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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
2001.1.i.c	$2001$	$1$	2001.i	2001.i	$4$	$4$	$2$	$0.999$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q+(\zeta_{12}^{4}+\zeta_{12}^{5})q^{2}-\zeta_{12}^{5}q^{3}+(-\zeta_{12}^{2}+\cdots)q^{4}+\cdots$
2001.1.i.d	$2001$	$1$	2001.i	2001.i	$4$	$4$	$2$	$0.999$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$2$	$-2$	$0$	$0$	$1$		$q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}-\zeta_{12}^{2}q^{3}+(\zeta_{12}^{2}+\cdots)q^{4}+\cdots$
2008.1.j.a	$2008$	$1$	2008.j	2008.j	$10$	$4$	$1$	$1.002$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$4$	$-2$	$0$	$0$	$1$		$q+q^{2}+(-\zeta_{10}+\zeta_{10}^{2})q^{3}+q^{4}+(-\zeta_{10}+\cdots)q^{6}+\cdots$
2013.1.bm.a	$2013$	$1$	2013.bm	2013.am	$10$	$4$	$1$	$1.005$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-183}) $	None		$4$	$0$	$-3$	$-1$	$0$	$0$	$1$		$q+(-1+\zeta_{10})q^{2}+\zeta_{10}^{4}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots$
2013.1.bm.b	$2013$	$1$	2013.bm	2013.am	$10$	$4$	$1$	$1.005$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-183}) $	None		$4$	$0$	$3$	$-1$	$0$	$0$	$1$		$q+(1-\zeta_{10})q^{2}+\zeta_{10}^{4}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots$
2015.1.h.a	$2015$	$1$	2015.h	2015.h	$2$	$4$	$4$	$1.006$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-155}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{8}-\zeta_{8}^{3})q^{3}-q^{4}+\zeta_{8}^{2}q^{5}+q^{9}+\cdots$
2015.1.bq.c	$2015$	$1$	2015.bq	2015.aq	$6$	$4$	$2$	$1.006$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q+\zeta_{12}q^{2}+\zeta_{12}^{4}q^{3}+\zeta_{12}^{3}q^{5}+\zeta_{12}^{5}q^{6}+\cdots$
2015.1.bq.d	$2015$	$1$	2015.bq	2015.aq	$6$	$4$	$2$	$1.006$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-155}) $	None		$8$	$0$	$0$	$0$	$-4$	$0$	$1$		$q-\zeta_{12}^{2}q^{4}-q^{5}+\zeta_{12}^{2}q^{9}+\zeta_{12}^{5}q^{13}+\cdots$
2015.1.bq.e	$2015$	$1$	2015.bq	2015.aq	$6$	$4$	$2$	$1.006$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}-\zeta_{12}^{4}q^{3}-\zeta_{12}^{3}q^{5}+\zeta_{12}^{5}q^{6}+\cdots$
2016.1.e.a	$2016$	$1$	2016.e	168.e	$2$	$4$	$4$	$1.006$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2$		$q+\zeta_{8}^{2}q^{7}+(\zeta_{8}+\zeta_{8}^{3})q^{11}+(-\zeta_{8}+\cdots)q^{23}+\cdots$
2016.1.f.a	$2016$	$1$	2016.f	7.b	$2$	$4$	$4$	$1.006$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-21}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{7}+(-\zeta_{8}+\cdots)q^{11}+\cdots$
2016.1.bi.a	$2016$	$1$	2016.bi	504.aa	$6$	$4$	$2$	$1.006$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-\zeta_{12}^{2}q^{3}-\zeta_{12}^{3}q^{5}+\zeta_{12}q^{7}+\zeta_{12}^{4}q^{9}+\cdots$
2016.1.bv.c	$2016$	$1$	2016.bv	504.an	$6$	$4$	$2$	$1.006$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-14}) $	None		$8$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-\zeta_{12}^{3}q^{3}+(-\zeta_{12}-\zeta_{12}^{3})q^{5}+\zeta_{12}^{4}q^{7}+\cdots$
2016.1.bw.a	$2016$	$1$	2016.bw	252.u	$6$	$4$	$2$	$1.006$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{3}-\zeta_{12}q^{7}+\zeta_{12}^{2}q^{9}+\zeta_{12}^{4}q^{13}+\cdots$
2016.1.cd.a	$2016$	$1$	2016.cd	28.g	$6$	$4$	$2$	$1.006$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}-\zeta_{12}q^{11}+\cdots$
2016.1.ce.a	$2016$	$1$	2016.ce	56.j	$6$	$4$	$2$	$1.006$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-6}) $	None		$8$	$0$	$0$	$0$	$0$	$2$	$1$		$q+(\zeta_{12}^{3}+\zeta_{12}^{5})q^{5}+\zeta_{12}^{2}q^{7}+\zeta_{12}^{5}q^{11}+\cdots$
2016.1.cm.a	$2016$	$1$	2016.cm	504.be	$6$	$4$	$2$	$1.006$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$4$	$0$	$0$	$1$		$q+q^{3}+\zeta_{12}^{5}q^{5}-\zeta_{12}^{3}q^{7}+q^{9}+\cdots$
2016.1.dd.a	$2016$	$1$	2016.dd	252.al	$6$	$4$	$2$	$1.006$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}^{3}q^{3}-\zeta_{12}^{3}q^{7}-q^{9}-\zeta_{12}^{2}q^{13}+\cdots$
2016.1.dn.a	$2016$	$1$	2016.dn	672.ar	$8$	$4$	$1$	$1.006$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-4$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}+\zeta_{8}^{3}q^{7}-q^{8}+(-\zeta_{8}^{2}+\cdots)q^{11}+\cdots$
2016.1.dn.b	$2016$	$1$	2016.dn	672.ar	$8$	$4$	$1$	$1.006$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}^{3}q^{7}-\zeta_{8}^{2}q^{8}+\cdots$
2016.1.dn.c	$2016$	$1$	2016.dn	672.ar	$8$	$4$	$1$	$1.006$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{8}+\cdots$
2016.1.dn.d	$2016$	$1$	2016.dn	672.ar	$8$	$4$	$1$	$1.006$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$4$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}+\zeta_{8}^{3}q^{7}+q^{8}+(\zeta_{8}^{2}-\zeta_{8}^{3}+\cdots)q^{11}+\cdots$
2016.1.dp.a	$2016$	$1$	2016.dp	224.v	$8$	$4$	$1$	$1.006$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}-\zeta_{8}^{3}q^{8}+\cdots$
2016.1.dp.b	$2016$	$1$	2016.dp	224.v	$8$	$4$	$1$	$1.006$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{7}+\zeta_{8}q^{8}+\cdots$
2016.1.dp.c	$2016$	$1$	2016.dp	224.v	$8$	$4$	$1$	$1.006$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{3}q^{8}+\cdots$
2019.1.c.c	$2019$	$1$	2019.c	2019.c	$2$	$4$	$4$	$1.008$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-2019}) $	None	✓	$4$	$0$	$0$	$-4$	$0$	$0$	$1$		$q-q^{3}+q^{4}-\beta _{1}q^{5}-\beta _{2}q^{7}+q^{9}+\cdots$
2019.1.m.a	$2019$	$1$	2019.m	2019.m	$8$	$4$	$1$	$1.008$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{2}q^{3}-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}-q^{9}+\cdots$
2020.1.d.d	$2020$	$1$	2020.d	2020.d	$2$	$4$	$4$	$1.008$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{505}) $		$8$	$0$	$0$	$0$	$-4$	$0$	$1$		$q-\zeta_{8}q^{2}+(\zeta_{8}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$
2020.1.k.a	$2020$	$1$	2020.k	505.h	$4$	$4$	$2$	$1.008$	$\Q(\zeta_{12})$	$D_{12}$	None	$\Q(\sqrt{101}) $		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{9}+(-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{13}+\cdots$
2020.1.x.a	$2020$	$1$	2020.x	2020.x	$10$	$4$	$1$	$1.008$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$-1$	$3$	$-1$	$3$	$1$		$q+\zeta_{10}^{4}q^{2}+(1+\zeta_{10}^{2})q^{3}-\zeta_{10}^{3}q^{4}+\cdots$
2020.1.x.b	$2020$	$1$	2020.x	2020.x	$10$	$4$	$1$	$1.008$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$1$	$-3$	$-1$	$-3$	$1$		$q-\zeta_{10}^{4}q^{2}+(-1-\zeta_{10}^{2})q^{3}-\zeta_{10}^{3}q^{4}+\cdots$
2020.1.z.a	$2020$	$1$	2020.z	2020.z	$10$	$4$	$1$	$1.008$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$1$	$0$	$1$		$q+\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}+\zeta_{10}^{3}q^{5}+\cdots$
2020.1.z.b	$2020$	$1$	2020.z	2020.z	$10$	$4$	$1$	$1.008$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$1$	$0$	$1$		$q-\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}-\zeta_{10}^{4}q^{5}+\cdots$
2021.1.h.a	$2021$	$1$	2021.h	2021.h	$6$	$4$	$2$	$1.009$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$-2$	$0$	$2$	$1$		$q-\zeta_{12}^{2}q^{3}-q^{4}+\zeta_{12}^{5}q^{5}-\zeta_{12}^{4}q^{7}+\cdots$
2023.1.c.e	$2023$	$1$	2023.c	7.b	$2$	$4$	$4$	$1.010$	$\Q(i, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q-\beta _{2}q^{2}-\beta _{1}q^{3}-\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots$
2023.1.f.a	$2023$	$1$	2023.f	119.f	$4$	$4$	$2$	$1.010$	$\Q(\zeta_{8})$	$D_{3}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}^{2}q^{2}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{8}+\zeta_{8}^{2}q^{9}+\cdots$
2024.1.bb.a	$2024$	$1$	2024.bb	2024.ab	$10$	$4$	$1$	$1.010$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-46}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
2024.1.bb.b	$2024$	$1$	2024.bb	2024.ab	$10$	$4$	$1$	$1.010$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-46}) $	None		$4$	$0$	$-1$	$0$	$2$	$0$	$1$		$q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+(\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
2025.1.i.a	$2025$	$1$	2025.i	45.h	$6$	$4$	$2$	$1.011$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{12}^{2}q^{4}-\zeta_{12}q^{7}-\zeta_{12}^{5}q^{13}+\cdots$
2025.1.j.c	$2025$	$1$	2025.j	9.d	$6$	$4$	$2$	$1.011$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{3}q^{8}-\zeta_{12}^{4}q^{16}+\cdots$
2025.1.p.a	$2025$	$1$	2025.p	45.k	$12$	$4$	$1$	$1.011$	$\Q(\zeta_{12})$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-15}) $	$\Q(\sqrt{5}) $		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}^{5}q^{4}-\zeta_{12}^{4}q^{16}-\zeta_{12}^{3}q^{19}+\cdots$
2028.1.o.b	$2028$	$1$	2028.o	39.i	$6$	$4$	$2$	$1.012$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$2$	$0$	$0$	$3$		$q+\zeta_{12}^{2}q^{3}+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{7}+\cdots$
2028.1.s.b	$2028$	$1$	2028.s	39.h	$6$	$4$	$2$	$1.012$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$-2$	$0$	$0$	$1$		$q+\zeta_{12}^{4}q^{3}+\zeta_{12}^{5}q^{7}-\zeta_{12}^{2}q^{9}+\cdots$
2028.1.v.a	$2028$	$1$	2028.v	156.v	$12$	$4$	$1$	$1.012$	$\Q(\zeta_{12})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$-2$	$0$	$4$	$0$	$1$		$q-\zeta_{12}^{2}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{4}q^{4}+\cdots$
2028.1.v.b	$2028$	$1$	2028.v	156.v	$12$	$4$	$1$	$1.012$	$\Q(\zeta_{12})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$-4$	$0$	$1$		$q+\zeta_{12}^{5}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{4}+\cdots$
2028.1.v.c	$2028$	$1$	2028.v	156.v	$12$	$4$	$1$	$1.012$	$\Q(\zeta_{12})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$4$	$0$	$1$		$q-\zeta_{12}^{5}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{4}+\cdots$
2028.1.v.d	$2028$	$1$	2028.v	156.v	$12$	$4$	$1$	$1.012$	$\Q(\zeta_{12})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$2$	$0$	$-4$	$0$	$1$		$q+\zeta_{12}^{2}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{4}q^{4}+\cdots$
2032.1.t.a	$2032$	$1$	2032.t	508.h	$6$	$4$	$2$	$1.014$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{12}^{5}q^{3}+\zeta_{12}^{5}q^{7}+\zeta_{12}q^{11}+\cdots$
2033.1.g.a	$2033$	$1$	2033.g	2033.g	$6$	$4$	$2$	$1.015$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{4}q^{3}+\zeta_{12}q^{5}-\zeta_{12}^{5}q^{6}+\cdots$
2035.1.bl.a	$2035$	$1$	2035.bl	2035.al	$12$	$4$	$1$	$1.016$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-4$	$-2$	$0$	$1$		$q+(-1+\zeta_{12})q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{2}q^{5}+\cdots$

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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.