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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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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	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	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1352.1.g.a	$1352$	$1$	1352.g	8.d	$2$	$2$	$2$	$0.675$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-26}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-iq^{2}-q^{3}-q^{4}+iq^{5}+iq^{6}-iq^{7}+\cdots$
1352.1.g.b	$1352$	$1$	1352.g	8.d	$2$	$3$	$3$	$0.675$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-2}) $	None	✓	$2$	$0$	$-3$	$-1$	$0$	$0$		$1$		$q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}-q^{8}+\cdots$
1352.1.g.c	$1352$	$1$	1352.g	8.d	$2$	$3$	$3$	$0.675$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-2}) $	None	✓	$2$	$0$	$3$	$-1$	$0$	$0$		$1$		$q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+q^{8}+\cdots$
1352.1.h.a	$1352$	$1$	1352.h	104.h	$2$	$6$	$6$	$0.675$	6.0.153664.1	$D_{7}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+\beta _{5}q^{2}-\beta _{4}q^{3}-q^{4}-\beta _{1}q^{6}-\beta _{5}q^{8}+\cdots$
1352.1.n.a	$1352$	$1$	1352.n	104.n	$6$	$4$	$2$	$0.675$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-26}) $	None		$8$	$0$	$0$	$2$	$0$	$0$		$1$		$q-\zeta_{12}q^{2}-\zeta_{12}^{4}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}+\cdots$
1352.1.n.b	$1352$	$1$	1352.n	104.n	$6$	$6$	$3$	$0.675$	6.0.64827.1	$D_{7}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-3$	$1$	$0$	$0$		$1$		$q-\beta _{5}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{3}+\cdots$
1352.1.n.c	$1352$	$1$	1352.n	104.n	$6$	$6$	$3$	$0.675$	6.0.64827.1	$D_{7}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$3$	$1$	$0$	$0$		$1$		$q+\beta _{5}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{3}+\cdots$
1352.1.p.a	$1352$	$1$	1352.p	104.p	$6$	$2$	$1$	$0.675$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-26}) $	None		$4$	$0$	$-1$	$1$	$-2$	$1$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-q^{5}-\zeta_{6}^{2}q^{6}+\cdots$
1352.1.p.b	$1352$	$1$	1352.p	104.p	$6$	$2$	$1$	$0.675$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-26}) $	None		$4$	$0$	$1$	$1$	$2$	$-1$		$1$		$q+\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+\zeta_{6}^{2}q^{6}+\cdots$
1352.1.p.c	$1352$	$1$	1352.p	104.p	$6$	$12$	$6$	$0.675$	12.0.$\cdots$.1	$D_{7}$	$\Q(\sqrt{-2}) $	None		$8$	$0$	$0$	$2$	$0$	$0$		$1$		$q-\beta _{6}q^{2}-\beta _{9}q^{3}+\beta _{7}q^{4}+\beta _{11}q^{6}+\cdots$
1352.2.a.a	$1352$	$2$	1352.a	1.a	$1$	$1$	$1$	$10.796$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{7}-2q^{9}-q^{11}-2q^{15}+\cdots$
1352.2.a.b	$1352$	$2$	1352.a	1.a	$1$	$1$	$1$	$10.796$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-5q^{7}-2q^{9}+2q^{11}+\cdots$
1352.2.a.c	$1352$	$2$	1352.a	1.a	$1$	$1$	$1$	$10.796$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}-q^{7}-2q^{9}+q^{11}+2q^{15}+\cdots$
1352.2.a.d	$1352$	$2$	1352.a	1.a	$1$	$2$	$2$	$10.796$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-1$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}-\beta q^{5}+(2+\beta )q^{7}+(1+\beta )q^{9}+\cdots$
1352.2.a.e	$1352$	$2$	1352.a	1.a	$1$	$2$	$2$	$10.796$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+\beta q^{5}+(-2-\beta )q^{7}+(1+\beta )q^{9}+\cdots$
1352.2.a.f	$1352$	$2$	1352.a	1.a	$1$	$2$	$2$	$10.796$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-1-\beta )q^{5}-\beta q^{7}+(1+\beta )q^{9}+\cdots$
1352.2.a.g	$1352$	$2$	1352.a	1.a	$1$	$2$	$2$	$10.796$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-2+\beta )q^{5}+\beta q^{7}+(1+\beta )q^{9}+\cdots$
1352.2.a.h	$1352$	$2$	1352.a	1.a	$1$	$2$	$2$	$10.796$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(1+\beta )q^{5}+\beta q^{7}+(1+\beta )q^{9}+\cdots$
1352.2.a.i	$1352$	$2$	1352.a	1.a	$1$	$3$	$3$	$10.796$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$1$	$0$	$-4$	$-4$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{3}+(-1-\beta _{1})q^{5}-\beta _{1}q^{7}+\cdots$
1352.2.a.j	$1352$	$2$	1352.a	1.a	$1$	$3$	$3$	$10.796$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$1$	$0$	$-4$	$4$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{3}+(1+\beta _{1})q^{5}+\beta _{1}q^{7}+\cdots$
1352.2.a.k	$1352$	$2$	1352.a	1.a	$1$	$4$	$4$	$10.796$	4.4.13968.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-4$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1-\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots$
1352.2.a.l	$1352$	$2$	1352.a	1.a	$1$	$4$	$4$	$10.796$	4.4.13968.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1+\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots$
1352.2.a.m	$1352$	$2$	1352.a	1.a	$1$	$6$	$6$	$10.796$	6.6.3728753.1	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$-2$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1}+\beta _{2}+\beta _{5})q^{3}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$
1352.2.a.n	$1352$	$2$	1352.a	1.a	$1$	$6$	$6$	$10.796$	6.6.3728753.1	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$2$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1}+\beta _{2}+\beta _{5})q^{3}+(\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots$
1352.2.f.a	$1352$	$2$	1352.f	13.b	$2$	$2$	$2$	$10.796$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+2iq^{5}+iq^{7}-2q^{9}-iq^{11}+\cdots$
1352.2.f.b	$1352$	$2$	1352.f	13.b	$2$	$2$	$2$	$10.796$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}-iq^{5}-5iq^{7}-2q^{9}+2iq^{11}+\cdots$
1352.2.f.c	$1352$	$2$	1352.f	13.b	$2$	$4$	$4$	$10.796$	$\Q(i, \sqrt{17})$	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{3})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{1}q^{7}+\cdots$
1352.2.f.d	$1352$	$2$	1352.f	13.b	$2$	$4$	$4$	$10.796$	$\Q(i, \sqrt{17})$	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{3})q^{3}+(\beta _{1}-\beta _{2})q^{5}-\beta _{1}q^{7}+\cdots$
1352.2.f.e	$1352$	$2$	1352.f	13.b	$2$	$6$	$6$	$10.796$	6.0.153664.1	$_{}$	None	None		$2$	$0$	$0$	$-8$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2+\beta _{2}+\beta _{4})q^{3}+(\beta _{3}-\beta _{5})q^{5}+\cdots$
1352.2.f.f	$1352$	$2$	1352.f	13.b	$2$	$8$	$8$	$10.796$	8.0.195105024.2	$_{}$	None	None		$2$	$0$	$0$	$-4$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{1})q^{3}+(\beta _{3}+\beta _{6}-\beta _{7})q^{5}+\cdots$
1352.2.f.g	$1352$	$2$	1352.f	13.b	$2$	$12$	$12$	$10.796$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{4}-\beta _{6})q^{3}+(-\beta _{1}-\beta _{7}-\beta _{8}+\cdots)q^{5}+\cdots$
1352.2.i.a	$1352$	$2$	1352.i	13.c	$3$	$2$	$1$	$10.796$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$0$	$-1$	$-4$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}-2q^{5}-\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots$
1352.2.i.b	$1352$	$2$	1352.i	13.c	$3$	$2$	$1$	$10.796$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$-2$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}-q^{5}-5\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots$
1352.2.i.c	$1352$	$2$	1352.i	13.c	$3$	$2$	$1$	$10.796$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$2$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+q^{5}+5\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots$
1352.2.i.d	$1352$	$2$	1352.i	13.c	$3$	$4$	$2$	$10.796$	$\Q(\sqrt{-3}, \sqrt{17})$	$_{}$	None	None		$2$	$0$	$0$	$-1$	$-6$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}+(-2-\beta _{3})q^{5}+(\beta _{1}+\beta _{3})q^{7}+\cdots$
1352.2.i.e	$1352$	$2$	1352.i	13.c	$3$	$4$	$2$	$10.796$	$\Q(\sqrt{-3}, \sqrt{17})$	$_{}$	None	None		$2$	$0$	$0$	$-1$	$6$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}+(1-\beta _{3})q^{5}+(\beta _{1}+\beta _{3})q^{7}+\cdots$
1352.2.i.f	$1352$	$2$	1352.i	13.c	$3$	$4$	$2$	$10.796$	$\Q(\sqrt{-3}, \sqrt{17})$	$_{}$	None	None		$2$	$0$	$0$	$-1$	$6$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}+(2+\beta _{3})q^{5}+(-\beta _{1}-\beta _{3})q^{7}+\cdots$
1352.2.i.g	$1352$	$2$	1352.i	13.c	$3$	$4$	$2$	$10.796$	$\Q(\sqrt{-3}, \sqrt{17})$	$_{}$	None	None		$2$	$0$	$0$	$1$	$-2$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{3}+\beta _{3}q^{5}+(-2+\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots$
1352.2.i.h	$1352$	$2$	1352.i	13.c	$3$	$4$	$2$	$10.796$	$\Q(\sqrt{-3}, \sqrt{17})$	$_{}$	None	None		$2$	$0$	$0$	$1$	$2$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{3}-\beta _{3}q^{5}+(2-\beta _{1}-2\beta _{2}-\beta _{3})q^{7}+\cdots$
1352.2.i.i	$1352$	$2$	1352.i	13.c	$3$	$6$	$3$	$10.796$	6.0.64827.1	$_{}$	None	None		$2$	$0$	$0$	$4$	$-8$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{4}-\beta _{5})q^{3}+(-1+\beta _{3})q^{5}+\cdots$
1352.2.i.j	$1352$	$2$	1352.i	13.c	$3$	$6$	$3$	$10.796$	6.0.64827.1	$_{}$	None	None		$2$	$0$	$0$	$4$	$8$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{4}-\beta _{5})q^{3}+(1-\beta _{3})q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots$
1352.2.i.k	$1352$	$2$	1352.i	13.c	$3$	$8$	$4$	$10.796$	8.0.195105024.2	$_{}$	None	None		$2$	$0$	$0$	$2$	$-8$	$4$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(-1-\beta _{2}+\cdots)q^{5}+\cdots$
1352.2.i.l	$1352$	$2$	1352.i	13.c	$3$	$8$	$4$	$10.796$	8.0.195105024.2	$_{}$	None	None		$2$	$0$	$0$	$2$	$8$	$-4$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{5}+\cdots$
1352.2.i.m	$1352$	$2$	1352.i	13.c	$3$	$12$	$6$	$10.796$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-3$	$-4$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{2}+\beta _{7}-\beta _{10})q^{3}+(-\beta _{1}+\cdots)q^{5}+\cdots$
1352.2.i.n	$1352$	$2$	1352.i	13.c	$3$	$12$	$6$	$10.796$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-3$	$4$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{2}+\beta _{7}-\beta _{10})q^{3}+(\beta _{1}+\cdots)q^{5}+\cdots$
1352.2.o.a	$1352$	$2$	1352.o	13.e	$6$	$4$	$2$	$10.796$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\zeta_{12}^{2})q^{3}+\zeta_{12}^{3}q^{5}+(5\zeta_{12}+\cdots)q^{7}+\cdots$
1352.2.o.b	$1352$	$2$	1352.o	13.e	$6$	$4$	$2$	$10.796$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\zeta_{12}^{2})q^{3}-2\zeta_{12}^{3}q^{5}+(-\zeta_{12}+\cdots)q^{7}+\cdots$
1352.2.o.c	$1352$	$2$	1352.o	13.e	$6$	$8$	$4$	$10.796$	8.0.1731891456.1	$_{}$	None	None		$4$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{2}+\beta _{4}-\beta _{5})q^{3}+(\beta _{6}-\beta _{7})q^{5}+\cdots$
1352.2.o.d	$1352$	$2$	1352.o	13.e	$6$	$8$	$4$	$10.796$	8.0.1731891456.1	$_{}$	None	None		$4$	$0$	$0$	$-2$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1-\beta _{3}+\beta _{5})q^{3}+(-\beta _{2}+\beta _{6}+\cdots)q^{5}+\cdots$
1352.2.o.e	$1352$	$2$	1352.o	13.e	$6$	$8$	$4$	$10.796$	8.0.1731891456.1	$_{}$	None	None		$4$	$0$	$0$	$2$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{2}-\beta _{7})q^{3}+(\beta _{1}-\beta _{5})q^{5}+(\beta _{5}+\cdots)q^{7}+\cdots$

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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.