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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (1-50 of 57 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1682.2.a.a	$1682$	$2$	1682.a	1.a	$1$	$1$	$1$	$13.431$	$\Q$	None	✓	✓			1682.2.a.a	$1$	$1$	$-1$	$-2$	$-2$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}-2q^{5}+2q^{6}-5q^{7}+\cdots$
1682.2.a.b	$1682$	$2$	1682.a	1.a	$1$	$1$	$1$	$13.431$	$\Q$	None	✓	✓			1682.2.a.b	$1$	$0$	$-1$	$-2$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{7}-q^{8}+\cdots$
1682.2.a.c	$1682$	$2$	1682.a	1.a	$1$	$1$	$1$	$13.431$	$\Q$	None	✓				58.2.b.a	$1$	$0$	$-1$	$-1$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots$
1682.2.a.d	$1682$	$2$	1682.a	1.a	$1$	$1$	$1$	$13.431$	$\Q$	None	✓				58.2.a.b	$1$	$1$	$-1$	$1$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots$
1682.2.a.e	$1682$	$2$	1682.a	1.a	$1$	$1$	$1$	$13.431$	$\Q$	None	✓	✓			1682.2.a.e	$1$	$0$	$-1$	$3$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}+q^{4}-3q^{6}+4q^{7}-q^{8}+\cdots$
1682.2.a.f	$1682$	$2$	1682.a	1.a	$1$	$1$	$1$	$13.431$	$\Q$	None	✓	✓			1682.2.a.e	$1$	$0$	$1$	$-3$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}+q^{4}-3q^{6}+4q^{7}+q^{8}+\cdots$
1682.2.a.g	$1682$	$2$	1682.a	1.a	$1$	$1$	$1$	$13.431$	$\Q$	None	✓				58.2.b.a	$1$	$1$	$1$	$1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots$
1682.2.a.h	$1682$	$2$	1682.a	1.a	$1$	$1$	$1$	$13.431$	$\Q$	None	✓	✓			1682.2.a.a	$1$	$1$	$1$	$2$	$-2$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}-2q^{5}+2q^{6}-5q^{7}+\cdots$
1682.2.a.i	$1682$	$2$	1682.a	1.a	$1$	$1$	$1$	$13.431$	$\Q$	None	✓	✓			1682.2.a.b	$1$	$0$	$1$	$2$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+2q^{6}-q^{7}+q^{8}+\cdots$
1682.2.a.j	$1682$	$2$	1682.a	1.a	$1$	$1$	$1$	$13.431$	$\Q$	None	✓				58.2.a.a	$1$	$0$	$1$	$3$	$-3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}+q^{4}-3q^{5}+3q^{6}-2q^{7}+\cdots$
1682.2.a.k	$1682$	$2$	1682.a	1.a	$1$	$2$	$2$	$13.431$	$\Q(\sqrt{5}) $	None	✓	✓			1682.2.a.k	$1$	$0$	$-2$	$-1$	$4$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta q^{3}+q^{4}+2q^{5}+\beta q^{6}+(4+\cdots)q^{7}+\cdots$
1682.2.a.l	$1682$	$2$	1682.a	1.a	$1$	$2$	$2$	$13.431$	$\Q(\sqrt{5}) $	None	✓	✓			1682.2.a.k	$1$	$0$	$2$	$1$	$4$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}+2q^{5}+\beta q^{6}+(4+\cdots)q^{7}+\cdots$
1682.2.a.m	$1682$	$2$	1682.a	1.a	$1$	$3$	$3$	$13.431$	$\Q(\zeta_{14})^+$	None	✓				58.2.d.a	$1$	$1$	$-3$	$-2$	$5$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$
1682.2.a.n	$1682$	$2$	1682.a	1.a	$1$	$3$	$3$	$13.431$	$\Q(\zeta_{14})^+$	None	✓				58.2.d.a	$1$	$0$	$3$	$2$	$5$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(2+\beta _{2})q^{5}+\cdots$
1682.2.a.o	$1682$	$2$	1682.a	1.a	$1$	$4$	$4$	$13.431$	$\Q(\zeta_{15})^+$	None	✓	✓			1682.2.a.o	$1$	$1$	$-4$	$2$	$-3$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots$
1682.2.a.p	$1682$	$2$	1682.a	1.a	$1$	$4$	$4$	$13.431$	$\Q(\zeta_{15})^+$	None	✓	✓			1682.2.a.o	$1$	$1$	$4$	$-2$	$-3$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots$
1682.2.a.q	$1682$	$2$	1682.a	1.a	$1$	$6$	$6$	$13.431$	6.6.13716913.1	None	✓		✓		58.2.d.b	$1$	$1$	$-6$	$-2$	$0$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
1682.2.a.r	$1682$	$2$	1682.a	1.a	$1$	$6$	$6$	$13.431$	$\Q(\zeta_{28})^+$	None	✓				58.2.e.a	$1$	$0$	$-6$	$8$	$-6$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1+\beta _{4})q^{3}+q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots$
1682.2.a.s	$1682$	$2$	1682.a	1.a	$1$	$6$	$6$	$13.431$	$\Q(\zeta_{28})^+$	None	✓		✓		58.2.e.a	$1$	$1$	$6$	$-8$	$-6$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-2+\beta _{2}+\beta _{4})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots$
1682.2.a.t	$1682$	$2$	1682.a	1.a	$1$	$6$	$6$	$13.431$	6.6.13716913.1	None	✓				58.2.d.b	$1$	$0$	$6$	$2$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
1682.2.a.u	$1682$	$2$	1682.a	1.a	$1$	$8$	$8$	$13.431$	8.8.$\cdots$.1	None	✓	✓	✓		1682.2.a.u	$1$	$0$	$-8$	$-1$	$5$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+(1-\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots$
1682.2.a.v	$1682$	$2$	1682.a	1.a	$1$	$8$	$8$	$13.431$	8.8.$\cdots$.1	None	✓	✓	✓		1682.2.a.u	$1$	$0$	$8$	$1$	$5$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots$
1682.2.b.a	$1682$	$2$	1682.b	29.b	$2$	$2$	$2$	$13.431$	$\Q(\sqrt{-1}) $	None					58.2.a.b	$2$	$0$	$0$	$0$	$-2$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}+i q^{3}-q^{4}-q^{5}+q^{6}+\cdots$
1682.2.b.b	$1682$	$2$	1682.b	29.b	$2$	$2$	$2$	$13.431$	$\Q(\sqrt{-1}) $	None		✓			1682.2.a.b	$2$	$0$	$0$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+2 i q^{3}-q^{4}-2 q^{6}-q^{7}+\cdots$
1682.2.b.c	$1682$	$2$	1682.b	29.b	$2$	$2$	$2$	$13.431$	$\Q(\sqrt{-1}) $	None		✓			1682.2.a.e	$2$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}+3 i q^{3}-q^{4}+3 q^{6}+4 q^{7}+\cdots$
1682.2.b.d	$1682$	$2$	1682.b	29.b	$2$	$2$	$2$	$13.431$	$\Q(\sqrt{-1}) $	None		✓			1682.2.a.a	$2$	$0$	$0$	$0$	$4$	$-10$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+2 i q^{3}-q^{4}+2 q^{5}-2 q^{6}+\cdots$
1682.2.b.e	$1682$	$2$	1682.b	29.b	$2$	$2$	$2$	$13.431$	$\Q(\sqrt{-1}) $	None					58.2.a.a	$2$	$0$	$0$	$0$	$6$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+3 i q^{3}-q^{4}+3 q^{5}-3 q^{6}+\cdots$
1682.2.b.f	$1682$	$2$	1682.b	29.b	$2$	$4$	$4$	$13.431$	$\Q(i, \sqrt{5})$	None		✓			1682.2.a.k	$2$	$0$	$0$	$0$	$-8$	$12$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+\beta _{1}q^{3}-q^{4}-2q^{5}+\beta _{2}q^{6}+\cdots$
1682.2.b.g	$1682$	$2$	1682.b	29.b	$2$	$6$	$6$	$13.431$	6.0.153664.1	None					58.2.d.a	$2$	$0$	$0$	$0$	$-10$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+(\beta _{3}+\beta _{5})q^{3}-q^{4}+(-2+\cdots)q^{5}+\cdots$
1682.2.b.h	$1682$	$2$	1682.b	29.b	$2$	$8$	$8$	$13.431$	8.0.324000000.1	None		✓			1682.2.a.o	$2$	$0$	$0$	$0$	$6$	$-10$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+(\beta _{1}+\beta _{3}+\beta _{5}+\beta _{7})q^{3}+\cdots$
1682.2.b.i	$1682$	$2$	1682.b	29.b	$2$	$12$	$12$	$13.431$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None					58.2.d.b	$2$	$0$	$0$	$0$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{2}+\beta _{1}q^{3}-q^{4}+(\beta _{4}+\beta _{11})q^{5}+\cdots$
1682.2.b.j	$1682$	$2$	1682.b	29.b	$2$	$12$	$12$	$13.431$	$\Q(\zeta_{28})$	None					58.2.e.a	$2$	$0$	$0$	$0$	$12$	$4$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_1 q^{2}+(-\beta_{3}-\beta_1)q^{3}-q^{4}+\cdots$
1682.2.b.k	$1682$	$2$	1682.b	29.b	$2$	$16$	$16$	$13.431$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓	✓		1682.2.a.u	$2$	$0$	$0$	$0$	$-10$	$14$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{13}q^{2}+\beta _{1}q^{3}-q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots$
1682.4.a.a	$1682$	$4$	1682.a	1.a	$1$	$1$	$1$	$99.241$	$\Q$	None	✓				58.4.a.b	$1$	$0$	$-2$	$7$	$-15$	$-18$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+7q^{3}+4q^{4}-15q^{5}-14q^{6}+\cdots$
1682.4.a.b	$1682$	$4$	1682.a	1.a	$1$	$1$	$1$	$99.241$	$\Q$	None	✓				58.4.a.a	$1$	$1$	$2$	$-7$	$5$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-7q^{3}+4q^{4}+5q^{5}-14q^{6}+\cdots$
1682.4.a.c	$1682$	$4$	1682.a	1.a	$1$	$2$	$2$	$99.241$	$\Q(\sqrt{6}) $	None	✓				58.4.a.c	$1$	$1$	$4$	$2$	$-10$	$-16$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(1+\beta )q^{3}+4q^{4}+(-5+6\beta )q^{5}+\cdots$
1682.4.a.d	$1682$	$4$	1682.a	1.a	$1$	$3$	$3$	$99.241$	3.3.19816.1	None	✓				58.4.a.d	$1$	$0$	$-6$	$-2$	$20$	$24$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+(6+2\beta _{1}+\cdots)q^{5}+\cdots$
1682.4.a.e	$1682$	$4$	1682.a	1.a	$1$	$3$	$3$	$99.241$	3.3.6549.1	None	✓	✓			1682.4.a.e	$1$	$1$	$-6$	$-1$	$-17$	$15$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+\beta _{2}q^{3}+4q^{4}+(-4-4\beta _{1}+\cdots)q^{5}+\cdots$
1682.4.a.f	$1682$	$4$	1682.a	1.a	$1$	$3$	$3$	$99.241$	3.3.6549.1	None	✓	✓			1682.4.a.e	$1$	$1$	$6$	$1$	$-17$	$15$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-\beta _{2}q^{3}+4q^{4}+(-4-4\beta _{1}+\cdots)q^{5}+\cdots$
1682.4.a.g	$1682$	$4$	1682.a	1.a	$1$	$4$	$4$	$99.241$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	✓			1682.4.a.g	$1$	$0$	$-8$	$-4$	$-7$	$39$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+(-2+\cdots)q^{5}+\cdots$
1682.4.a.h	$1682$	$4$	1682.a	1.a	$1$	$4$	$4$	$99.241$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓				58.4.b.a	$1$	$1$	$-8$	$-1$	$11$	$6$	$-$	$2$	$\mathrm{SU}(2)$	$q-2q^{2}-\beta _{1}q^{3}+4q^{4}+(3+\beta _{2})q^{5}+\cdots$
1682.4.a.i	$1682$	$4$	1682.a	1.a	$1$	$4$	$4$	$99.241$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓				58.4.b.a	$1$	$0$	$8$	$1$	$11$	$6$	$+$	$2$	$\mathrm{SU}(2)$	$q+2q^{2}+\beta _{1}q^{3}+4q^{4}+(3+\beta _{2})q^{5}+\cdots$
1682.4.a.j	$1682$	$4$	1682.a	1.a	$1$	$4$	$4$	$99.241$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	✓			1682.4.a.g	$1$	$0$	$8$	$4$	$-7$	$39$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(-2-\beta _{1}+\cdots)q^{5}+\cdots$
1682.4.a.k	$1682$	$4$	1682.a	1.a	$1$	$6$	$6$	$99.241$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	✓			1682.4.a.k	$1$	$1$	$-12$	$-10$	$-10$	$-26$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(-2+\beta _{5})q^{3}+4q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
1682.4.a.l	$1682$	$4$	1682.a	1.a	$1$	$6$	$6$	$99.241$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	✓			1682.4.a.k	$1$	$1$	$12$	$10$	$-10$	$-26$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(2-\beta _{5})q^{3}+4q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
1682.4.a.m	$1682$	$4$	1682.a	1.a	$1$	$8$	$8$	$99.241$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓			1682.4.a.m	$1$	$0$	$-16$	$5$	$10$	$32$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(\beta _{1}-\beta _{2})q^{3}+4q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
1682.4.a.n	$1682$	$4$	1682.a	1.a	$1$	$8$	$8$	$99.241$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓			1682.4.a.m	$1$	$0$	$16$	$-5$	$10$	$32$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-\beta _{1}+\beta _{2})q^{3}+4q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
1682.4.a.o	$1682$	$4$	1682.a	1.a	$1$	$9$	$9$	$99.241$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓				58.4.d.a	$1$	$0$	$-18$	$8$	$-15$	$9$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q-2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(-1+2\beta _{3}+\cdots)q^{5}+\cdots$
1682.4.a.p	$1682$	$4$	1682.a	1.a	$1$	$9$	$9$	$99.241$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓				58.4.d.a	$1$	$1$	$18$	$-8$	$-15$	$9$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+(-1+\cdots)q^{5}+\cdots$
1682.4.a.q	$1682$	$4$	1682.a	1.a	$1$	$12$	$12$	$99.241$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓				58.4.d.b	$1$	$0$	$-24$	$8$	$-20$	$-3$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q-2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots$

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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.