-6q^{13}-8q^{17}-4q^{29}-2q^{37}+\cdots$
6400.2.a.k	$6400$	$2$	6400.a	1.a	$1$	$1$	$1$	$51.104$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	$q-3q^{9}-6q^{13}+8q^{17}+4q^{29}-2q^{37}+\cdots$
6400.2.a.l	$6400$	$2$	6400.a	1.a	$1$	$1$	$1$	$51.104$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	$q-3q^{9}-4q^{13}+2q^{17}+4q^{29}+12q^{37}+\cdots$
6400.2.a.m	$6400$	$2$	6400.a	1.a	$1$	$1$	$1$	$51.104$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	$q-3q^{9}+4q^{13}+2q^{17}-4q^{29}-12q^{37}+\cdots$
6400.2.a.n	$6400$	$2$	6400.a	1.a	$1$	$1$	$1$	$51.104$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	$q-3q^{9}+6q^{13}-8q^{17}+4q^{29}+2q^{37}+\cdots$
6400.2.a.o	$6400$	$2$	6400.a	1.a	$1$	$1$	$1$	$51.104$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	$q-3q^{9}+6q^{13}+8q^{17}-4q^{29}+2q^{37}+\cdots$
6400.2.a.p	$6400$	$2$	6400.a	1.a	$1$	$1$	$1$	$51.104$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$-4$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{7}-2q^{9}-3q^{11}+q^{17}+\cdots$
6400.2.a.q	$6400$	$2$	6400.a	1.a	$1$	$1$	$1$	$51.104$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$-4$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{7}-2q^{9}+3q^{11}-q^{17}+\cdots$
6400.2.a.r	$6400$	$2$	6400.a	1.a	$1$	$1$	$1$	$51.104$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$-2$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}-2q^{9}-5q^{11}-6q^{13}+\cdots$
6400.2.a.s	$6400$	$2$	6400.a	1.a	$1$	$1$	$1$	$51.104$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$-2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}-2q^{9}+5q^{11}+6q^{13}+\cdots$
6400.2.a.t	$6400$	$2$	6400.a	1.a	$1$	$1$	$1$	$51.104$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$2$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{7}-2q^{9}-5q^{11}+6q^{13}+\cdots$
6400.2.a.u	$6400$	$2$	6400.a	1.a	$1$	$1$	$1$	$51.104$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{7}-2q^{9}+5q^{11}-6q^{13}+\cdots$
6400.2.a.v	$6400$	$2$	6400.a	1.a	$1$	$1$	$1$	$51.104$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$4$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{7}-2q^{9}-3q^{11}+q^{17}+\cdots$
6400.2.a.w	$6400$	$2$	6400.a	1.a	$1$	$1$	$1$	$51.104$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$4$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{7}-2q^{9}+3q^{11}-q^{17}+\cdots$
6400.2.a.x	$6400$	$2$	6400.a	1.a	$1$	$1$	$1$	$51.104$	$\Q$	$\Q(\sqrt{-2}) $	✓	$2$	$1$	$0$	$2$	$0$	$0$	$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	$q+2q^{3}+q^{9}-6q^{11}+6q^{17}-2q^{19}+\cdots$
6400.2.a.y	$6400$	$2$	6400.a	1.a	$1$	$2$	$2$	$51.104$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$0$	$-2$	$0$	$-6$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+(-3+\beta )q^{7}+(1-2\beta )q^{9}+\cdots$
6400.2.a.z	$6400$	$2$	6400.a	1.a	$1$	$2$	$2$	$51.104$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$0$	$-2$	$0$	$-2$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+(-1-\beta )q^{7}+(1-2\beta )q^{9}+\cdots$
6400.2.a.ba	$6400$	$2$	6400.a	1.a	$1$	$2$	$2$	$51.104$	$\Q(\sqrt{3}) $	None	✓	$2$	$1$	$0$	$-2$	$0$	$0$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}-\beta q^{7}-2q^{9}-3q^{11}+\beta q^{13}+\cdots$
6400.2.a.bb	$6400$	$2$	6400.a	1.a	$1$	$2$	$2$	$51.104$	$\Q(\sqrt{3}) $	None	✓	$2$	$1$	$0$	$-2$	$0$	$0$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}-\beta q^{7}-2q^{9}+3q^{11}-\beta q^{13}+\cdots$
6400.2.a.bc	$6400$	$2$	6400.a	1.a	$1$	$2$	$2$	$51.104$	$\Q(\sqrt{6}) $	$\Q(\sqrt{-2}) $	✓	$2$	$1$	$0$	$-2$	$0$	$0$	$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	$q+(-1+\beta )q^{3}+(4-2\beta )q^{9}+(-3+\beta )q^{11}+\cdots$
6400.2.a.bd	$6400$	$2$	6400.a	1.a	$1$	$2$	$2$	$51.104$	$\Q(\sqrt{6}) $	$\Q(\sqrt{-2}) $	✓	$2$	$1$	$0$	$-2$	$0$	$0$	$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	$q+(-1+\beta )q^{3}+(4-2\beta )q^{9}+(3-\beta )q^{11}+\cdots$
6400.2.a.be	$6400$	$2$	6400.a	1.a	$1$	$2$	$2$	$51.104$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$-2$	$0$	$2$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+(1+\beta )q^{7}+(1-2\beta )q^{9}+\cdots$
6400.2.a.bf	$6400$	$2$	6400.a	1.a	$1$	$2$	$2$	$51.104$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$0$	$-2$	$0$	$6$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+(3-\beta )q^{7}+(1-2\beta )q^{9}+\cdots$
6400.2.a.bg	$6400$	$2$	6400.a	1.a	$1$	$2$	$2$	$51.104$	$\Q(\sqrt{7}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$-8$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-4q^{7}+4q^{9}+\beta q^{11}-3q^{17}+\cdots$
6400.2.a.bh	$6400$	$2$	6400.a	1.a	$1$	$2$	$2$	$51.104$	$\Q(\sqrt{7}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$-8$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-4q^{7}+4q^{9}-\beta q^{11}+3q^{17}+\cdots$
6400.2.a.bi	$6400$	$2$	6400.a	1.a	$1$	$2$	$2$	$51.104$	$\Q(\sqrt{5}) $	$\Q(\sqrt{-10}) $	✓	$4$	$1$	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$2^{2}$	$N(\mathrm{U}(1))$	$q+\beta q^{7}-3q^{9}-2q^{11}-\beta q^{13}+6q^{19}+\cdots$
6400.2.a.bj	$6400$	$2$	6400.a	1.a	$1$	$2$	$2$	$51.104$	$\Q(\sqrt{5}) $	$\Q(\sqrt{-10}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$2^{2}$	$N(\mathrm{U}(1))$	$q+\beta q^{7}-3q^{9}+2q^{11}+\beta q^{13}-6q^{19}+\cdots$
6400.2.a.bk	$6400$	$2$	6400.a	1.a	$1$	$2$	$2$	$51.104$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+3\beta q^{7}-q^{9}-2\beta q^{11}-6q^{13}+\cdots$
6400.2.a.bl	$6400$	$2$	6400.a	1.a	$1$	$2$	$2$	$51.104$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-3\beta q^{7}-q^{9}-4\beta q^{11}-2q^{13}+\cdots$
6400.2.a.bm	$6400$	$2$	6400.a	1.a	$1$	$2$	$2$	$51.104$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+\beta q^{7}-q^{9}+2\beta q^{11}-2q^{13}+\cdots$
6400.2.a.bn	$6400$	$2$	6400.a	1.a	$1$	$2$	$2$	$51.104$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+3\beta q^{7}-q^{9}-4\beta q^{11}+2q^{13}+\cdots$
6400.2.a.bo	$6400$	$2$	6400.a	1.a	$1$	$2$	$2$	$51.104$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-\beta q^{7}-q^{9}+2\beta q^{11}+2q^{13}+\cdots$
6400.2.a.bp	$6400$	$2$	6400.a	1.a	$1$	$2$	$2$	$51.104$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-3\beta q^{7}-q^{9}-2\beta q^{11}+6q^{13}+\cdots$
6400.2.a.bq	$6400$	$2$	6400.a	1.a	$1$	$2$	$2$	$51.104$	$\Q(\sqrt{5}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{3}+2q^{9}-\beta q^{11}-4q^{13}-3q^{17}+\cdots$
6400.2.a.br	$6400$	$2$	6400.a	1.a	$1$	$2$	$2$	$51.104$	$\Q(\sqrt{5}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{3}+2q^{9}+\beta q^{11}-4q^{13}+3q^{17}+\cdots$
6400.2.a.bs	$6400$	$2$	6400.a	1.a	$1$	$2$	$2$	$51.104$	$\Q(\sqrt{5}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{3}+2q^{9}-\beta q^{11}+4q^{13}-3q^{17}+\cdots$
6400.2.a.bt	$6400$	$2$	6400.a	1.a	$1$	$2$	$2$	$51.104$	$\Q(\sqrt{5}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{3}+2q^{9}+\beta q^{11}+4q^{13}+3q^{17}+\cdots$
6400.2.a.bu	$6400$	$2$	6400.a	1.a	$1$	$2$	$2$	$51.104$	$\Q(\sqrt{6}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-\beta q^{7}+3q^{9}+2\beta q^{11}-4q^{17}+\cdots$
6400.2.a.bv	$6400$	$2$	6400.a	1.a	$1$	$2$	$2$	$51.104$	$\Q(\sqrt{6}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+\beta q^{7}+3q^{9}+2\beta q^{11}-4q^{17}+\cdots$
6400.2.a.bw	$6400$	$2$	6400.a	1.a	$1$	$2$	$2$	$51.104$	$\Q(\sqrt{6}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-\beta q^{7}+3q^{9}-2\beta q^{11}+4q^{17}+\cdots$
6400.2.a.bx	$6400$	$2$	6400.a	1.a	$1$	$2$	$2$	$51.104$	$\Q(\sqrt{6}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+\beta q^{7}+3q^{9}-2\beta q^{11}+4q^{17}+\cdots$

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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.