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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 69 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
1694.2.a.a	$1694$	$2$	1694.a	1.a	$1$	$1$	$1$	$13.527$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots$
1694.2.a.b	$1694$	$2$	1694.a	1.a	$1$	$1$	$1$	$13.527$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}-3q^{9}+\cdots$
1694.2.a.c	$1694$	$2$	1694.a	1.a	$1$	$1$	$1$	$13.527$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-3q^{9}+\cdots$
1694.2.a.d	$1694$	$2$	1694.a	1.a	$1$	$1$	$1$	$13.527$	$\Q$	None	✓	$1$	$0$	$-1$	$3$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}+q^{4}+2q^{5}-3q^{6}-q^{7}+\cdots$
1694.2.a.e	$1694$	$2$	1694.a	1.a	$1$	$1$	$1$	$13.527$	$\Q$	None	✓	$1$	$1$	$1$	$-2$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}-2q^{6}-q^{7}+q^{8}+\cdots$
1694.2.a.f	$1694$	$2$	1694.a	1.a	$1$	$1$	$1$	$13.527$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots$
1694.2.a.g	$1694$	$2$	1694.a	1.a	$1$	$1$	$1$	$13.527$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$-4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-4q^{5}+q^{7}+q^{8}-3q^{9}+\cdots$
1694.2.a.h	$1694$	$2$	1694.a	1.a	$1$	$1$	$1$	$13.527$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-3q^{9}+\cdots$
1694.2.a.i	$1694$	$2$	1694.a	1.a	$1$	$1$	$1$	$13.527$	$\Q$	None	✓	$1$	$0$	$1$	$2$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+2q^{5}+2q^{6}+q^{7}+\cdots$
1694.2.a.j	$1694$	$2$	1694.a	1.a	$1$	$1$	$1$	$13.527$	$\Q$	None	✓	$1$	$0$	$1$	$3$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}+q^{4}+2q^{5}+3q^{6}+q^{7}+\cdots$
1694.2.a.k	$1694$	$2$	1694.a	1.a	$1$	$2$	$2$	$13.527$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$-2$	$-3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots$
1694.2.a.l	$1694$	$2$	1694.a	1.a	$1$	$2$	$2$	$13.527$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$-2$	$2$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+(-1-\beta )q^{3}+q^{4}+(1+\beta )q^{5}+\cdots$
1694.2.a.m	$1694$	$2$	1694.a	1.a	$1$	$2$	$2$	$13.527$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$-1$	$4$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta q^{3}+q^{4}+2q^{5}+\beta q^{6}-q^{7}+\cdots$
1694.2.a.n	$1694$	$2$	1694.a	1.a	$1$	$2$	$2$	$13.527$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$0$	$-3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-2\beta )q^{3}+q^{4}+(-1-\beta )q^{5}+\cdots$
1694.2.a.o	$1694$	$2$	1694.a	1.a	$1$	$2$	$2$	$13.527$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$0$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-2\beta )q^{3}+q^{4}+(-1+\beta )q^{5}+\cdots$
1694.2.a.p	$1694$	$2$	1694.a	1.a	$1$	$2$	$2$	$13.527$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$-2$	$2$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1+\beta )q^{3}+q^{4}+(1+\beta )q^{5}+\cdots$
1694.2.a.q	$1694$	$2$	1694.a	1.a	$1$	$2$	$2$	$13.527$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$-2$	$-3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots$
1694.2.a.r	$1694$	$2$	1694.a	1.a	$1$	$2$	$2$	$13.527$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$2$	$-1$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta q^{3}+q^{4}+2q^{5}-\beta q^{6}+q^{7}+\cdots$
1694.2.a.s	$1694$	$2$	1694.a	1.a	$1$	$2$	$2$	$13.527$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$2$	$0$	$-3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-2\beta )q^{3}+q^{4}+(-1-\beta )q^{5}+\cdots$
1694.2.a.t	$1694$	$2$	1694.a	1.a	$1$	$2$	$2$	$13.527$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$2$	$0$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-2\beta )q^{3}+q^{4}+(-1+\beta )q^{5}+\cdots$
1694.2.a.u	$1694$	$2$	1694.a	1.a	$1$	$2$	$2$	$13.527$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$2$	$2$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta )q^{3}+q^{4}+(1+\beta )q^{5}+\cdots$
1694.2.a.v	$1694$	$2$	1694.a	1.a	$1$	$3$	$3$	$13.527$	3.3.2024.1	None	✓	$1$	$0$	$-3$	$2$	$-1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{1})q^{3}+q^{4}-\beta _{2}q^{5}+(-1+\cdots)q^{6}+\cdots$
1694.2.a.w	$1694$	$2$	1694.a	1.a	$1$	$3$	$3$	$13.527$	3.3.2024.1	None	✓	$1$	$0$	$3$	$2$	$-1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-\beta _{1})q^{3}+q^{4}-\beta _{2}q^{5}+(1+\cdots)q^{6}+\cdots$
1694.2.a.x	$1694$	$2$	1694.a	1.a	$1$	$4$	$4$	$13.527$	4.4.7625.1	None	✓	$1$	$0$	$-4$	$-3$	$-5$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots$
1694.2.a.y	$1694$	$2$	1694.a	1.a	$1$	$4$	$4$	$13.527$	4.4.13824.1	None	✓	$1$	$0$	$-4$	$4$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1+\beta _{1})q^{3}+q^{4}+(1+\beta _{2}-\beta _{3})q^{5}+\cdots$
1694.2.a.z	$1694$	$2$	1694.a	1.a	$1$	$4$	$4$	$13.527$	4.4.7625.1	None	✓	$1$	$1$	$4$	$-3$	$-5$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots$
1694.2.a.ba	$1694$	$2$	1694.a	1.a	$1$	$4$	$4$	$13.527$	4.4.13824.1	None	✓	$1$	$0$	$4$	$4$	$4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta _{1})q^{3}+q^{4}+(1+\beta _{2}-\beta _{3})q^{5}+\cdots$
1694.2.c.a	$1694$	$2$	1694.c	77.b	$2$	$8$	$8$	$13.527$	$\Q(\zeta_{16})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{16}q^{2}+\zeta_{16}^{2}q^{3}-q^{4}+\zeta_{16}^{2}q^{5}+\cdots$
1694.2.c.b	$1694$	$2$	1694.c	77.b	$2$	$32$	$32$	$13.527$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1694.2.c.c	$1694$	$2$	1694.c	77.b	$2$	$32$	$32$	$13.527$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1694.4.a.a	$1694$	$4$	1694.a	1.a	$1$	$1$	$1$	$99.949$	$\Q$	None	✓	$1$	$1$	$-2$	$-10$	$-14$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-10q^{3}+4q^{4}-14q^{5}+20q^{6}+\cdots$
1694.4.a.b	$1694$	$4$	1694.a	1.a	$1$	$1$	$1$	$99.949$	$\Q$	None	✓	$1$	$1$	$-2$	$-2$	$-12$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-2q^{3}+4q^{4}-12q^{5}+4q^{6}+\cdots$
1694.4.a.c	$1694$	$4$	1694.a	1.a	$1$	$1$	$1$	$99.949$	$\Q$	None	✓	$1$	$1$	$-2$	$-2$	$18$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-2q^{3}+4q^{4}+18q^{5}+4q^{6}+\cdots$
1694.4.a.d	$1694$	$4$	1694.a	1.a	$1$	$1$	$1$	$99.949$	$\Q$	None	✓	$1$	$1$	$-2$	$7$	$3$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+7q^{3}+4q^{4}+3q^{5}-14q^{6}+\cdots$
1694.4.a.e	$1694$	$4$	1694.a	1.a	$1$	$1$	$1$	$99.949$	$\Q$	None	✓	$1$	$1$	$2$	$-5$	$-1$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-5q^{3}+4q^{4}-q^{5}-10q^{6}+\cdots$
1694.4.a.f	$1694$	$4$	1694.a	1.a	$1$	$1$	$1$	$99.949$	$\Q$	None	✓	$1$	$1$	$2$	$0$	$2$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}+2q^{5}+7q^{7}+8q^{8}+\cdots$
1694.4.a.g	$1694$	$4$	1694.a	1.a	$1$	$1$	$1$	$99.949$	$\Q$	None	✓	$1$	$1$	$2$	$8$	$-14$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+8q^{3}+4q^{4}-14q^{5}+2^{4}q^{6}+\cdots$
1694.4.a.h	$1694$	$4$	1694.a	1.a	$1$	$2$	$2$	$99.949$	$\Q(\sqrt{57}) $	None	✓	$1$	$0$	$-4$	$-5$	$-17$	$14$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(-2-\beta )q^{3}+4q^{4}+(-10+\cdots)q^{5}+\cdots$
1694.4.a.i	$1694$	$4$	1694.a	1.a	$1$	$2$	$2$	$99.949$	$\Q(\sqrt{133}) $	None	✓	$1$	$1$	$-4$	$-5$	$-2$	$-14$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(-2-\beta )q^{3}+4q^{4}-q^{5}+\cdots$
1694.4.a.j	$1694$	$4$	1694.a	1.a	$1$	$2$	$2$	$99.949$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-4$	$-4$	$-13$	$-14$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(1-6\beta )q^{3}+4q^{4}+(-12+\cdots)q^{5}+\cdots$
1694.4.a.k	$1694$	$4$	1694.a	1.a	$1$	$2$	$2$	$99.949$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-4$	$6$	$2$	$-14$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(2+2\beta )q^{3}+4q^{4}+(6-10\beta )q^{5}+\cdots$
1694.4.a.l	$1694$	$4$	1694.a	1.a	$1$	$2$	$2$	$99.949$	$\Q(\sqrt{137}) $	None	✓	$1$	$0$	$4$	$-5$	$-7$	$-14$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-2-\beta )q^{3}+4q^{4}+(-4+\cdots)q^{5}+\cdots$
1694.4.a.m	$1694$	$4$	1694.a	1.a	$1$	$2$	$2$	$99.949$	$\Q(\sqrt{133}) $	None	✓	$1$	$1$	$4$	$-5$	$-2$	$14$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-2-\beta )q^{3}+4q^{4}-q^{5}+\cdots$
1694.4.a.n	$1694$	$4$	1694.a	1.a	$1$	$2$	$2$	$99.949$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$4$	$-4$	$-13$	$14$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(1-6\beta )q^{3}+4q^{4}+(-12+\cdots)q^{5}+\cdots$
1694.4.a.o	$1694$	$4$	1694.a	1.a	$1$	$2$	$2$	$99.949$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$4$	$6$	$2$	$14$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(2+2\beta )q^{3}+4q^{4}+(6-10\beta )q^{5}+\cdots$
1694.4.a.p	$1694$	$4$	1694.a	1.a	$1$	$2$	$2$	$99.949$	$\Q(\sqrt{37}) $	None	✓	$1$	$0$	$4$	$6$	$26$	$-14$	$+$	$2$	$\mathrm{SU}(2)$	$q+2q^{2}+(3+\beta )q^{3}+4q^{4}+(13-\beta )q^{5}+\cdots$
1694.4.a.q	$1694$	$4$	1694.a	1.a	$1$	$3$	$3$	$99.949$	3.3.27093.1	None	✓	$1$	$1$	$-6$	$-5$	$-5$	$-21$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(-2+\beta _{1})q^{3}+4q^{4}+(-1+\cdots)q^{5}+\cdots$
1694.4.a.r	$1694$	$4$	1694.a	1.a	$1$	$3$	$3$	$99.949$	3.3.46700.1	None	✓	$1$	$1$	$-6$	$-5$	$5$	$21$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(-2+\beta _{1})q^{3}+4q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$
1694.4.a.s	$1694$	$4$	1694.a	1.a	$1$	$3$	$3$	$99.949$	3.3.7636.1	None	✓	$1$	$0$	$-6$	$6$	$26$	$21$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-2q^{2}+(2-\beta _{1})q^{3}+4q^{4}+(9-\beta _{2})q^{5}+\cdots$
1694.4.a.t	$1694$	$4$	1694.a	1.a	$1$	$3$	$3$	$99.949$	3.3.27093.1	None	✓	$1$	$1$	$6$	$-5$	$-5$	$21$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-2+\beta _{1})q^{3}+4q^{4}+(-1+\cdots)q^{5}+\cdots$

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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.