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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
2004.1.g.e	$2004$	$1$	2004.g	2004.g	$2$	$10$	$10$	$1.000$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-167}) $	None		$4$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q+\zeta_{22}^{6}q^{2}+\zeta_{22}^{2}q^{3}-\zeta_{22}q^{4}+\zeta_{22}^{8}q^{6}+\cdots$
2004.1.g.f	$2004$	$1$	2004.g	2004.g	$2$	$10$	$10$	$1.000$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-167}) $	None		$4$	$0$	$1$	$1$	$0$	$0$	$1$		$q-\zeta_{22}^{6}q^{2}+\zeta_{22}^{9}q^{3}-\zeta_{22}q^{4}+\zeta_{22}^{4}q^{6}+\cdots$
2005.1.g.b	$2005$	$1$	2005.g	2005.g	$4$	$8$	$4$	$1.001$	$\Q(\zeta_{20})$	$D_{20}$	None	$\Q(\sqrt{401}) $		$4$	$0$	$-2$	$0$	$-2$	$2$	$1$		$q+(-\zeta_{20}+\zeta_{20}^{4})q^{2}+(\zeta_{20}^{2}-\zeta_{20}^{5}+\cdots)q^{4}+\cdots$
2007.1.d.c	$2007$	$1$	2007.d	223.b	$2$	$6$	$6$	$1.002$	$\Q(\zeta_{28})^+$	$D_{14}$	$\Q(\sqrt{-223}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots$
2009.1.i.a	$2009$	$1$	2009.i	287.i	$6$	$6$	$3$	$1.003$	6.0.64827.1	$D_{7}$	$\Q(\sqrt{-287}) $	None		$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3}-\beta _{4}-\beta _{5})q^{3}+\cdots$
2009.1.i.b	$2009$	$1$	2009.i	287.i	$6$	$6$	$3$	$1.003$	6.0.64827.1	$D_{7}$	$\Q(\sqrt{-287}) $	None		$4$	$0$	$1$	$1$	$0$	$0$	$1$		$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{3}+\cdots$
2013.1.bm.c	$2013$	$1$	2013.bm	2013.am	$10$	$8$	$2$	$1.005$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-183}) $	None		$8$	$0$	$0$	$-2$	$0$	$0$	$1$		$q+(\zeta_{20}^{5}+\zeta_{20}^{7})q^{2}+\zeta_{20}^{8}q^{3}+(-1+\cdots)q^{4}+\cdots$
2015.1.h.b	$2015$	$1$	2015.h	2015.h	$2$	$6$	$6$	$1.006$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-2015}) $	None	✓	$2$	$0$	$-1$	$-1$	$6$	$-1$	$1$		$q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
2015.1.h.c	$2015$	$1$	2015.h	2015.h	$2$	$6$	$6$	$1.006$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-2015}) $	None	✓	$2$	$0$	$-1$	$1$	$6$	$-1$	$1$		$q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
2015.1.h.d	$2015$	$1$	2015.h	2015.h	$2$	$6$	$6$	$1.006$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-2015}) $	None	✓	$2$	$0$	$1$	$-1$	$-6$	$1$	$1$		$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
2015.1.h.e	$2015$	$1$	2015.h	2015.h	$2$	$6$	$6$	$1.006$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-2015}) $	None	✓	$2$	$0$	$1$	$1$	$-6$	$1$	$1$		$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
2015.1.bf.a	$2015$	$1$	2015.bf	2015.af	$6$	$8$	$4$	$1.006$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-155}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{24}^{5}+\zeta_{24}^{11})q^{3}+\zeta_{24}^{4}q^{4}-\zeta_{24}^{6}q^{5}+\cdots$
2019.1.p.a	$2019$	$1$	2019.p	2019.p	$14$	$6$	$1$	$1.008$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$2$	$1$		$q-\zeta_{14}^{3}q^{3}+q^{4}+(\zeta_{14}^{3}+\zeta_{14}^{5})q^{7}+\cdots$
2019.1.q.a	$2019$	$1$	2019.q	2019.q	$14$	$6$	$1$	$1.008$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q-\zeta_{14}^{3}q^{3}+q^{4}+(-\zeta_{14}^{3}-\zeta_{14}^{5}+\cdots)q^{7}+\cdots$
2019.1.s.a	$2019$	$1$	2019.s	2019.s	$16$	$8$	$1$	$1.008$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{16}^{2}q^{3}-\zeta_{16}^{2}q^{4}+\zeta_{16}^{4}q^{9}+\cdots$
2020.1.z.c	$2020$	$1$	2020.z	2020.z	$10$	$8$	$2$	$1.008$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$2$	$0$	$1$		$q-\zeta_{20}^{3}q^{2}+(-\zeta_{20}^{5}-\zeta_{20}^{9})q^{3}+\cdots$
2020.1.bc.a	$2020$	$1$	2020.bc	2020.ac	$20$	$8$	$1$	$1.008$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+\zeta_{20}^{6}q^{2}-\zeta_{20}^{2}q^{4}+\zeta_{20}^{7}q^{5}+\cdots$
2020.1.bm.a	$2020$	$1$	2020.bm	2020.am	$20$	$8$	$1$	$1.008$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{20}^{3}q^{2}+\zeta_{20}^{6}q^{4}-\zeta_{20}^{3}q^{5}+\cdots$
2023.1.d.b	$2023$	$1$	2023.d	119.d	$2$	$6$	$6$	$1.010$	6.0.419904.1	$D_{9}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\beta _{2}+\beta _{4})q^{2}+(1-\beta _{2})q^{4}+\beta _{3}q^{7}+\cdots$
2023.1.f.b	$2023$	$1$	2023.f	119.f	$4$	$8$	$4$	$1.010$	8.0.40960000.1	$D_{5}$	$\Q(\sqrt{-119}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\beta _{4}-\beta _{5})q^{2}+(-\beta _{6}+\beta _{7})q^{3}+(-1+\cdots)q^{4}+\cdots$
2023.1.l.a	$2023$	$1$	2023.l	119.l	$8$	$8$	$2$	$1.010$	$\Q(\zeta_{16})$	$D_{3}$	$\Q(\sqrt{-7}) $	None		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}^{2}q^{2}-\zeta_{16}q^{7}-\zeta_{16}^{6}q^{8}+\zeta_{16}^{6}q^{9}+\cdots$
2024.1.bb.c	$2024$	$1$	2024.bb	2024.ab	$10$	$8$	$2$	$1.010$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-46}) $	None		$8$	$0$	$2$	$0$	$0$	$0$	$1$		$q+\zeta_{20}^{2}q^{2}+\zeta_{20}^{4}q^{4}+(\zeta_{20}^{7}+\zeta_{20}^{9}+\cdots)q^{5}+\cdots$
2024.1.bu.a	$2024$	$1$	2024.bu	2024.au	$22$	$10$	$1$	$1.010$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-22}) $	None		$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-\zeta_{22}^{9}q^{2}-\zeta_{22}^{7}q^{4}-\zeta_{22}^{5}q^{8}+\cdots$
2024.1.bu.b	$2024$	$1$	2024.bu	2024.au	$22$	$10$	$1$	$1.010$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-22}) $	None		$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q+\zeta_{22}^{9}q^{2}-\zeta_{22}^{7}q^{4}+\zeta_{22}^{5}q^{8}+\cdots$
2025.1.p.b	$2025$	$1$	2025.p	45.k	$12$	$8$	$2$	$1.011$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-15}) $	None		$16$	$0$	$0$	$0$	$0$	$0$	$3^{2}$		$q+(-\zeta_{24}^{3}-\zeta_{24}^{7})q^{2}+(-\zeta_{24}^{2}+\zeta_{24}^{6}+\cdots)q^{4}+\cdots$
2025.1.p.c	$2025$	$1$	2025.p	45.k	$12$	$8$	$2$	$1.011$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-3}) $	None		$16$	$0$	$0$	$0$	$0$	$0$	$3^{2}$		$q-\zeta_{24}^{10}q^{4}+(-\zeta_{24}^{3}-\zeta_{24}^{7})q^{7}+\cdots$
2031.1.d.a	$2031$	$1$	2031.d	2031.d	$2$	$9$	$9$	$1.014$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-2031}) $	None	✓	$2$	$0$	$-1$	$9$	$-1$	$0$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots$
2031.1.d.b	$2031$	$1$	2031.d	2031.d	$2$	$9$	$9$	$1.014$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-2031}) $	None	✓	$2$	$0$	$1$	$-9$	$1$	$0$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots$
2032.1.m.b	$2032$	$1$	2032.m	2032.m	$4$	$8$	$4$	$1.014$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-127}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q+\zeta_{20}^{8}q^{2}-\zeta_{20}^{6}q^{4}+\zeta_{20}^{4}q^{8}+\cdots$
2033.1.g.b	$2033$	$1$	2033.g	2033.g	$6$	$6$	$3$	$1.015$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-107}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{3}-\zeta_{18}^{3}q^{4}+(-\zeta_{18}^{3}+\cdots)q^{9}+\cdots$
2035.1.x.c	$2035$	$1$	2035.x	2035.x	$6$	$8$	$4$	$1.016$	$\Q(\zeta_{24})$	$S_{4}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{2}$		$q+(-\zeta_{24}^{5}-\zeta_{24}^{11})q^{2}+\zeta_{24}^{10}q^{3}+\cdots$
2035.1.by.a	$2035$	$1$	2035.by	2035.ay	$18$	$6$	$1$	$1.016$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-3$	$0$	$0$	$1$		$q+(-\zeta_{18}^{3}+\zeta_{18}^{7})q^{3}-\zeta_{18}^{8}q^{4}+\cdots$
2035.1.by.b	$2035$	$1$	2035.by	2035.ay	$18$	$6$	$1$	$1.016$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$3$	$0$	$0$	$1$		$q+(\zeta_{18}^{3}-\zeta_{18}^{7})q^{3}-\zeta_{18}^{8}q^{4}+\zeta_{18}^{5}q^{5}+\cdots$
2035.1.ce.a	$2035$	$1$	2035.ce	2035.be	$18$	$6$	$1$	$1.016$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-3$	$0$	$0$	$1$		$q+(\zeta_{18}-\zeta_{18}^{3})q^{3}-\zeta_{18}^{5}q^{4}+\zeta_{18}^{2}q^{5}+\cdots$
2035.1.ce.b	$2035$	$1$	2035.ce	2035.be	$18$	$6$	$1$	$1.016$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$3$	$0$	$0$	$1$		$q+(-\zeta_{18}+\zeta_{18}^{3})q^{3}-\zeta_{18}^{5}q^{4}+\zeta_{18}^{5}q^{5}+\cdots$
2037.1.cr.a	$2037$	$1$	2037.cr	2037.br	$24$	$8$	$1$	$1.017$	$\Q(\zeta_{24})$	$D_{24}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$4$	$1$		$q-\zeta_{24}^{11}q^{3}-\zeta_{24}^{6}q^{4}+\zeta_{24}^{4}q^{7}+\cdots$
2037.1.db.a	$2037$	$1$	2037.db	2037.cb	$24$	$8$	$1$	$1.017$	$\Q(\zeta_{24})$	$D_{24}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{24}^{3}q^{3}+\zeta_{24}^{2}q^{4}+\zeta_{24}^{11}q^{7}+\cdots$
2040.1.df.a	$2040$	$1$	2040.df	2040.cf	$8$	$8$	$2$	$1.018$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-30}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{16}^{6}q^{2}+\zeta_{16}^{5}q^{3}-\zeta_{16}^{4}q^{4}+\cdots$
2040.1.df.b	$2040$	$1$	2040.df	2040.cf	$8$	$8$	$2$	$1.018$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-30}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}^{6}q^{2}+\zeta_{16}^{5}q^{3}-\zeta_{16}^{4}q^{4}+\cdots$
2040.1.df.c	$2040$	$1$	2040.df	2040.cf	$8$	$8$	$2$	$1.018$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}^{5}q^{2}+\zeta_{16}q^{3}-\zeta_{16}^{2}q^{4}+\zeta_{16}^{5}q^{5}+\cdots$
2040.1.df.d	$2040$	$1$	2040.df	2040.cf	$8$	$8$	$2$	$1.018$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{16}^{7}q^{2}+\zeta_{16}q^{3}-\zeta_{16}^{6}q^{4}+\zeta_{16}^{5}q^{5}+\cdots$
2043.1.g.b	$2043$	$1$	2043.g	2043.g	$6$	$8$	$4$	$1.020$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-227}) $	None		$4$	$0$	$0$	$-2$	$0$	$2$	$1$		$q+\zeta_{30}^{12}q^{3}-\zeta_{30}^{5}q^{4}+(-\zeta_{30}+\zeta_{30}^{4}+\cdots)q^{7}+\cdots$
2048.1.f.a	$2048$	$1$	2048.f	16.f	$4$	$8$	$4$	$1.022$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-2}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{3}$		$q+(\zeta_{16}-\zeta_{16}^{3})q^{3}+(\zeta_{16}^{2}-\zeta_{16}^{4}+\cdots)q^{9}+\cdots$
2052.1.cq.a	$2052$	$1$	2052.cq	19.f	$18$	$6$	$1$	$1.024$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}+\zeta_{18}^{5})q^{7}+(\zeta_{18}^{3}+\zeta_{18}^{8}+\cdots)q^{13}+\cdots$
2052.1.cr.a	$2052$	$1$	2052.cr	57.l	$18$	$6$	$1$	$1.024$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}-\zeta_{18}^{5})q^{7}+(-\zeta_{18}^{3}+\zeta_{18}^{8}+\cdots)q^{13}+\cdots$
2056.1.t.a	$2056$	$1$	2056.t	2056.t	$16$	$8$	$1$	$1.026$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-8$	$0$	$0$	$0$	$1$		$q-q^{2}+(-\zeta_{16}^{3}-\zeta_{16}^{4})q^{3}+q^{4}+\cdots$
2059.1.b.c	$2059$	$1$	2059.b	2059.b	$2$	$6$	$6$	$1.028$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-71}) $	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+(\zeta_{14}^{2}+\zeta_{14}^{5})q^{2}+(\zeta_{14}+\zeta_{14}^{6}+\cdots)q^{3}+\cdots$
2064.1.cb.a	$2064$	$1$	2064.cb	516.t	$14$	$6$	$1$	$1.030$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$2$	$1$		$q-\zeta_{14}^{5}q^{3}+(\zeta_{14}-\zeta_{14}^{6})q^{7}-\zeta_{14}^{3}q^{9}+\cdots$
2064.1.cb.b	$2064$	$1$	2064.cb	516.t	$14$	$6$	$1$	$1.030$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-2$	$1$		$q+\zeta_{14}^{5}q^{3}+(-\zeta_{14}+\zeta_{14}^{6})q^{7}-\zeta_{14}^{3}q^{9}+\cdots$
2064.1.cj.a	$2064$	$1$	2064.cj	129.l	$14$	$6$	$1$	$1.030$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$2$	$1$		$q-\zeta_{14}^{4}q^{3}+(-\zeta_{14}^{2}+\zeta_{14}^{5})q^{7}+\cdots$

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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.