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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
159.1.d.a	$159$	$1$	159.d	159.d	$2$	$2$	$2$	$0.079$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-159}) $	None	✓	$2$	$0$	$-1$	$2$	$-1$	$-1$	$1$		$q+(-1+\beta )q^{2}+q^{3}+(1-\beta )q^{4}-\beta q^{5}+\cdots$
159.1.d.b	$159$	$1$	159.d	159.d	$2$	$2$	$2$	$0.079$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-159}) $	None	✓	$2$	$0$	$1$	$-2$	$1$	$-1$	$1$		$q+(1-\beta )q^{2}-q^{3}+(1-\beta )q^{4}+\beta q^{5}+\cdots$
795.1.b.a	$795$	$1$	795.b	795.b	$2$	$2$	$2$	$0.397$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-159}) $	$\Q(\sqrt{265}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-iq^{3}-3q^{4}-iq^{5}-2q^{6}+\cdots$
795.1.b.b	$795$	$1$	795.b	795.b	$2$	$8$	$8$	$0.397$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-159}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{20}^{3}+\zeta_{20}^{7})q^{2}-\zeta_{20}^{5}q^{3}+(-1+\cdots)q^{4}+\cdots$
1113.1.n.a	$1113$	$1$	1113.n	1113.n	$6$	$2$	$1$	$0.555$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-159}) $	None		$4$	$0$	$-1$	$1$	$-1$	$-1$	$1$		$q-\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{5}-q^{6}+\zeta_{6}^{2}q^{7}+\cdots$
1113.1.n.b	$1113$	$1$	1113.n	1113.n	$6$	$2$	$1$	$0.555$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-159}) $	None		$4$	$0$	$1$	$-1$	$1$	$-1$	$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{5}-q^{6}+\zeta_{6}^{2}q^{7}+\cdots$
1113.1.n.c	$1113$	$1$	1113.n	1113.n	$6$	$8$	$4$	$0.555$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-159}) $	None		$4$	$0$	$-1$	$-4$	$-1$	$1$	$1$		$q+(\zeta_{30}^{8}+\zeta_{30}^{12})q^{2}-\zeta_{30}^{5}q^{3}+(-\zeta_{30}+\cdots)q^{4}+\cdots$
1113.1.n.d	$1113$	$1$	1113.n	1113.n	$6$	$8$	$4$	$0.555$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-159}) $	None		$4$	$0$	$1$	$4$	$1$	$1$	$1$		$q+(-\zeta_{30}^{6}-\zeta_{30}^{14})q^{2}+\zeta_{30}^{5}q^{3}+\cdots$
1272.1.h.e	$1272$	$1$	1272.h	1272.h	$2$	$2$	$2$	$0.635$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-6}) $, $\Q(\sqrt{-159}) $	$\Q(\sqrt{106}) $		$8$	$0$	$0$	$0$	$0$	$4$	$1$		$q-iq^{2}+iq^{3}-q^{4}-iq^{5}+q^{6}+q^{7}+\cdots$
1272.1.h.f	$1272$	$1$	1272.h	1272.h	$2$	$8$	$8$	$0.635$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-159}) $	None		$8$	$0$	$0$	$0$	$0$	$-4$	$1$		$q-\zeta_{20}q^{2}+\zeta_{20}^{5}q^{3}+\zeta_{20}^{2}q^{4}+(\zeta_{20}^{3}+\cdots)q^{5}+\cdots$
1431.1.d.a	$1431$	$1$	1431.d	159.d	$2$	$1$	$1$	$0.714$	$\Q$	$D_{3}$	$\Q(\sqrt{-159}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$2$	$1$		$q-q^{2}-q^{5}+2q^{7}+q^{8}+q^{10}-q^{13}+\cdots$
1431.1.d.b	$1431$	$1$	1431.d	159.d	$2$	$1$	$1$	$0.714$	$\Q$	$D_{3}$	$\Q(\sqrt{-159}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$2$	$1$		$q+q^{2}+q^{5}+2q^{7}-q^{8}+q^{10}-q^{13}+\cdots$
1431.1.d.c	$1431$	$1$	1431.d	159.d	$2$	$4$	$4$	$0.714$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-159}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$-2$	$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots$
1431.1.d.d	$1431$	$1$	1431.d	159.d	$2$	$4$	$4$	$0.714$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-159}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$-2$	$1$		$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots$
1908.1.b.c	$1908$	$1$	1908.b	212.d	$2$	$2$	$2$	$0.952$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-159}) $	$\Q(\sqrt{159}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-q^{4}+iq^{5}+iq^{8}+2q^{10}+\cdots$
1908.1.b.d	$1908$	$1$	1908.b	212.d	$2$	$8$	$8$	$0.952$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-159}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{20}q^{2}+\zeta_{20}^{2}q^{4}+(-\zeta_{20}^{3}-\zeta_{20}^{7}+\cdots)q^{5}+\cdots$
2067.1.c.a	$2067$	$1$	2067.c	2067.c	$2$	$1$	$1$	$1.032$	$\Q$	$D_{2}$	$\Q(\sqrt{-159}) $, $\Q(\sqrt{-2067}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-q^{3}+q^{4}+q^{9}-q^{12}-q^{13}+q^{16}+\cdots$
2067.1.c.b	$2067$	$1$	2067.c	2067.c	$2$	$1$	$1$	$1.032$	$\Q$	$D_{2}$	$\Q(\sqrt{-159}) $, $\Q(\sqrt{-2067}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\cdots$
2067.1.c.c	$2067$	$1$	2067.c	2067.c	$2$	$4$	$4$	$1.032$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-159}) $	None		$4$	$0$	$0$	$-4$	$0$	$0$	$1$		$q+(\zeta_{10}+\zeta_{10}^{4})q^{2}-q^{3}+(-1+\zeta_{10}^{2}+\cdots)q^{4}+\cdots$
2067.1.c.d	$2067$	$1$	2067.c	2067.c	$2$	$4$	$4$	$1.032$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-159}) $	None		$4$	$0$	$0$	$4$	$0$	$0$	$1$		$q+(\zeta_{10}+\zeta_{10}^{4})q^{2}+q^{3}+(-1+\zeta_{10}^{2}+\cdots)q^{4}+\cdots$
2067.1.v.a	$2067$	$1$	2067.v	2067.v	$6$	$2$	$1$	$1.032$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-159}) $	None		$4$	$0$	$-1$	$1$	$2$	$1$	$1$		$q-\zeta_{6}q^{2}+\zeta_{6}q^{3}+q^{5}-\zeta_{6}^{2}q^{6}-\zeta_{6}^{2}q^{7}+\cdots$
2067.1.v.b	$2067$	$1$	2067.v	2067.v	$6$	$2$	$1$	$1.032$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-159}) $	None		$4$	$0$	$1$	$-1$	$-2$	$1$	$1$		$q+\zeta_{6}q^{2}-\zeta_{6}q^{3}-q^{5}-\zeta_{6}^{2}q^{6}-\zeta_{6}^{2}q^{7}+\cdots$
2067.1.v.c	$2067$	$1$	2067.v	2067.v	$6$	$8$	$4$	$1.032$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-159}) $	None		$4$	$0$	$-1$	$-4$	$2$	$-1$	$1$		$q+(\zeta_{30}^{8}+\zeta_{30}^{12})q^{2}+\zeta_{30}^{10}q^{3}+\cdots$
2067.1.v.d	$2067$	$1$	2067.v	2067.v	$6$	$8$	$4$	$1.032$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-159}) $	None		$4$	$0$	$1$	$4$	$-2$	$-1$	$1$		$q+(-\zeta_{30}^{6}-\zeta_{30}^{14})q^{2}-\zeta_{30}^{10}q^{3}+\cdots$
2067.1.ba.a	$2067$	$1$	2067.ba	2067.aa	$6$	$2$	$1$	$1.032$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-159}) $	None		$4$	$0$	$-3$	$1$	$0$	$3$	$1$		$q+(-1+\zeta_{6}^{2})q^{2}+\zeta_{6}q^{3}+(1-\zeta_{6}+\cdots)q^{4}+\cdots$
2067.1.ba.b	$2067$	$1$	2067.ba	2067.aa	$6$	$2$	$1$	$1.032$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-159}) $	None		$4$	$0$	$3$	$-1$	$0$	$3$	$1$		$q+(1-\zeta_{6}^{2})q^{2}-\zeta_{6}q^{3}+(1-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{4}+\cdots$
2067.1.ba.c	$2067$	$1$	2067.ba	2067.aa	$6$	$8$	$4$	$1.032$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-159}) $	None		$4$	$0$	$-3$	$-4$	$0$	$-3$	$1$		$q+(-\zeta_{30}^{8}+\zeta_{30}^{12})q^{2}+\zeta_{30}^{10}q^{3}+\cdots$
2067.1.ba.d	$2067$	$1$	2067.ba	2067.aa	$6$	$8$	$4$	$1.032$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-159}) $	None		$4$	$0$	$3$	$4$	$0$	$-3$	$1$		$q+(-\zeta_{30}^{6}+\zeta_{30}^{14})q^{2}-\zeta_{30}^{10}q^{3}+\cdots$
2385.1.q.a	$2385$	$1$	2385.q	265.i	$4$	$4$	$2$	$1.190$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-159}) $	None		$8$	$0$	$0$	$0$	$0$	$4$	$1$		$q-\zeta_{8}q^{2}+3\zeta_{8}^{2}q^{4}-\zeta_{8}q^{5}+(1-\zeta_{8}^{2}+\cdots)q^{7}+\cdots$
2385.1.q.b	$2385$	$1$	2385.q	265.i	$4$	$16$	$8$	$1.190$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-159}) $	None		$8$	$0$	$0$	$0$	$0$	$-4$	$1$		$q+(-\zeta_{40}^{3}+\zeta_{40}^{7})q^{2}+(\zeta_{40}^{6}-\zeta_{40}^{10}+\cdots)q^{4}+\cdots$
2544.1.o.a	$2544$	$1$	2544.o	159.d	$2$	$2$	$2$	$1.270$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-159}) $	None	✓	$2$	$0$	$0$	$-2$	$-1$	$1$	$1$		$q-q^{3}+(-1+\beta )q^{5}+\beta q^{7}+q^{9}+(-1+\cdots)q^{13}+\cdots$
2544.1.o.b	$2544$	$1$	2544.o	159.d	$2$	$2$	$2$	$1.270$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-159}) $	None	✓	$2$	$0$	$0$	$2$	$1$	$1$	$1$		$q+q^{3}+(1-\beta )q^{5}+\beta q^{7}+q^{9}+(-1+\cdots)q^{13}+\cdots$
2544.1.w.a	$2544$	$1$	2544.w	2544.w	$4$	$4$	$2$	$1.270$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-159}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}q^{3}-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+\cdots$
2544.1.w.b	$2544$	$1$	2544.w	2544.w	$4$	$16$	$8$	$1.270$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-159}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{40}^{11}q^{2}+\zeta_{40}^{5}q^{3}-\zeta_{40}^{2}q^{4}+\cdots$
3180.1.bd.a	$3180$	$1$	3180.bd	3180.ad	$4$	$4$	$2$	$1.587$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-159}) $	None		$8$	$0$	$0$	$0$	$0$	$-4$	$1$		$q+\zeta_{8}q^{2}-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}-\zeta_{8}q^{5}+\cdots$
3180.1.bd.b	$3180$	$1$	3180.bd	3180.ad	$4$	$4$	$2$	$1.587$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-159}) $	None		$8$	$0$	$0$	$0$	$0$	$4$	$1$		$q-\zeta_{8}q^{2}-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}+\cdots$
3180.1.bd.c	$3180$	$1$	3180.bd	3180.ad	$4$	$16$	$8$	$1.587$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-159}) $	None		$8$	$0$	$0$	$0$	$0$	$-4$	$1$		$q+\zeta_{40}^{11}q^{2}-\zeta_{40}^{15}q^{3}-\zeta_{40}^{2}q^{4}+\cdots$
3180.1.bd.d	$3180$	$1$	3180.bd	3180.ad	$4$	$16$	$8$	$1.587$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-159}) $	None		$8$	$0$	$0$	$0$	$0$	$4$	$1$		$q-\zeta_{40}^{11}q^{2}-\zeta_{40}^{15}q^{3}-\zeta_{40}^{2}q^{4}+\cdots$
3339.1.e.b	$3339$	$1$	3339.e	371.c	$2$	$2$	$2$	$1.666$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-159}) $	$\Q(\sqrt{1113}) $		$8$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-iq^{2}-3q^{4}-q^{7}+4iq^{8}+2iq^{14}+\cdots$
3339.1.e.d	$3339$	$1$	3339.e	371.c	$2$	$8$	$8$	$1.666$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-159}) $	None		$8$	$0$	$0$	$0$	$0$	$2$	$1$		$q+(-\zeta_{20}^{3}-\zeta_{20}^{7})q^{2}+(-1-\zeta_{20}^{4}+\cdots)q^{4}+\cdots$
3339.1.bh.b	$3339$	$1$	3339.bh	371.i	$6$	$4$	$2$	$1.666$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-159}) $	None		$8$	$0$	$0$	$0$	$0$	$2$	$1$		$q+\zeta_{12}^{5}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{5}-\zeta_{12}^{4}q^{7}+\cdots$
3339.1.bh.c	$3339$	$1$	3339.bh	371.i	$6$	$16$	$8$	$1.666$	$\Q(\zeta_{60})$	$D_{30}$	$\Q(\sqrt{-159}) $	None		$8$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+(-\zeta_{60}^{13}+\zeta_{60}^{27})q^{2}+(\zeta_{60}^{10}+\cdots)q^{4}+\cdots$
3657.1.o.a	$3657$	$1$	3657.o	3657.o	$22$	$10$	$1$	$1.825$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-159}) $	None		$4$	$0$	$-2$	$-1$	$-2$	$9$	$1$		$q+(\zeta_{22}^{8}-\zeta_{22}^{9})q^{2}+\zeta_{22}^{2}q^{3}+(-\zeta_{22}^{5}+\cdots)q^{4}+\cdots$
3657.1.o.b	$3657$	$1$	3657.o	3657.o	$22$	$10$	$1$	$1.825$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-159}) $	None		$4$	$0$	$2$	$1$	$2$	$9$	$1$		$q+(-\zeta_{22}^{8}+\zeta_{22}^{9})q^{2}-\zeta_{22}^{2}q^{3}+\cdots$
3657.1.o.c	$3657$	$1$	3657.o	3657.o	$22$	$40$	$4$	$1.825$	$\Q(\zeta_{55})$	$D_{55}$	$\Q(\sqrt{-159}) $	None		$4$	$0$	$-2$	$4$	$-2$	$-9$	$1$		$q+(-\zeta_{110}^{14}+\zeta_{110}^{21})q^{2}-\zeta_{110}^{30}q^{3}+\cdots$
3657.1.o.d	$3657$	$1$	3657.o	3657.o	$22$	$40$	$4$	$1.825$	$\Q(\zeta_{55})$	$D_{55}$	$\Q(\sqrt{-159}) $	None		$4$	$0$	$2$	$-4$	$2$	$-9$	$1$		$q+(\zeta_{110}^{14}-\zeta_{110}^{21})q^{2}+\zeta_{110}^{30}q^{3}+\cdots$
3816.1.l.b	$3816$	$1$	3816.l	424.e	$2$	$1$	$1$	$1.904$	$\Q$	$D_{2}$	$\Q(\sqrt{-159}) $, $\Q(\sqrt{-106}) $	$\Q(\sqrt{6}) $	✓	$4$	$0$	$-1$	$0$	$2$	$0$	$1$		$q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}+q^{16}+\cdots$
3816.1.l.c	$3816$	$1$	3816.l	424.e	$2$	$1$	$1$	$1.904$	$\Q$	$D_{2}$	$\Q(\sqrt{-159}) $, $\Q(\sqrt{-106}) $	$\Q(\sqrt{6}) $	✓	$4$	$0$	$1$	$0$	$-2$	$0$	$1$		$q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}+q^{16}+\cdots$
3816.1.l.g	$3816$	$1$	3816.l	424.e	$2$	$4$	$4$	$1.904$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-159}) $	None		$4$	$0$	$-1$	$0$	$2$	$0$	$1$		$q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+(\zeta_{10}-\zeta_{10}^{4}+\cdots)q^{5}+\cdots$
3816.1.l.h	$3816$	$1$	3816.l	424.e	$2$	$4$	$4$	$1.904$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-159}) $	None		$4$	$0$	$1$	$0$	$-2$	$0$	$1$		$q+\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+(\zeta_{10}^{2}-\zeta_{10}^{3}+\cdots)q^{5}+\cdots$

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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.