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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 106 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
1782.2.a.a	$1782$	$2$	1782.a	1.a	$1$	$1$	$1$	$14.229$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$-3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-3q^{5}+2q^{7}-q^{8}+3q^{10}+\cdots$
1782.2.a.b	$1782$	$2$	1782.a	1.a	$1$	$1$	$1$	$14.229$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{7}-q^{8}+q^{11}+2q^{13}+\cdots$
1782.2.a.c	$1782$	$2$	1782.a	1.a	$1$	$1$	$1$	$14.229$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots$
1782.2.a.d	$1782$	$2$	1782.a	1.a	$1$	$1$	$1$	$14.229$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-2q^{7}-q^{8}-q^{10}+\cdots$
1782.2.a.e	$1782$	$2$	1782.a	1.a	$1$	$1$	$1$	$14.229$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3q^{5}+2q^{7}-q^{8}-3q^{10}+\cdots$
1782.2.a.f	$1782$	$2$	1782.a	1.a	$1$	$1$	$1$	$14.229$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{5}+2q^{7}-q^{8}-4q^{10}+\cdots$
1782.2.a.g	$1782$	$2$	1782.a	1.a	$1$	$1$	$1$	$14.229$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$-4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-4q^{5}+2q^{7}+q^{8}-4q^{10}+\cdots$
1782.2.a.h	$1782$	$2$	1782.a	1.a	$1$	$1$	$1$	$14.229$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{5}+2q^{7}+q^{8}-3q^{10}+\cdots$
1782.2.a.i	$1782$	$2$	1782.a	1.a	$1$	$1$	$1$	$14.229$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots$
1782.2.a.j	$1782$	$2$	1782.a	1.a	$1$	$1$	$1$	$14.229$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots$
1782.2.a.k	$1782$	$2$	1782.a	1.a	$1$	$1$	$1$	$14.229$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{7}+q^{8}-q^{11}+2q^{13}+\cdots$
1782.2.a.l	$1782$	$2$	1782.a	1.a	$1$	$1$	$1$	$14.229$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{5}+2q^{7}+q^{8}+3q^{10}+\cdots$
1782.2.a.m	$1782$	$2$	1782.a	1.a	$1$	$2$	$2$	$14.229$	$\Q(\sqrt{6}) $	None	✓	$1$	$0$	$-2$	$0$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta )q^{5}+(-2+\beta )q^{7}+\cdots$
1782.2.a.n	$1782$	$2$	1782.a	1.a	$1$	$2$	$2$	$14.229$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$-2$	$0$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+(-1+\beta )q^{7}-q^{8}+\cdots$
1782.2.a.o	$1782$	$2$	1782.a	1.a	$1$	$2$	$2$	$14.229$	$\Q(\sqrt{6}) $	None	✓	$1$	$1$	$2$	$0$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1+\beta )q^{5}+(-2-\beta )q^{7}+\cdots$
1782.2.a.p	$1782$	$2$	1782.a	1.a	$1$	$2$	$2$	$14.229$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$2$	$0$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+(-1+\beta )q^{7}+q^{8}+\cdots$
1782.2.a.q	$1782$	$2$	1782.a	1.a	$1$	$3$	$3$	$14.229$	3.3.564.1	None	✓	$1$	$1$	$-3$	$0$	$-5$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-2+\beta _{1})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots$
1782.2.a.r	$1782$	$2$	1782.a	1.a	$1$	$3$	$3$	$14.229$	3.3.564.1	None	✓	$1$	$1$	$-3$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
1782.2.a.s	$1782$	$2$	1782.a	1.a	$1$	$3$	$3$	$14.229$	3.3.564.1	None	✓	$1$	$0$	$3$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
1782.2.a.t	$1782$	$2$	1782.a	1.a	$1$	$3$	$3$	$14.229$	3.3.564.1	None	✓	$1$	$0$	$3$	$0$	$5$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(2-\beta _{1})q^{5}+(1-\beta _{1})q^{7}+\cdots$
1782.2.a.u	$1782$	$2$	1782.a	1.a	$1$	$4$	$4$	$14.229$	4.4.62352.1	None	✓	$1$	$0$	$-4$	$0$	$2$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta _{1}q^{5}+(2+\beta _{3})q^{7}-q^{8}+\cdots$
1782.2.a.v	$1782$	$2$	1782.a	1.a	$1$	$4$	$4$	$14.229$	4.4.62352.1	None	✓	$1$	$0$	$4$	$0$	$-2$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-\beta _{1}q^{5}+(2+\beta _{3})q^{7}+q^{8}+\cdots$
1782.2.b.a	$1782$	$2$	1782.b	33.d	$2$	$4$	$4$	$14.229$	$\Q(\sqrt{-2}, \sqrt{3})$	None		$2$	$0$	$-4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+2\beta _{1}q^{5}+(-2\beta _{1}-2\beta _{3})q^{7}+\cdots$
1782.2.b.b	$1782$	$2$	1782.b	33.d	$2$	$4$	$4$	$14.229$	$\Q(\sqrt{-2}, \sqrt{3})$	None		$2$	$0$	$4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+2\beta _{1}q^{5}+(2\beta _{1}+2\beta _{3})q^{7}+\cdots$
1782.2.b.c	$1782$	$2$	1782.b	33.d	$2$	$8$	$8$	$14.229$	8.0.3057647616.5	None		$2$	$0$	$-8$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+(\beta _{1}+\beta _{4}+\beta _{5})q^{5}+\beta _{5}q^{7}+\cdots$
1782.2.b.d	$1782$	$2$	1782.b	33.d	$2$	$8$	$8$	$14.229$	8.0.3057647616.5	None		$2$	$0$	$8$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+(\beta _{1}+\beta _{4}+\beta _{5})q^{5}-\beta _{5}q^{7}+\cdots$
1782.2.b.e	$1782$	$2$	1782.b	33.d	$2$	$12$	$12$	$14.229$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$-12$	$0$	$0$	$0$		$2^{5}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+\beta _{1}q^{5}+\beta _{8}q^{7}-q^{8}+\cdots$
1782.2.b.f	$1782$	$2$	1782.b	33.d	$2$	$12$	$12$	$14.229$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$12$	$0$	$0$	$0$		$2^{5}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+\beta _{1}q^{5}-\beta _{8}q^{7}+q^{8}+\cdots$
1782.2.e.a	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$-3$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots$
1782.2.e.b	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$-3$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots$
1782.2.e.c	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$-2$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots$
1782.2.e.d	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$-2$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots$
1782.2.e.e	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$-2$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots$
1782.2.e.f	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{7}+\cdots$
1782.2.e.g	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{7}+\cdots$
1782.2.e.h	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{7}+\cdots$
1782.2.e.i	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	$\Q(\sqrt{-3}) $	None		$2$	$1$	$-1$	$0$	$1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-4+\cdots)q^{7}+\cdots$
1782.2.e.j	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$1$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots$
1782.2.e.k	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	$\Q(\sqrt{-3}) $	None		$2$	$1$	$-1$	$0$	$4$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+4\zeta_{6}q^{5}+\cdots$
1782.2.e.l	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$4$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+4\zeta_{6}q^{5}+\cdots$
1782.2.e.m	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	$\Q(\sqrt{-3}) $	None		$2$	$1$	$1$	$0$	$-4$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-4\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots$
1782.2.e.n	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$0$	$-4$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-4\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots$
1782.2.e.o	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$0$	$-1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-4+\cdots)q^{7}+\cdots$
1782.2.e.p	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$0$	$-1$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+\cdots$
1782.2.e.q	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{7}+\cdots$
1782.2.e.r	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{7}+\cdots$
1782.2.e.s	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	$\Q(\sqrt{-3}) $	None		$2$	$1$	$1$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-2+2\zeta_{6})q^{7}+\cdots$
1782.2.e.t	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$0$	$2$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+2\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots$
1782.2.e.u	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$0$	$2$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+2\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots$
1782.2.e.v	$1782$	$2$	1782.e	9.c	$3$	$2$	$1$	$14.229$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$0$	$2$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+2\zeta_{6}q^{5}+(4+\cdots)q^{7}+\cdots$

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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.