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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 514 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
23.1.b.a	$23$	$1$	23.b	23.b	$2$	$1$	$1$	$0.011$	$\Q$	$D_{3}$	$\Q(\sqrt{-23}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q-q^{2}-q^{3}+q^{6}+q^{8}-q^{13}-q^{16}+\cdots$
184.1.e.a	$184$	$1$	184.e	184.e	$2$	$1$	$1$	$0.092$	$\Q$	$D_{2}$	$\Q(\sqrt{-23}) $, $\Q(\sqrt{-46}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{18}+\cdots$
184.1.e.b	$184$	$1$	184.e	184.e	$2$	$2$	$2$	$0.092$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{2}+(\zeta_{6}+\zeta_{6}^{2})q^{3}-\zeta_{6}q^{4}+\cdots$
207.1.d.a	$207$	$1$	207.d	23.b	$2$	$1$	$1$	$0.103$	$\Q$	$D_{3}$	$\Q(\sqrt{-23}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}-q^{8}-q^{13}-q^{16}-q^{23}+q^{25}+\cdots$
207.1.f.a	$207$	$1$	207.f	207.f	$6$	$6$	$3$	$0.103$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{2}+\zeta_{18}^{2}q^{3}+(-\zeta_{18}^{3}+\cdots)q^{4}+\cdots$
276.1.h.a	$276$	$1$	276.h	276.h	$2$	$1$	$1$	$0.138$	$\Q$	$D_{2}$	$\Q(\sqrt{-23}) $, $\Q(\sqrt{-69}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$-1$	$1$	$0$	$0$	$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
276.1.h.b	$276$	$1$	276.h	276.h	$2$	$1$	$1$	$0.138$	$\Q$	$D_{2}$	$\Q(\sqrt{-23}) $, $\Q(\sqrt{-69}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
276.1.h.c	$276$	$1$	276.h	276.h	$2$	$2$	$2$	$0.138$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$-1$	$1$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots$
276.1.h.d	$276$	$1$	276.h	276.h	$2$	$2$	$2$	$0.138$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-q^{6}-q^{8}+\cdots$
299.1.c.a	$299$	$1$	299.c	299.c	$2$	$1$	$1$	$0.149$	$\Q$	$D_{2}$	$\Q(\sqrt{-23}) $, $\Q(\sqrt{-299}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-2q^{3}+q^{4}+3q^{9}-2q^{12}+q^{13}+\cdots$
299.1.c.c	$299$	$1$	299.c	299.c	$2$	$2$	$2$	$0.149$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{2}+q^{3}+(-1-\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{4}+\cdots$
299.1.h.a	$299$	$1$	299.h	299.h	$6$	$6$	$3$	$0.149$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}-\zeta_{18}^{5})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{4}+\cdots)q^{3}+\cdots$
299.1.j.a	$299$	$1$	299.j	299.j	$6$	$6$	$3$	$0.149$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{4}-\zeta_{18}^{8})q^{2}+(\zeta_{18}^{5}+\zeta_{18}^{7}+\cdots)q^{3}+\cdots$
368.1.f.a	$368$	$1$	368.f	23.b	$2$	$1$	$1$	$0.184$	$\Q$	$D_{3}$	$\Q(\sqrt{-23}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}-q^{13}-q^{23}+q^{25}-q^{27}+\cdots$
368.1.k.a	$368$	$1$	368.k	368.k	$4$	$2$	$1$	$0.184$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q-iq^{2}+(1-i)q^{3}-q^{4}+(-1-i+\cdots)q^{6}+\cdots$
368.1.k.b	$368$	$1$	368.k	368.k	$4$	$4$	$2$	$0.184$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q+\zeta_{12}^{5}q^{2}+(\zeta_{12}-\zeta_{12}^{2})q^{3}-\zeta_{12}^{4}q^{4}+\cdots$
529.1.d.a	$529$	$1$	529.d	23.d	$22$	$10$	$1$	$0.264$	$\Q(\zeta_{22})$	$D_{3}$	$\Q(\sqrt{-23}) $	None		$20$	$0$	$1$	$1$	$0$	$0$	$1$		$q-\zeta_{22}^{2}q^{2}+\zeta_{22}^{5}q^{3}-\zeta_{22}^{7}q^{6}+\cdots$
552.1.h.a	$552$	$1$	552.h	552.h	$2$	$1$	$1$	$0.275$	$\Q$	$D_{2}$	$\Q(\sqrt{-23}) $, $\Q(\sqrt{-138}) $	$\Q(\sqrt{6}) $	✓	$4$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
552.1.h.b	$552$	$1$	552.h	552.h	$2$	$1$	$1$	$0.275$	$\Q$	$D_{2}$	$\Q(\sqrt{-23}) $, $\Q(\sqrt{-138}) $	$\Q(\sqrt{6}) $	✓	$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
552.1.h.c	$552$	$1$	552.h	552.h	$2$	$2$	$2$	$0.275$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$-1$	$1$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-q^{6}+q^{8}+\cdots$
552.1.h.d	$552$	$1$	552.h	552.h	$2$	$2$	$2$	$0.275$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$1$	$1$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots$
575.1.c.a	$575$	$1$	575.c	115.c	$2$	$2$	$2$	$0.287$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}+iq^{3}+q^{6}-iq^{8}+iq^{13}+\cdots$
575.1.c.b	$575$	$1$	575.c	115.c	$2$	$6$	$6$	$0.287$	6.0.419904.1	$D_{9}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+(-\beta _{1}-\beta _{5})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$
575.1.d.a	$575$	$1$	575.d	23.b	$2$	$1$	$1$	$0.287$	$\Q$	$D_{3}$	$\Q(\sqrt{-23}) $	None	✓	$2$	$0$	$1$	$1$	$0$	$0$	$1$		$q+q^{2}+q^{3}+q^{6}-q^{8}+q^{13}-q^{16}+\cdots$
575.1.d.b	$575$	$1$	575.d	23.b	$2$	$3$	$3$	$0.287$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-23}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+\beta _{2}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots$
575.1.d.c	$575$	$1$	575.d	23.b	$2$	$3$	$3$	$0.287$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-23}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\beta _{1}q^{2}-\beta _{2}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots$
621.1.f.a	$621$	$1$	621.f	207.f	$6$	$6$	$3$	$0.310$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$3$		$q+(\zeta_{18}-\zeta_{18}^{2})q^{2}+(\zeta_{18}^{2}-\zeta_{18}^{3}+\cdots)q^{4}+\cdots$
621.1.k.a	$621$	$1$	621.k	621.k	$18$	$18$	$3$	$0.310$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{54}+\zeta_{54}^{20})q^{2}-\zeta_{54}^{5}q^{3}+\cdots$
667.1.b.a	$667$	$1$	667.b	667.b	$2$	$1$	$1$	$0.333$	$\Q$	$D_{2}$	$\Q(\sqrt{-23}) $, $\Q(\sqrt{-667}) $	$\Q(\sqrt{29}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}+q^{9}-2q^{13}+q^{16}-q^{23}+\cdots$
667.1.b.b	$667$	$1$	667.b	667.b	$2$	$2$	$2$	$0.333$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{2}+(\zeta_{6}+\zeta_{6}^{2})q^{3}+(-1+\cdots)q^{4}+\cdots$
667.1.i.a	$667$	$1$	667.i	667.i	$14$	$6$	$1$	$0.333$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$5$	$-2$	$0$	$0$	$1$		$q+(1+\zeta_{14}^{4})q^{2}+(-\zeta_{14}-\zeta_{14}^{5})q^{3}+\cdots$
667.1.i.b	$667$	$1$	667.i	667.i	$14$	$12$	$2$	$0.333$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$-5$	$2$	$0$	$0$	$1$		$q+(-\zeta_{42}+\zeta_{42}^{14})q^{2}+(\zeta_{42}^{16}-\zeta_{42}^{17}+\cdots)q^{3}+\cdots$
667.1.k.a	$667$	$1$	667.k	667.k	$14$	$6$	$1$	$0.333$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$-7$	$0$	$0$	$0$	$1$		$q+(-1+\zeta_{14}^{4})q^{2}+(-\zeta_{14}+\zeta_{14}^{5}+\cdots)q^{3}+\cdots$
667.1.k.b	$667$	$1$	667.k	667.k	$14$	$12$	$2$	$0.333$	$\Q(\zeta_{21})$	$D_{42}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$7$	$0$	$0$	$0$	$1$		$q+(\zeta_{42}^{7}+\zeta_{42}^{8})q^{2}+(\zeta_{42}^{2}-\zeta_{42}^{10}+\cdots)q^{3}+\cdots$
713.1.g.b	$713$	$1$	713.g	713.g	$6$	$6$	$3$	$0.356$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+(-\zeta_{18}^{5}-\zeta_{18}^{7}+\cdots)q^{3}+\cdots$
713.1.j.a	$713$	$1$	713.j	713.j	$10$	$4$	$1$	$0.356$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$3$	$-2$	$0$	$0$	$1$		$q+(1-\zeta_{10})q^{2}+(-\zeta_{10}-\zeta_{10}^{3})q^{3}+\cdots$
713.1.j.b	$713$	$1$	713.j	713.j	$10$	$8$	$2$	$0.356$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$-3$	$2$	$0$	$0$	$1$		$q+(-\zeta_{30}^{5}-\zeta_{30}^{13})q^{2}+(\zeta_{30}^{4}+\zeta_{30}^{8}+\cdots)q^{3}+\cdots$
713.1.t.a	$713$	$1$	713.t	713.t	$30$	$24$	$3$	$0.356$	$\Q(\zeta_{45})$	$D_{45}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{90}^{25}-\zeta_{90}^{29})q^{2}+(\zeta_{90}^{2}-\zeta_{90}^{19}+\cdots)q^{3}+\cdots$
736.1.e.a	$736$	$1$	736.e	184.e	$2$	$1$	$1$	$0.367$	$\Q$	$D_{2}$	$\Q(\sqrt{-23}) $, $\Q(\sqrt{-46}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{9}+q^{23}-q^{25}+2q^{31}-2q^{41}+\cdots$
736.1.e.b	$736$	$1$	736.e	184.e	$2$	$2$	$2$	$0.367$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$2$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{3}+(-1-\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{9}+\cdots$
736.1.p.a	$736$	$1$	736.p	736.p	$8$	$4$	$1$	$0.367$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$-4$	$0$	$0$	$1$		$q+\zeta_{8}q^{2}+(-1+\zeta_{8})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$
736.1.p.b	$736$	$1$	736.p	736.p	$8$	$8$	$2$	$0.367$	$\Q(\zeta_{24})$	$D_{24}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$4$	$0$	$0$	$1$		$q-\zeta_{24}^{5}q^{2}+(\zeta_{24}-\zeta_{24}^{8})q^{3}+\zeta_{24}^{10}q^{4}+\cdots$
828.1.j.a	$828$	$1$	828.j	828.j	$6$	$6$	$3$	$0.413$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{4}q^{2}+\zeta_{18}q^{3}+\zeta_{18}^{8}q^{4}+\zeta_{18}^{5}q^{6}+\cdots$
828.1.j.b	$828$	$1$	828.j	828.j	$6$	$6$	$3$	$0.413$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{2}q^{2}-\zeta_{18}q^{3}+\zeta_{18}^{4}q^{4}+\zeta_{18}^{3}q^{6}+\cdots$
897.1.m.a	$897$	$1$	897.m	897.m	$4$	$2$	$1$	$0.448$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q+(-1-i)q^{2}+iq^{3}+iq^{4}+(1-i+\cdots)q^{6}+\cdots$
897.1.m.d	$897$	$1$	897.m	897.m	$4$	$2$	$1$	$0.448$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+(1+i)q^{2}-iq^{3}+iq^{4}+(1-i)q^{6}+\cdots$
897.1.m.e	$897$	$1$	897.m	897.m	$4$	$4$	$2$	$0.448$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q+(-\zeta_{12}-\zeta_{12}^{2})q^{2}+\zeta_{12}^{5}q^{3}+(\zeta_{12}^{2}+\cdots)q^{4}+\cdots$
897.1.m.f	$897$	$1$	897.m	897.m	$4$	$4$	$2$	$0.448$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+\zeta_{12}q^{3}+(\zeta_{12}^{2}+\cdots)q^{4}+\cdots$
897.1.w.a	$897$	$1$	897.w	897.w	$12$	$12$	$3$	$0.448$	$\Q(\zeta_{36})$	$D_{36}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{36}^{7}+\zeta_{36}^{8})q^{2}+\zeta_{36}^{5}q^{3}+(\zeta_{36}^{14}+\cdots)q^{4}+\cdots$
897.1.w.b	$897$	$1$	897.w	897.w	$12$	$12$	$3$	$0.448$	$\Q(\zeta_{36})$	$D_{36}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{36}^{2}+\zeta_{36}^{13})q^{2}+\zeta_{36}^{7}q^{3}+(\zeta_{36}^{4}+\cdots)q^{4}+\cdots$

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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.