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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 152 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
2450.2.a.a	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$0$	$-1$	$-3$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-3q^{3}+q^{4}+3q^{6}-q^{8}+6q^{9}+\cdots$
2450.2.a.b	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$1$	$-1$	$-3$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-3q^{3}+q^{4}+3q^{6}-q^{8}+6q^{9}+\cdots$
2450.2.a.c	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$1$	$-1$	$-3$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-3q^{3}+q^{4}+3q^{6}-q^{8}+6q^{9}+\cdots$
2450.2.a.d	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$0$	$-1$	$-2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{8}+q^{9}+\cdots$
2450.2.a.e	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$0$	$-1$	$-2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{8}+q^{9}+\cdots$
2450.2.a.f	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$0$	$-1$	$-2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{8}+q^{9}+\cdots$
2450.2.a.g	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}-2q^{9}+\cdots$
2450.2.a.h	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{8}-3q^{9}-2q^{11}+q^{16}+\cdots$
2450.2.a.i	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{8}-3q^{9}-2q^{11}+q^{16}+\cdots$
2450.2.a.j	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{8}-3q^{9}+3q^{11}-5q^{13}+\cdots$
2450.2.a.k	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{8}-3q^{9}+3q^{11}+5q^{13}+\cdots$
2450.2.a.l	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{8}-3q^{9}+4q^{11}-6q^{13}+\cdots$
2450.2.a.m	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}-2q^{9}+\cdots$
2450.2.a.n	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$0$	$-1$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{8}+q^{9}+\cdots$
2450.2.a.o	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$1$	$-1$	$2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{8}+q^{9}+\cdots$
2450.2.a.p	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$1$	$-1$	$2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{6}-q^{8}+q^{9}+\cdots$
2450.2.a.q	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$0$	$-1$	$3$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}+q^{4}-3q^{6}-q^{8}+6q^{9}+\cdots$
2450.2.a.r	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$0$	$-1$	$3$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}+q^{4}-3q^{6}-q^{8}+6q^{9}+\cdots$
2450.2.a.s	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$1$	$1$	$-3$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}+q^{4}-3q^{6}+q^{8}+6q^{9}+\cdots$
2450.2.a.t	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$1$	$1$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{8}+q^{9}+\cdots$
2450.2.a.u	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$1$	$1$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{8}+q^{9}+\cdots$
2450.2.a.v	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$1$	$1$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{6}+q^{8}+q^{9}+\cdots$
2450.2.a.w	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-2q^{9}+\cdots$
2450.2.a.x	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-2q^{9}+\cdots$
2450.2.a.y	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}-3q^{9}-2q^{11}+q^{16}+\cdots$
2450.2.a.z	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}-3q^{9}-2q^{11}+q^{16}+\cdots$
2450.2.a.ba	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}-3q^{9}+3q^{11}-5q^{13}+\cdots$
2450.2.a.bb	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}-3q^{9}+3q^{11}+5q^{13}+\cdots$
2450.2.a.bc	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}-2q^{9}+\cdots$
2450.2.a.bd	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}-2q^{9}+\cdots$
2450.2.a.be	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$0$	$1$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{8}+q^{9}+\cdots$
2450.2.a.bf	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$0$	$1$	$2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+2q^{6}+q^{8}+q^{9}+\cdots$
2450.2.a.bg	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$0$	$1$	$3$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}+q^{4}+3q^{6}+q^{8}+6q^{9}+\cdots$
2450.2.a.bh	$2450$	$2$	2450.a	1.a	$1$	$1$	$1$	$19.563$	$\Q$	None	✓	$1$	$0$	$1$	$3$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}+q^{4}+3q^{6}+q^{8}+6q^{9}+\cdots$
2450.2.a.bi	$2450$	$2$	2450.a	1.a	$1$	$2$	$2$	$19.563$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$-2$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{8}-3q^{9}-4q^{11}+3\beta q^{13}+\cdots$
2450.2.a.bj	$2450$	$2$	2450.a	1.a	$1$	$2$	$2$	$19.563$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$-2$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{8}-q^{9}+\cdots$
2450.2.a.bk	$2450$	$2$	2450.a	1.a	$1$	$2$	$2$	$19.563$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$-2$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{8}-q^{9}+\cdots$
2450.2.a.bl	$2450$	$2$	2450.a	1.a	$1$	$2$	$2$	$19.563$	$\Q(\sqrt{6}) $	None	✓	$1$	$1$	$-2$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{8}+3q^{9}+\cdots$
2450.2.a.bm	$2450$	$2$	2450.a	1.a	$1$	$2$	$2$	$19.563$	$\Q(\sqrt{7}) $	None	✓	$2$	$0$	$-2$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{8}+4q^{9}+\cdots$
2450.2.a.bn	$2450$	$2$	2450.a	1.a	$1$	$2$	$2$	$19.563$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$2$	$-4$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-2+\beta )q^{3}+q^{4}+(-2+\beta )q^{6}+\cdots$
2450.2.a.bo	$2450$	$2$	2450.a	1.a	$1$	$2$	$2$	$19.563$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$2$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}-3q^{9}-4q^{11}+3\beta q^{13}+\cdots$
2450.2.a.bp	$2450$	$2$	2450.a	1.a	$1$	$2$	$2$	$19.563$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$2$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+q^{8}-q^{9}+\cdots$
2450.2.a.bq	$2450$	$2$	2450.a	1.a	$1$	$2$	$2$	$19.563$	$\Q(\sqrt{6}) $	None	✓	$1$	$0$	$2$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+q^{8}+3q^{9}+\cdots$
2450.2.a.br	$2450$	$2$	2450.a	1.a	$1$	$2$	$2$	$19.563$	$\Q(\sqrt{7}) $	None	✓	$2$	$0$	$2$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+q^{8}+4q^{9}+\cdots$
2450.2.a.bs	$2450$	$2$	2450.a	1.a	$1$	$2$	$2$	$19.563$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$2$	$4$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(2+\beta )q^{3}+q^{4}+(2+\beta )q^{6}+\cdots$
2450.2.a.bt	$2450$	$2$	2450.a	1.a	$1$	$4$	$4$	$19.563$	$\Q(\sqrt{2}, \sqrt{11})$	None	✓	$2$	$0$	$-4$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}-q^{8}+\cdots$
2450.2.a.bu	$2450$	$2$	2450.a	1.a	$1$	$4$	$4$	$19.563$	$\Q(\sqrt{2}, \sqrt{11})$	None	✓	$2$	$0$	$4$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+q^{8}+\cdots$
2450.2.c.a	$2450$	$2$	2450.c	5.b	$2$	$2$	$2$	$19.563$	$\Q(\sqrt{-1}) $	None		$2$	$1$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+3iq^{3}-q^{4}-3q^{6}-iq^{8}+\cdots$
2450.2.c.b	$2450$	$2$	2450.c	5.b	$2$	$2$	$2$	$19.563$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{8}+\cdots$
2450.2.c.c	$2450$	$2$	2450.c	5.b	$2$	$2$	$2$	$19.563$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{8}+\cdots$

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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.