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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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Results (1-50 of 71 matches)

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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
152.1.g.a	$152$	$1$	152.g	152.g	$2$	$1$	$1$	$0.076$	$\Q$	$D_{3}$	$\Q(\sqrt{-38}) $	None	✓	$2$	$0$	$-1$	$1$	$0$	$-1$	$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots$
152.1.g.b	$152$	$1$	152.g	152.g	$2$	$1$	$1$	$0.076$	$\Q$	$D_{3}$	$\Q(\sqrt{-38}) $	None	✓	$2$	$0$	$1$	$-1$	$0$	$-1$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots$
608.1.g.a	$608$	$1$	608.g	152.g	$2$	$1$	$1$	$0.303$	$\Q$	$D_{3}$	$\Q(\sqrt{-38}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$1$	$1$		$q-q^{3}+q^{7}+q^{13}-q^{17}+q^{19}-q^{21}+\cdots$
608.1.g.b	$608$	$1$	608.g	152.g	$2$	$1$	$1$	$0.303$	$\Q$	$D_{3}$	$\Q(\sqrt{-38}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$1$	$1$		$q+q^{3}+q^{7}-q^{13}-q^{17}-q^{19}+q^{21}+\cdots$
1064.1.br.a	$1064$	$1$	1064.br	1064.ar	$6$	$6$	$3$	$0.531$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{6}q^{2}+(-\zeta_{18}-\zeta_{18}^{5})q^{3}-\zeta_{18}^{3}q^{4}+\cdots$
1064.1.br.b	$1064$	$1$	1064.br	1064.ar	$6$	$6$	$3$	$0.531$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$3$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{6}q^{2}+(-\zeta_{18}^{2}-\zeta_{18}^{4})q^{3}+\cdots$
1368.1.i.a	$1368$	$1$	1368.i	152.g	$2$	$1$	$1$	$0.683$	$\Q$	$D_{3}$	$\Q(\sqrt{-38}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q-q^{2}+q^{4}-q^{7}-q^{8}-q^{13}+q^{14}+\cdots$
1368.1.i.b	$1368$	$1$	1368.i	152.g	$2$	$1$	$1$	$0.683$	$\Q$	$D_{3}$	$\Q(\sqrt{-38}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$-1$	$1$		$q+q^{2}+q^{4}-q^{7}+q^{8}+q^{13}-q^{14}+\cdots$
1368.1.ce.a	$1368$	$1$	1368.ce	1368.be	$6$	$6$	$3$	$0.683$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{6}q^{2}+\zeta_{18}^{4}q^{3}-\zeta_{18}^{3}q^{4}+\cdots$
1368.1.ce.b	$1368$	$1$	1368.ce	1368.be	$6$	$6$	$3$	$0.683$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$3$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{6}q^{2}+\zeta_{18}^{7}q^{3}-\zeta_{18}^{3}q^{4}+\cdots$
1976.1.o.a	$1976$	$1$	1976.o	1976.o	$2$	$2$	$2$	$0.986$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-38}) $, $\Q(\sqrt{-247}) $	$\Q(\sqrt{26}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-q^{4}+iq^{8}-q^{9}+iq^{13}+\cdots$
1976.1.o.f	$1976$	$1$	1976.o	1976.o	$2$	$4$	$4$	$0.986$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-38}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}^{3}q^{2}+(-\zeta_{12}+\zeta_{12}^{5})q^{3}-q^{4}+\cdots$
1976.1.bl.a	$1976$	$1$	1976.bl	1976.al	$6$	$6$	$3$	$0.986$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{3}q^{2}+(-\zeta_{18}-\zeta_{18}^{5})q^{3}+\zeta_{18}^{6}q^{4}+\cdots$
1976.1.bl.b	$1976$	$1$	1976.bl	1976.al	$6$	$6$	$3$	$0.986$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$3$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{3}q^{2}+(-\zeta_{18}^{2}-\zeta_{18}^{4})q^{3}+\cdots$
1976.1.cd.a	$1976$	$1$	1976.cd	1976.bd	$6$	$12$	$6$	$0.986$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-38}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{36}^{15}q^{2}+(\zeta_{36}^{5}+\zeta_{36}^{7})q^{3}-\zeta_{36}^{12}q^{4}+\cdots$
2432.1.g.a	$2432$	$1$	2432.g	152.g	$2$	$1$	$1$	$1.214$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-38}) $	$\Q(\sqrt{19}) $	✓	$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-2q^{3}+3q^{9}-2q^{17}+q^{19}+q^{25}+\cdots$
2432.1.g.b	$2432$	$1$	2432.g	152.g	$2$	$1$	$1$	$1.214$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-38}) $	$\Q(\sqrt{19}) $	✓	$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+2q^{3}+3q^{9}-2q^{17}-q^{19}+q^{25}+\cdots$
2432.1.g.c	$2432$	$1$	2432.g	152.g	$2$	$2$	$2$	$1.214$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-38}) $	None	✓	$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-q^{3}-\beta q^{7}-\beta q^{13}+q^{17}-q^{19}+\cdots$
2432.1.g.d	$2432$	$1$	2432.g	152.g	$2$	$2$	$2$	$1.214$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-38}) $	None	✓	$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+q^{3}-\beta q^{7}+\beta q^{13}+q^{17}+q^{19}+\cdots$
2584.1.g.a	$2584$	$1$	2584.g	2584.g	$2$	$1$	$1$	$1.290$	$\Q$	$D_{2}$	$\Q(\sqrt{-38}) $, $\Q(\sqrt{-646}) $	$\Q(\sqrt{17}) $	✓	$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-q^{8}+q^{9}+2q^{13}+q^{16}+\cdots$
2584.1.g.b	$2584$	$1$	2584.g	2584.g	$2$	$1$	$1$	$1.290$	$\Q$	$D_{2}$	$\Q(\sqrt{-38}) $, $\Q(\sqrt{-646}) $	$\Q(\sqrt{17}) $	✓	$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}+q^{8}+q^{9}-2q^{13}+q^{16}+\cdots$
2584.1.g.c	$2584$	$1$	2584.g	2584.g	$2$	$2$	$2$	$1.290$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-q^{2}+(\zeta_{6}+\zeta_{6}^{2})q^{3}+q^{4}+(-\zeta_{6}+\cdots)q^{6}+\cdots$
2584.1.g.e	$2584$	$1$	2584.g	2584.g	$2$	$2$	$2$	$1.290$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+q^{2}+(\zeta_{6}+\zeta_{6}^{2})q^{3}+q^{4}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{6}+\cdots$
2584.1.x.a	$2584$	$1$	2584.x	2584.x	$4$	$2$	$1$	$1.290$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$0$	$-2$	$0$	$-2$	$1$		$q+iq^{2}+(-1+i)q^{3}-q^{4}+(-1-i+\cdots)q^{6}+\cdots$
2584.1.x.b	$2584$	$1$	2584.x	2584.x	$4$	$2$	$1$	$1.290$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$0$	$2$	$0$	$-2$	$1$		$q-iq^{2}+(1-i)q^{3}-q^{4}+(-1-i+\cdots)q^{6}+\cdots$
2584.1.x.c	$2584$	$1$	2584.x	2584.x	$4$	$4$	$2$	$1.290$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$0$	$-2$	$0$	$2$	$1$		$q-\zeta_{12}^{3}q^{2}+(\zeta_{12}^{4}+\zeta_{12}^{5})q^{3}-q^{4}+\cdots$
2584.1.x.d	$2584$	$1$	2584.x	2584.x	$4$	$4$	$2$	$1.290$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$0$	$2$	$0$	$2$	$1$		$q+\zeta_{12}^{3}q^{2}+(-\zeta_{12}+\zeta_{12}^{2})q^{3}-q^{4}+\cdots$
2584.1.bo.a	$2584$	$1$	2584.bo	2584.ao	$8$	$4$	$1$	$1.290$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{3}q^{2}+(-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots$
2584.1.bo.b	$2584$	$1$	2584.bo	2584.ao	$8$	$4$	$1$	$1.290$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}^{3}q^{2}+(\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots$
2584.1.bo.c	$2584$	$1$	2584.bo	2584.ao	$8$	$8$	$2$	$1.290$	$\Q(\zeta_{24})$	$D_{24}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{24}^{3}q^{2}+(\zeta_{24}^{10}+\zeta_{24}^{11})q^{3}+\cdots$
2584.1.bo.d	$2584$	$1$	2584.bo	2584.ao	$8$	$8$	$2$	$1.290$	$\Q(\zeta_{24})$	$D_{24}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{24}^{3}q^{2}+(-\zeta_{24}^{2}-\zeta_{24}^{7})q^{3}+\cdots$
2888.1.l.a	$2888$	$1$	2888.l	152.l	$6$	$2$	$1$	$1.441$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$-1$	$1$	$0$	$-2$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots$
2888.1.l.b	$2888$	$1$	2888.l	152.l	$6$	$2$	$1$	$1.441$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$1$	$-1$	$0$	$-2$	$1$		$q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots$
2888.1.s.a	$2888$	$1$	2888.s	152.s	$18$	$6$	$1$	$1.441$	$\Q(\zeta_{18})$	$D_{3}$	$\Q(\sqrt{-38}) $	None		$12$	$0$	$0$	$0$	$0$	$3$	$1$		$q-\zeta_{18}^{5}q^{2}-\zeta_{18}^{2}q^{3}-\zeta_{18}q^{4}+\zeta_{18}^{7}q^{6}+\cdots$
2888.1.s.b	$2888$	$1$	2888.s	152.s	$18$	$6$	$1$	$1.441$	$\Q(\zeta_{18})$	$D_{3}$	$\Q(\sqrt{-38}) $	None		$12$	$0$	$0$	$0$	$0$	$3$	$1$		$q+\zeta_{18}^{5}q^{2}+\zeta_{18}^{2}q^{3}-\zeta_{18}q^{4}+\zeta_{18}^{7}q^{6}+\cdots$
3192.1.m.f	$3192$	$1$	3192.m	3192.m	$2$	$2$	$2$	$1.593$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-38}) $, $\Q(\sqrt{-399}) $	$\Q(\sqrt{42}) $		$8$	$0$	$0$	$0$	$0$	$2$	$1$		$q-iq^{2}-iq^{3}-q^{4}-q^{6}+q^{7}+iq^{8}+\cdots$
3192.1.m.g	$3192$	$1$	3192.m	3192.m	$2$	$2$	$2$	$1.593$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-38}) $, $\Q(\sqrt{-399}) $	$\Q(\sqrt{42}) $		$8$	$0$	$0$	$0$	$0$	$2$	$1$		$q+iq^{2}-iq^{3}-q^{4}+q^{6}+q^{7}-iq^{8}+\cdots$
3192.1.m.i	$3192$	$1$	3192.m	3192.m	$2$	$4$	$4$	$1.593$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-38}) $	None		$8$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+\zeta_{12}^{3}q^{2}+\zeta_{12}q^{3}-q^{4}+\zeta_{12}^{4}q^{6}+\cdots$
3192.1.m.j	$3192$	$1$	3192.m	3192.m	$2$	$4$	$4$	$1.593$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-38}) $	None		$8$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-\zeta_{12}^{3}q^{2}+\zeta_{12}^{5}q^{3}-q^{4}+\zeta_{12}^{2}q^{6}+\cdots$
3192.1.eb.a	$3192$	$1$	3192.eb	3192.db	$6$	$12$	$6$	$1.593$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-38}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{36}^{15}q^{2}-\zeta_{36}q^{3}-\zeta_{36}^{12}q^{4}+\cdots$
3192.1.eb.b	$3192$	$1$	3192.eb	3192.db	$6$	$12$	$6$	$1.593$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-38}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{36}^{3}q^{2}-\zeta_{36}q^{3}+\zeta_{36}^{6}q^{4}+\zeta_{36}^{4}q^{6}+\cdots$
3496.1.cb.a	$3496$	$1$	3496.cb	3496.bb	$22$	$10$	$1$	$1.745$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$-1$	$-2$	$0$	$-2$	$1$		$q+\zeta_{22}^{10}q^{2}+(\zeta_{22}^{8}-\zeta_{22}^{9})q^{3}-\zeta_{22}^{9}q^{4}+\cdots$
3496.1.cb.b	$3496$	$1$	3496.cb	3496.bb	$22$	$10$	$1$	$1.745$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$1$	$2$	$0$	$-2$	$1$		$q-\zeta_{22}^{10}q^{2}+(-\zeta_{22}^{8}+\zeta_{22}^{9})q^{3}+\cdots$
3496.1.cb.c	$3496$	$1$	3496.cb	3496.bb	$22$	$20$	$2$	$1.745$	$\Q(\zeta_{33})$	$D_{33}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$-2$	$2$	$0$	$2$	$1$		$q-\zeta_{66}^{27}q^{2}+(\zeta_{66}^{10}+\zeta_{66}^{26})q^{3}+\cdots$
3496.1.cb.d	$3496$	$1$	3496.cb	3496.bb	$22$	$20$	$2$	$1.745$	$\Q(\zeta_{33})$	$D_{33}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$2$	$-2$	$0$	$2$	$1$		$q+\zeta_{66}^{27}q^{2}+(-\zeta_{66}^{4}-\zeta_{66}^{32})q^{3}+\cdots$
3648.1.l.a	$3648$	$1$	3648.l	456.l	$2$	$2$	$2$	$1.821$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-38}) $	$\Q(\sqrt{114}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{3}-iq^{7}-q^{9}-q^{13}+iq^{19}+\cdots$
3648.1.l.b	$3648$	$1$	3648.l	456.l	$2$	$2$	$2$	$1.821$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-38}) $	$\Q(\sqrt{114}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}-iq^{7}-q^{9}+q^{13}-iq^{19}+\cdots$
3648.1.l.c	$3648$	$1$	3648.l	456.l	$2$	$4$	$4$	$1.821$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-38}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{12}q^{3}+\zeta_{12}^{3}q^{7}+\zeta_{12}^{2}q^{9}-q^{13}+\cdots$
3648.1.l.d	$3648$	$1$	3648.l	456.l	$2$	$4$	$4$	$1.821$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-38}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{12}^{5}q^{3}-\zeta_{12}^{3}q^{7}-\zeta_{12}^{4}q^{9}+\cdots$
3800.1.b.a	$3800$	$1$	3800.b	760.b	$2$	$2$	$2$	$1.896$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-iq^{3}-q^{4}-q^{6}-iq^{7}+iq^{8}+\cdots$

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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.