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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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
103.1.b.a	$103$	$1$	103.b	103.b	$2$	$2$	$2$	$0.051$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-103}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{7}-q^{8}+\cdots$
721.1.p.a	$721$	$1$	721.p	721.p	$6$	$2$	$1$	$0.360$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$1$	$0$	$0$	$-1$	$1$		$q+\zeta_{6}q^{2}-\zeta_{6}q^{7}+q^{8}-\zeta_{6}q^{9}+q^{13}+\cdots$
721.1.p.b	$721$	$1$	721.p	721.p	$6$	$8$	$4$	$0.360$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$-1$	$0$	$0$	$1$	$1$		$q+(\zeta_{30}^{8}+\zeta_{30}^{12})q^{2}+(-\zeta_{30}-\zeta_{30}^{5}+\cdots)q^{4}+\cdots$
824.1.h.a	$824$	$1$	824.h	824.h	$2$	$1$	$1$	$0.411$	$\Q$	$D_{2}$	$\Q(\sqrt{-103}) $, $\Q(\sqrt{-206}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$-1$	$0$	$0$	$2$	$1$		$q-q^{2}+q^{4}+2q^{7}-q^{8}-q^{9}-2q^{14}+\cdots$
824.1.h.e	$824$	$1$	824.h	824.h	$2$	$4$	$4$	$0.411$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$1$	$0$	$0$	$-2$	$1$		$q+\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+(\zeta_{10}^{2}-\zeta_{10}^{3}+\cdots)q^{7}+\cdots$
927.1.d.a	$927$	$1$	927.d	103.b	$2$	$1$	$1$	$0.463$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-103}) $	$\Q(\sqrt{309}) $	✓	$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q-q^{4}+2q^{7}-2q^{13}+q^{16}+2q^{19}+\cdots$
927.1.d.b	$927$	$1$	927.d	103.b	$2$	$2$	$2$	$0.463$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-103}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$-1$	$1$		$q+(1-\beta )q^{2}+(1-\beta )q^{4}-\beta q^{7}+q^{8}+\cdots$
927.1.d.c	$927$	$1$	927.d	103.b	$2$	$4$	$4$	$0.463$	$\Q(\zeta_{20})^+$	$D_{10}$	$\Q(\sqrt{-103}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{2})q^{7}+\cdots$
1339.1.b.a	$1339$	$1$	1339.b	1339.b	$2$	$1$	$1$	$0.668$	$\Q$	$D_{2}$	$\Q(\sqrt{-103}) $, $\Q(\sqrt{-1339}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}+q^{9}+q^{13}+q^{16}-2q^{17}+\cdots$
1339.1.b.c	$1339$	$1$	1339.b	1339.b	$2$	$4$	$4$	$0.668$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{10}+\zeta_{10}^{4})q^{2}+(-1+\zeta_{10}^{2}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots$
1339.1.n.a	$1339$	$1$	1339.n	1339.n	$6$	$2$	$1$	$0.668$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$-2$	$0$	$0$	$1$	$1$		$q-\zeta_{6}q^{2}+3\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{7}-2q^{8}+\cdots$
1339.1.n.c	$1339$	$1$	1339.n	1339.n	$6$	$8$	$4$	$0.668$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$2$	$0$	$0$	$-1$	$1$		$q+(-\zeta_{30}^{7}-\zeta_{30}^{13})q^{2}+(-\zeta_{30}^{5}+\cdots)q^{4}+\cdots$
1339.1.t.a	$1339$	$1$	1339.t	1339.t	$6$	$2$	$1$	$0.668$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$0$	$0$	$0$	$-3$	$1$		$q-\zeta_{6}q^{4}+(-1+\zeta_{6}^{2})q^{7}-\zeta_{6}q^{9}+\cdots$
1339.1.t.b	$1339$	$1$	1339.t	1339.t	$6$	$8$	$4$	$0.668$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$0$	$0$	$0$	$3$	$1$		$q+(-\zeta_{30}^{2}+\zeta_{30}^{8})q^{2}+(-\zeta_{30}+\zeta_{30}^{4}+\cdots)q^{4}+\cdots$
1648.1.c.a	$1648$	$1$	1648.c	103.b	$2$	$2$	$2$	$0.822$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-103}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$1$	$1$		$q+(1-\beta )q^{7}+q^{9}-\beta q^{13}+(-1+\beta )q^{17}+\cdots$
1648.1.j.a	$1648$	$1$	1648.j	1648.j	$4$	$2$	$1$	$0.822$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{2}-q^{4}-iq^{8}-iq^{9}+(-1+i+\cdots)q^{13}+\cdots$
1648.1.j.b	$1648$	$1$	1648.j	1648.j	$4$	$8$	$4$	$0.822$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{20}^{3}q^{2}+\zeta_{20}^{6}q^{4}+(-\zeta_{20}^{4}-\zeta_{20}^{6}+\cdots)q^{7}+\cdots$
1751.1.d.c	$1751$	$1$	1751.d	1751.d	$2$	$1$	$1$	$0.874$	$\Q$	$D_{2}$	$\Q(\sqrt{-103}) $, $\Q(\sqrt{-1751}) $	$\Q(\sqrt{17}) $	✓	$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+2q^{2}+3q^{4}+4q^{8}-q^{9}-2q^{13}+\cdots$
1751.1.d.f	$1751$	$1$	1751.d	1751.d	$2$	$4$	$4$	$0.874$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q+(\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(1-\zeta_{10}+\zeta_{10}^{4}+\cdots)q^{4}+\cdots$
1751.1.f.a	$1751$	$1$	1751.f	1751.f	$4$	$2$	$1$	$0.874$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+q^{4}+(-1-i)q^{7}-iq^{9}+q^{16}+\cdots$
1751.1.f.b	$1751$	$1$	1751.f	1751.f	$4$	$8$	$4$	$0.874$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+(\zeta_{20}^{2}+\zeta_{20}^{8})q^{2}+(-1+\zeta_{20}^{4}+\cdots)q^{4}+\cdots$
1751.1.l.a	$1751$	$1$	1751.l	1751.l	$8$	$4$	$1$	$0.874$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$-4$	$0$	$0$	$0$	$1$		$q+(-1-\zeta_{8}^{2})q^{2}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}^{2}+\cdots)q^{7}+\cdots$
1751.1.l.b	$1751$	$1$	1751.l	1751.l	$8$	$16$	$4$	$0.874$	$\Q(\zeta_{40})$	$D_{40}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$4$	$0$	$0$	$0$	$1$		$q+(\zeta_{40}^{12}+\zeta_{40}^{18})q^{2}+(-\zeta_{40}^{4}-\zeta_{40}^{10}+\cdots)q^{4}+\cdots$
1957.1.m.a	$1957$	$1$	1957.m	1957.m	$6$	$2$	$1$	$0.977$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$1$	$0$	$0$	$-2$	$1$		$q+\zeta_{6}q^{2}-q^{7}+q^{8}+\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{13}+\cdots$
1957.1.m.d	$1957$	$1$	1957.m	1957.m	$6$	$8$	$4$	$0.977$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$-1$	$0$	$0$	$2$	$1$		$q+(\zeta_{30}^{8}+\zeta_{30}^{12})q^{2}+(-\zeta_{30}-\zeta_{30}^{5}+\cdots)q^{4}+\cdots$
1957.1.z.a	$1957$	$1$	1957.z	1957.z	$18$	$6$	$1$	$0.977$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$6$	$0$	$0$	$0$	$1$		$q+(1+\zeta_{18}^{2})q^{2}+(1+\zeta_{18}^{2}+\zeta_{18}^{4}+\cdots)q^{4}+\cdots$
1957.1.z.b	$1957$	$1$	1957.z	1957.z	$18$	$24$	$4$	$0.977$	$\Q(\zeta_{45})$	$D_{45}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$-6$	$0$	$0$	$0$	$1$		$q+(\zeta_{90}^{2}+\zeta_{90}^{18})q^{2}+(\zeta_{90}^{4}+\zeta_{90}^{20}+\cdots)q^{4}+\cdots$
2369.1.m.a	$2369$	$1$	2369.m	2369.m	$22$	$10$	$1$	$1.182$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$-2$	$0$	$0$	$-2$	$1$		$q+(-\zeta_{22}^{5}-\zeta_{22}^{9})q^{2}+(-\zeta_{22}^{3}-\zeta_{22}^{7}+\cdots)q^{4}+\cdots$
2369.1.m.b	$2369$	$1$	2369.m	2369.m	$22$	$40$	$4$	$1.182$	$\Q(\zeta_{55})$	$D_{55}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$2$	$0$	$0$	$2$	$1$		$q+(-\zeta_{110}+\zeta_{110}^{4})q^{2}+(\zeta_{110}^{2}-\zeta_{110}^{5}+\cdots)q^{4}+\cdots$
2575.1.c.a	$2575$	$1$	2575.c	515.c	$2$	$2$	$2$	$1.285$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-3q^{4}+iq^{7}+4iq^{8}-q^{9}+\cdots$
2575.1.c.b	$2575$	$1$	2575.c	515.c	$2$	$4$	$4$	$1.285$	$\Q(i, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\beta _{1}+\beta _{3})q^{2}+(-1-\beta _{2})q^{4}-\beta _{1}q^{7}+\cdots$
2575.1.c.c	$2575$	$1$	2575.c	515.c	$2$	$8$	$8$	$1.285$	8.0.324000000.1	$D_{15}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\beta _{3}q^{2}+(-1+\beta _{6})q^{4}+(\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots$
2575.1.d.a	$2575$	$1$	2575.d	103.b	$2$	$1$	$1$	$1.285$	$\Q$	$D_{3}$	$\Q(\sqrt{-103}) $	None	✓	$2$	$0$	$-2$	$0$	$0$	$1$	$1$		$q-2q^{2}+3q^{4}+q^{7}-4q^{8}+q^{9}+q^{13}+\cdots$
2575.1.d.b	$2575$	$1$	2575.d	103.b	$2$	$1$	$1$	$1.285$	$\Q$	$D_{3}$	$\Q(\sqrt{-103}) $	None	✓	$2$	$0$	$2$	$0$	$0$	$-1$	$1$		$q+2q^{2}+3q^{4}-q^{7}+4q^{8}+q^{9}-q^{13}+\cdots$
2575.1.d.d	$2575$	$1$	2575.d	103.b	$2$	$2$	$2$	$1.285$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-103}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$1$	$1$		$q+\beta q^{2}+\beta q^{4}+(1-\beta )q^{7}+q^{8}+q^{9}+\cdots$
2575.1.d.e	$2575$	$1$	2575.d	103.b	$2$	$4$	$4$	$1.285$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-103}) $	None	✓	$2$	$0$	$-2$	$0$	$0$	$1$	$1$		$q+\beta _{3}q^{2}-\beta _{3}q^{4}+\beta _{1}q^{7}-q^{8}+q^{9}+\cdots$
2575.1.d.f	$2575$	$1$	2575.d	103.b	$2$	$4$	$4$	$1.285$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-103}) $	None	✓	$2$	$0$	$2$	$0$	$0$	$-1$	$1$		$q-\beta _{3}q^{2}-\beta _{3}q^{4}-\beta _{1}q^{7}+q^{8}+q^{9}+\cdots$
2884.1.e.a	$2884$	$1$	2884.e	2884.e	$2$	$1$	$1$	$1.439$	$\Q$	$D_{2}$	$\Q(\sqrt{-103}) $, $\Q(\sqrt{-721}) $	$\Q(\sqrt{7}) $	✓	$4$	$0$	$1$	$0$	$0$	$-1$	$1$		$q+q^{2}+q^{4}-q^{7}+q^{8}+q^{9}-q^{14}+\cdots$
2884.1.e.b	$2884$	$1$	2884.e	2884.e	$2$	$1$	$1$	$1.439$	$\Q$	$D_{2}$	$\Q(\sqrt{-103}) $, $\Q(\sqrt{-721}) $	$\Q(\sqrt{7}) $	✓	$4$	$0$	$1$	$0$	$0$	$1$	$1$		$q+q^{2}+q^{4}+q^{7}+q^{8}+q^{9}+q^{14}+\cdots$
2884.1.e.e	$2884$	$1$	2884.e	2884.e	$2$	$4$	$4$	$1.439$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}-\zeta_{10}^{3}q^{7}-\zeta_{10}^{3}q^{8}+\cdots$
2884.1.e.f	$2884$	$1$	2884.e	2884.e	$2$	$4$	$4$	$1.439$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$-1$	$0$	$0$	$1$	$1$		$q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+\zeta_{10}q^{7}+\zeta_{10}^{4}q^{8}+\cdots$
2884.1.bc.a	$2884$	$1$	2884.bc	2884.ac	$6$	$2$	$1$	$1.439$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$-1$	$0$	$0$	$1$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{7}+q^{8}-\zeta_{6}q^{9}+\cdots$
2884.1.bc.b	$2884$	$1$	2884.bc	2884.ac	$6$	$2$	$1$	$1.439$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$2$	$0$	$0$	$-1$	$1$		$q+q^{2}+q^{4}-\zeta_{6}q^{7}+q^{8}-\zeta_{6}q^{9}+\cdots$
2884.1.bc.c	$2884$	$1$	2884.bc	2884.ac	$6$	$8$	$4$	$1.439$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$-2$	$0$	$0$	$1$	$1$		$q+\zeta_{30}^{12}q^{2}-\zeta_{30}^{9}q^{4}-\zeta_{30}q^{7}+\cdots$
2884.1.bc.d	$2884$	$1$	2884.bc	2884.ac	$6$	$8$	$4$	$1.439$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$1$	$0$	$0$	$-1$	$1$		$q-\zeta_{30}^{11}q^{2}-\zeta_{30}^{7}q^{4}+\zeta_{30}^{7}q^{7}+\cdots$
2987.1.c.a	$2987$	$1$	2987.c	2987.c	$2$	$1$	$1$	$1.491$	$\Q$	$D_{2}$	$\Q(\sqrt{-103}) $, $\Q(\sqrt{-2987}) $	$\Q(\sqrt{29}) $	✓	$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+q^{4}-2q^{7}-q^{9}+2q^{13}+q^{16}+\cdots$
2987.1.c.d	$2987$	$1$	2987.c	2987.c	$2$	$4$	$4$	$1.491$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+(\zeta_{10}+\zeta_{10}^{4})q^{2}+(-1+\zeta_{10}^{2}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots$
2987.1.n.a	$2987$	$1$	2987.n	2987.n	$14$	$6$	$1$	$1.491$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$5$	$0$	$0$	$-2$	$1$		$q+(1-\zeta_{14}^{5})q^{2}+(1-\zeta_{14}^{3}-\zeta_{14}^{5}+\cdots)q^{4}+\cdots$
2987.1.n.b	$2987$	$1$	2987.n	2987.n	$14$	$24$	$4$	$1.491$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$-5$	$0$	$0$	$2$	$1$		$q+(-\zeta_{70}^{3}-\zeta_{70}^{7})q^{2}+(\zeta_{70}^{6}+\zeta_{70}^{10}+\cdots)q^{4}+\cdots$
2987.1.o.a	$2987$	$1$	2987.o	2987.o	$14$	$6$	$1$	$1.491$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$-7$	$0$	$0$	$2$	$1$		$q+(-1+\zeta_{14}^{2})q^{2}+(1-\zeta_{14}^{2}+\zeta_{14}^{4}+\cdots)q^{4}+\cdots$

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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.