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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 53 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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	11	17	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
2057.2.a.a	$2057$	$2$	2057.a	1.a	$1$	$1$	$1$	$16.425$	$\Q$	None	✓	$1$	$0$	$-2$	$0$	$4$	$5$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+4q^{5}+5q^{7}-3q^{9}+\cdots$
2057.2.a.b	$2057$	$2$	2057.a	1.a	$1$	$1$	$1$	$16.425$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$3$	$-2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+3q^{5}-2q^{7}-2q^{9}+\cdots$
2057.2.a.c	$2057$	$2$	2057.a	1.a	$1$	$1$	$1$	$16.425$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$0$	$-3$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{4}-3q^{7}+q^{9}-4q^{12}+\cdots$
2057.2.a.d	$2057$	$2$	2057.a	1.a	$1$	$1$	$1$	$16.425$	$\Q$	None	✓	$1$	$0$	$0$	$2$	$0$	$3$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{4}+3q^{7}+q^{9}-4q^{12}+\cdots$
2057.2.a.e	$2057$	$2$	2057.a	1.a	$1$	$1$	$1$	$16.425$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$-2$	$-4$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-2q^{5}-4q^{7}-3q^{8}-3q^{9}+\cdots$
2057.2.a.f	$2057$	$2$	2057.a	1.a	$1$	$2$	$2$	$16.425$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$-4$	$-1$	$1$	$-3$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(-1+\beta )q^{3}+2q^{4}+(1-\beta )q^{5}+\cdots$
2057.2.a.g	$2057$	$2$	2057.a	1.a	$1$	$2$	$2$	$16.425$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-1$	$0$	$0$	$1$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots$
2057.2.a.h	$2057$	$2$	2057.a	1.a	$1$	$2$	$2$	$16.425$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-1$	$2$	$-2$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(2-2\beta )q^{3}+(-1+\beta )q^{4}+\cdots$
2057.2.a.i	$2057$	$2$	2057.a	1.a	$1$	$2$	$2$	$16.425$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-1$	$3$	$-3$	$-1$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(1+\beta )q^{3}+(-1+\beta )q^{4}+(-1+\cdots)q^{5}+\cdots$
2057.2.a.j	$2057$	$2$	2057.a	1.a	$1$	$2$	$2$	$16.425$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$-3$	$-4$	$1$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-2\beta )q^{2}+(-2+\beta )q^{3}+3q^{4}+\cdots$
2057.2.a.k	$2057$	$2$	2057.a	1.a	$1$	$2$	$2$	$16.425$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$-3$	$-4$	$-1$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-2\beta )q^{2}+(-1-\beta )q^{3}+3q^{4}+\cdots$
2057.2.a.l	$2057$	$2$	2057.a	1.a	$1$	$2$	$2$	$16.425$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$1$	$0$	$0$	$-1$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots$
2057.2.a.m	$2057$	$2$	2057.a	1.a	$1$	$2$	$2$	$16.425$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$1$	$2$	$-2$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(2-2\beta )q^{3}+(-1+\beta )q^{4}+\cdots$
2057.2.a.n	$2057$	$2$	2057.a	1.a	$1$	$2$	$2$	$16.425$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$1$	$3$	$-3$	$1$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{3}+(-1+\beta )q^{4}+(-1+\cdots)q^{5}+\cdots$
2057.2.a.o	$2057$	$2$	2057.a	1.a	$1$	$2$	$2$	$16.425$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$2$	$0$	$-4$	$4$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+\beta q^{3}+(2+2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots$
2057.2.a.p	$2057$	$2$	2057.a	1.a	$1$	$3$	$3$	$16.425$	3.3.148.1	None	✓	$1$	$1$	$2$	$-3$	$-7$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(-1-\beta _{2})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
2057.2.a.q	$2057$	$2$	2057.a	1.a	$1$	$4$	$4$	$16.425$	$\Q(\sqrt{3}, \sqrt{5})$	None	✓	$1$	$1$	$-2$	$-2$	$2$	$6$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(\beta _{2}+\beta _{3})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
2057.2.a.r	$2057$	$2$	2057.a	1.a	$1$	$4$	$4$	$16.425$	4.4.725.1	None	✓	$1$	$1$	$-2$	$-1$	$1$	$6$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(\beta _{1}-\beta _{3})q^{3}+(\beta _{2}-\beta _{3})q^{4}+\cdots$
2057.2.a.s	$2057$	$2$	2057.a	1.a	$1$	$4$	$4$	$16.425$	4.4.33844.1	None	✓	$1$	$0$	$-1$	$1$	$3$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots$
2057.2.a.t	$2057$	$2$	2057.a	1.a	$1$	$4$	$4$	$16.425$	$\Q(\sqrt{3}, \sqrt{5})$	None	✓	$1$	$1$	$2$	$-2$	$2$	$-6$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(\beta _{2}-\beta _{3})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
2057.2.a.u	$2057$	$2$	2057.a	1.a	$1$	$4$	$4$	$16.425$	4.4.725.1	None	✓	$1$	$1$	$2$	$-1$	$1$	$-6$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(\beta _{1}-\beta _{3})q^{3}+(\beta _{2}-\beta _{3})q^{4}+\cdots$
2057.2.a.v	$2057$	$2$	2057.a	1.a	$1$	$5$	$5$	$16.425$	5.5.475929.1	None	✓	$1$	$1$	$-3$	$-4$	$-1$	$-9$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+(-1-\beta _{3})q^{3}+(2+\cdots)q^{4}+\cdots$
2057.2.a.w	$2057$	$2$	2057.a	1.a	$1$	$5$	$5$	$16.425$	5.5.984016.1	None	✓	$1$	$1$	$-2$	$-1$	$1$	$-6$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$
2057.2.a.x	$2057$	$2$	2057.a	1.a	$1$	$5$	$5$	$16.425$	5.5.984016.1	None	✓	$1$	$0$	$2$	$-1$	$1$	$6$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$
2057.2.a.y	$2057$	$2$	2057.a	1.a	$1$	$5$	$5$	$16.425$	5.5.475929.1	None	✓	$1$	$0$	$3$	$-4$	$-1$	$9$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}+(-1-\beta _{3})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots$
2057.2.a.z	$2057$	$2$	2057.a	1.a	$1$	$7$	$7$	$16.425$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$-2$	$-2$	$-3$	$-13$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}-\beta _{4}q^{3}+(1-\beta _{2}-\beta _{5})q^{4}+\cdots$
2057.2.a.ba	$2057$	$2$	2057.a	1.a	$1$	$7$	$7$	$16.425$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$2$	$-2$	$-3$	$13$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}-\beta _{4}q^{3}+(1-\beta _{2}-\beta _{5})q^{4}+\cdots$
2057.2.a.bb	$2057$	$2$	2057.a	1.a	$1$	$14$	$14$	$16.425$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$1$	$-4$	$0$	$2$	$-18$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots$
2057.2.a.bc	$2057$	$2$	2057.a	1.a	$1$	$14$	$14$	$16.425$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$0$	$4$	$0$	$2$	$18$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots$
2057.2.a.bd	$2057$	$2$	2057.a	1.a	$1$	$18$	$18$	$16.425$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	$1$	$0$	$-2$	$7$	$8$	$3$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{11}q^{3}+(2+\beta _{2})q^{4}-\beta _{12}q^{5}+\cdots$
2057.2.a.be	$2057$	$2$	2057.a	1.a	$1$	$18$	$18$	$16.425$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	$1$	$0$	$2$	$7$	$8$	$-3$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{11}q^{3}+(2+\beta _{2})q^{4}-\beta _{12}q^{5}+\cdots$
2057.4.a.a	$2057$	$4$	2057.a	1.a	$1$	$1$	$1$	$121.367$	$\Q$	None	✓	$1$	$1$	$-1$	$4$	$6$	$24$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+4q^{3}-7q^{4}+6q^{5}-4q^{6}+\cdots$
2057.4.a.b	$2057$	$4$	2057.a	1.a	$1$	$1$	$1$	$121.367$	$\Q$	None	✓	$1$	$1$	$-1$	$4$	$17$	$-9$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+4q^{3}-7q^{4}+17q^{5}-4q^{6}+\cdots$
2057.4.a.c	$2057$	$4$	2057.a	1.a	$1$	$1$	$1$	$121.367$	$\Q$	None	✓	$1$	$0$	$1$	$4$	$17$	$9$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+4q^{3}-7q^{4}+17q^{5}+4q^{6}+\cdots$
2057.4.a.d	$2057$	$4$	2057.a	1.a	$1$	$1$	$1$	$121.367$	$\Q$	None	✓	$1$	$1$	$3$	$-8$	$6$	$28$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{2}-8q^{3}+q^{4}+6q^{5}-24q^{6}+\cdots$
2057.4.a.e	$2057$	$4$	2057.a	1.a	$1$	$3$	$3$	$121.367$	3.3.2636.1	None	✓	$1$	$0$	$-1$	$4$	$-8$	$-22$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}+\beta _{2})q^{2}+(2-\beta _{1}+2\beta _{2})q^{3}+\cdots$
2057.4.a.f	$2057$	$4$	2057.a	1.a	$1$	$3$	$3$	$121.367$	3.3.138385.1	None	✓	$1$	$1$	$9$	$1$	$-19$	$-9$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{2}+\beta _{1}q^{3}+q^{4}+(-6-\beta _{2})q^{5}+\cdots$
2057.4.a.g	$2057$	$4$	2057.a	1.a	$1$	$4$	$4$	$121.367$	4.4.22000.1	None	✓	$1$	$1$	$-2$	$-6$	$-10$	$-16$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{2})q^{2}+(-1+\beta _{2}+\beta _{3})q^{3}+\cdots$
2057.4.a.h	$2057$	$4$	2057.a	1.a	$1$	$10$	$10$	$121.367$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$-4$	$11$	$47$	$17$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{1}-\beta _{5})q^{3}+(4+\beta _{1}+\cdots)q^{4}+\cdots$
2057.4.a.i	$2057$	$4$	2057.a	1.a	$1$	$10$	$10$	$121.367$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$8$	$-9$	$-41$	$63$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(-1+\beta _{7})q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots$
2057.4.a.j	$2057$	$4$	2057.a	1.a	$1$	$12$	$12$	$121.367$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$-10$	$3$	$29$	$-39$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-\beta _{5}q^{3}+(5-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
2057.4.a.k	$2057$	$4$	2057.a	1.a	$1$	$19$	$19$	$121.367$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	None	✓	$1$	$1$	$-3$	$4$	$-11$	$-59$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{8}q^{3}+(5+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
2057.4.a.l	$2057$	$4$	2057.a	1.a	$1$	$19$	$19$	$121.367$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	None	✓	$1$	$0$	$3$	$4$	$-11$	$59$	$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{8}q^{3}+(5+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
2057.4.a.m	$2057$	$4$	2057.a	1.a	$1$	$20$	$20$	$121.367$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓	$1$	$1$	$-4$	$2$	$-14$	$-80$	$+$	$-$	$-$	$2^{4}\cdot 3$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{7})q^{3}+(4+\beta _{2})q^{4}+\cdots$
2057.4.a.n	$2057$	$4$	2057.a	1.a	$1$	$20$	$20$	$121.367$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓	$1$	$1$	$-4$	$8$	$6$	$-52$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{7}q^{3}+(4+\beta _{2})q^{4}-\beta _{14}q^{5}+\cdots$
2057.4.a.o	$2057$	$4$	2057.a	1.a	$1$	$20$	$20$	$121.367$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓	$1$	$0$	$4$	$2$	$-14$	$80$	$+$	$+$	$+$	$2^{4}\cdot 3$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{7})q^{3}+(4+\beta _{2})q^{4}+\cdots$
2057.4.a.p	$2057$	$4$	2057.a	1.a	$1$	$20$	$20$	$121.367$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓	$1$	$0$	$4$	$8$	$6$	$52$	$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{7}q^{3}+(4+\beta _{2})q^{4}-\beta _{14}q^{5}+\cdots$
2057.4.a.q	$2057$	$4$	2057.a	1.a	$1$	$40$	$40$	$121.367$		None	✓	$1$	$1$	$-8$	$-8$	$-28$	$-160$	$+$	$-$	$-$		$\mathrm{SU}(2)$
2057.4.a.r	$2057$	$4$	2057.a	1.a	$1$	$40$	$40$	$121.367$		None	✓	$1$	$0$	$8$	$-8$	$-28$	$160$	$+$	$+$	$+$		$\mathrm{SU}(2)$
2057.4.a.s	$2057$	$4$	2057.a	1.a	$1$	$44$	$44$	$121.367$		None	✓	$1$	$1$	$-1$	$-28$	$-24$	$2$	$-$	$+$	$-$		$\mathrm{SU}(2)$

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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.