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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
120.1.i.a	$120$	$1$	120.i	120.i	$2$	$2$	$2$	$0.060$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{10}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-iq^{3}-q^{4}+iq^{5}-q^{6}+iq^{8}+\cdots$
135.1.d.a	$135$	$1$	135.d	15.d	$2$	$1$	$1$	$0.067$	$\Q$	$D_{3}$	$\Q(\sqrt{-15}) $	None	✓	$2$	$0$	$-1$	$0$	$1$	$0$	$1$		$q-q^{2}+q^{5}+q^{8}-q^{10}-q^{16}-q^{17}+\cdots$
135.1.d.b	$135$	$1$	135.d	15.d	$2$	$1$	$1$	$0.067$	$\Q$	$D_{3}$	$\Q(\sqrt{-15}) $	None	✓	$2$	$0$	$1$	$0$	$-1$	$0$	$1$		$q+q^{2}-q^{5}-q^{8}-q^{10}-q^{16}+q^{17}+\cdots$
180.1.f.a	$180$	$1$	180.f	20.d	$2$	$2$	$2$	$0.090$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-15}) $	$\Q(\sqrt{15}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-q^{4}-iq^{5}+iq^{8}-q^{10}+\cdots$
225.1.g.a	$225$	$1$	225.g	5.c	$4$	$2$	$1$	$0.112$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-15}) $	$\Q(\sqrt{5}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{4}-q^{16}-iq^{19}-q^{31}+iq^{49}+\cdots$
240.1.bm.a	$240$	$1$	240.bm	240.am	$4$	$4$	$2$	$0.120$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{5}+\cdots$
255.1.h.e	$255$	$1$	255.h	255.h	$2$	$2$	$2$	$0.127$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-51}) $	$\Q(\sqrt{85}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}-q^{4}-iq^{5}-q^{9}+iq^{12}+\cdots$
255.1.i.a	$255$	$1$	255.i	255.i	$4$	$4$	$2$	$0.127$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+\zeta_{8}^{3}q^{3}-q^{4}+\cdots$
255.1.y.a	$255$	$1$	255.y	255.y	$8$	$8$	$2$	$0.127$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{16}-\zeta_{16}^{3})q^{2}-\zeta_{16}^{7}q^{3}+(\zeta_{16}^{2}+\cdots)q^{4}+\cdots$
285.1.n.a	$285$	$1$	285.n	285.n	$6$	$2$	$1$	$0.142$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-1$	$1$	$1$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{6}+\cdots$
285.1.n.b	$285$	$1$	285.n	285.n	$6$	$2$	$1$	$0.142$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$1$	$-1$	$-1$	$0$	$1$		$q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{6}+\cdots$
285.1.bd.a	$285$	$1$	285.bd	285.ad	$18$	$6$	$1$	$0.142$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{4}+\zeta_{18}^{6})q^{2}+\zeta_{18}^{2}q^{3}+(-\zeta_{18}+\cdots)q^{4}+\cdots$
285.1.bd.b	$285$	$1$	285.bd	285.ad	$18$	$6$	$1$	$0.142$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$3$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}^{4}-\zeta_{18}^{6})q^{2}-\zeta_{18}^{2}q^{3}+\cdots$
300.1.l.a	$300$	$1$	300.l	60.l	$4$	$4$	$2$	$0.150$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{3}) $		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}-q^{6}+\cdots$
345.1.p.a	$345$	$1$	345.p	345.p	$22$	$10$	$1$	$0.172$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-2$	$-1$	$-1$	$0$	$1$		$q+(-\zeta_{22}^{3}-\zeta_{22}^{5})q^{2}+\zeta_{22}^{10}q^{3}+\cdots$
345.1.p.b	$345$	$1$	345.p	345.p	$22$	$10$	$1$	$0.172$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$2$	$1$	$1$	$0$	$1$		$q+(\zeta_{22}^{3}+\zeta_{22}^{5})q^{2}-\zeta_{22}^{10}q^{3}+(\zeta_{22}^{6}+\cdots)q^{4}+\cdots$
360.1.p.a	$360$	$1$	360.p	40.e	$2$	$1$	$1$	$0.180$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-10}) $	$\Q(\sqrt{6}) $	✓	$4$	$0$	$-1$	$0$	$1$	$0$	$1$		$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+q^{16}+\cdots$
360.1.p.b	$360$	$1$	360.p	40.e	$2$	$1$	$1$	$0.180$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-10}) $	$\Q(\sqrt{6}) $	✓	$4$	$0$	$1$	$0$	$-1$	$0$	$1$		$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+q^{16}+\cdots$
375.1.c.a	$375$	$1$	375.c	3.b	$2$	$4$	$4$	$0.187$	$\Q(i, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{4}+\beta _{2}q^{6}+\cdots$
375.1.d.a	$375$	$1$	375.d	15.d	$2$	$2$	$2$	$0.187$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-15}) $	None	✓	$2$	$0$	$-1$	$2$	$0$	$0$	$1$		$q+(-1+\beta )q^{2}+q^{3}+(1-\beta )q^{4}+(-1+\cdots)q^{6}+\cdots$
375.1.d.b	$375$	$1$	375.d	15.d	$2$	$2$	$2$	$0.187$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-15}) $	None	✓	$2$	$0$	$1$	$-2$	$0$	$0$	$1$		$q+(1-\beta )q^{2}-q^{3}+(1-\beta )q^{4}+(-1+\cdots)q^{6}+\cdots$
405.1.h.a	$405$	$1$	405.h	45.h	$6$	$2$	$1$	$0.202$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-1$	$0$	$1$	$0$	$1$		$q-\zeta_{6}q^{2}-\zeta_{6}^{2}q^{5}-q^{8}-q^{10}+\zeta_{6}q^{16}+\cdots$
405.1.h.b	$405$	$1$	405.h	45.h	$6$	$2$	$1$	$0.202$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$1$	$0$	$-1$	$0$	$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{5}+q^{8}-q^{10}+\zeta_{6}q^{16}+\cdots$
465.1.u.a	$465$	$1$	465.u	465.u	$6$	$2$	$1$	$0.232$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-2$	$-1$	$-1$	$0$	$1$		$q-q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{6}+q^{8}+\cdots$
465.1.u.b	$465$	$1$	465.u	465.u	$6$	$2$	$1$	$0.232$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$2$	$1$	$1$	$0$	$1$		$q+q^{2}+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{6}-q^{8}+\cdots$
465.1.x.a	$465$	$1$	465.x	465.x	$10$	$4$	$1$	$0.232$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-2$	$-1$	$4$	$0$	$1$		$q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}-\zeta_{10}q^{3}+(\zeta_{10}^{2}+\cdots)q^{4}+\cdots$
465.1.x.b	$465$	$1$	465.x	465.x	$10$	$4$	$1$	$0.232$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$2$	$1$	$-4$	$0$	$1$		$q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}q^{3}+(\zeta_{10}^{2}+\cdots)q^{4}+\cdots$
465.1.bl.a	$465$	$1$	465.bl	465.al	$30$	$8$	$1$	$0.232$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-2$	$-1$	$4$	$0$	$1$		$q+(\zeta_{30}^{11}+\zeta_{30}^{13})q^{2}-\zeta_{30}^{8}q^{3}+\cdots$
465.1.bl.b	$465$	$1$	465.bl	465.al	$30$	$8$	$1$	$0.232$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$2$	$1$	$-4$	$0$	$1$		$q+(-\zeta_{30}^{11}-\zeta_{30}^{13})q^{2}+\zeta_{30}^{8}q^{3}+\cdots$
480.1.i.a	$480$	$1$	480.i	120.i	$2$	$2$	$2$	$0.240$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{10}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}-iq^{5}-q^{9}-q^{15}-q^{25}+\cdots$
480.1.bu.a	$480$	$1$	480.bu	480.au	$8$	$8$	$2$	$0.240$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}^{3}q^{2}-\zeta_{16}^{7}q^{3}+\zeta_{16}^{6}q^{4}+\cdots$
540.1.f.a	$540$	$1$	540.f	20.d	$2$	$4$	$4$	$0.269$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{5}-\zeta_{12}^{3}q^{8}+\cdots$
600.1.n.a	$600$	$1$	600.n	24.h	$2$	$1$	$1$	$0.299$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{10}) $	✓	$4$	$0$	$-1$	$1$	$0$	$0$	$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
600.1.n.b	$600$	$1$	600.n	24.h	$2$	$1$	$1$	$0.299$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{10}) $	✓	$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
600.1.q.a	$600$	$1$	600.q	120.q	$4$	$4$	$2$	$0.299$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-15}) $	$\Q(\sqrt{30}) $		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}^{3}q^{2}-\zeta_{8}q^{3}-\zeta_{8}^{2}q^{4}+q^{6}+\cdots$
675.1.c.c	$675$	$1$	675.c	3.b	$2$	$2$	$2$	$0.337$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-iq^{8}-q^{16}-iq^{17}+q^{19}+\cdots$
675.1.g.a	$675$	$1$	675.g	5.c	$4$	$4$	$2$	$0.337$	$\Q(i, \sqrt{6})$	$D_{6}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+2\beta _{2}q^{4}-\beta _{3}q^{8}-q^{16}+\cdots$
705.1.p.a	$705$	$1$	705.p	705.p	$46$	$22$	$1$	$0.352$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-2$	$-1$	$-1$	$0$	$1$		$q+(\zeta_{46}^{4}+\zeta_{46}^{6})q^{2}-\zeta_{46}^{3}q^{3}+(\zeta_{46}^{8}+\cdots)q^{4}+\cdots$
705.1.p.b	$705$	$1$	705.p	705.p	$46$	$22$	$1$	$0.352$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$2$	$1$	$1$	$0$	$1$		$q+(-\zeta_{46}^{4}-\zeta_{46}^{6})q^{2}+\zeta_{46}^{3}q^{3}+\cdots$
45.2.b.a	$45$	$2$	45.b	5.b	$2$	$2$	$2$	$0.359$	$\Q(\sqrt{-5}) $	$_{}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{2}-3q^{4}-\beta q^{5}-\beta q^{8}+5q^{10}+\cdots$
720.1.r.a	$720$	$1$	720.r	80.k	$4$	$4$	$2$	$0.359$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}-\zeta_{8}^{3}q^{8}+\cdots$
735.1.f.a	$735$	$1$	735.f	15.d	$2$	$1$	$1$	$0.367$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-35}) $	$\Q(\sqrt{21}) $	✓	$4$	$0$	$0$	$-1$	$-1$	$0$	$1$		$q-q^{3}-q^{4}-q^{5}+q^{9}+q^{12}+q^{15}+\cdots$
735.1.f.b	$735$	$1$	735.f	15.d	$2$	$1$	$1$	$0.367$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-35}) $	$\Q(\sqrt{21}) $	✓	$4$	$0$	$0$	$1$	$1$	$0$	$1$		$q+q^{3}-q^{4}+q^{5}+q^{9}-q^{12}+q^{15}+\cdots$
735.1.f.c	$735$	$1$	735.f	15.d	$2$	$2$	$2$	$0.367$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-15}) $	None	✓	$4$	$0$	$0$	$-2$	$2$	$0$	$1$		$q-\beta q^{2}-q^{3}+q^{4}+q^{5}+\beta q^{6}+q^{9}+\cdots$
735.1.f.d	$735$	$1$	735.f	15.d	$2$	$2$	$2$	$0.367$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-15}) $	None	✓	$4$	$0$	$0$	$2$	$-2$	$0$	$1$		$q-\beta q^{2}+q^{3}+q^{4}-q^{5}-\beta q^{6}+q^{9}+\cdots$
735.1.o.a	$735$	$1$	735.o	105.o	$6$	$2$	$1$	$0.367$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-35}) $	$\Q(\sqrt{21}) $		$8$	$0$	$0$	$-1$	$-1$	$0$	$1$		$q-\zeta_{6}q^{3}+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}+\cdots$
735.1.o.b	$735$	$1$	735.o	105.o	$6$	$2$	$1$	$0.367$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-35}) $	$\Q(\sqrt{21}) $		$8$	$0$	$0$	$1$	$1$	$0$	$1$		$q+\zeta_{6}q^{3}+\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}+\cdots$
735.1.o.c	$735$	$1$	735.o	105.o	$6$	$4$	$2$	$0.367$	$\Q(\sqrt{2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$-2$	$2$	$0$	$1$		$q-\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots$
735.1.o.d	$735$	$1$	735.o	105.o	$6$	$4$	$2$	$0.367$	$\Q(\sqrt{2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$2$	$-2$	$0$	$1$		$q-\beta _{1}q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots$
765.1.bz.a	$765$	$1$	765.bz	85.p	$16$	$16$	$2$	$0.382$	$\Q(\zeta_{32})$	$D_{16}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{32}-\zeta_{32}^{3})q^{2}+(\zeta_{32}^{2}-\zeta_{32}^{4}+\cdots)q^{4}+\cdots$

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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.