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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 461 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
145.1.f.a	$145$	$1$	145.f	145.f	$4$	$2$	$1$	$0.072$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{4}-iq^{5}+iq^{9}+(-1-i)q^{11}+\cdots$
145.1.h.a	$145$	$1$	145.h	145.h	$4$	$2$	$1$	$0.072$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{29}) $		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-iq^{4}-iq^{5}+(-1+i)q^{7}+iq^{9}+\cdots$
328.1.n.a	$328$	$1$	328.n	328.n	$8$	$4$	$1$	$0.164$	$\Q(\zeta_{8})$	$D_{8}$	None	$\Q(\sqrt{2}) $		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\zeta_{8}^{2})q^{7}+\cdots$
371.1.i.a	$371$	$1$	371.i	371.i	$6$	$2$	$1$	$0.185$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{53}) $		$4$	$0$	$0$	$0$	$0$	$-1$	$1$		$q+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{7}+\zeta_{6}q^{9}+\zeta_{6}^{2}q^{11}+\cdots$
380.1.o.a	$380$	$1$	380.o	95.h	$6$	$2$	$1$	$0.190$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{9}+q^{11}+\zeta_{6}^{2}q^{19}+\cdots$
396.1.d.a	$396$	$1$	396.d	132.d	$2$	$4$	$4$	$0.198$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{11}) $		$8$	$0$	$0$	$0$	$0$	$0$	$2$		$q+\zeta_{8}^{2}q^{2}-q^{4}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$
435.1.b.a	$435$	$1$	435.b	435.b	$2$	$4$	$4$	$0.217$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{145}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-\zeta_{8}q^{3}-q^{4}+\zeta_{8}^{2}q^{5}+\cdots$
444.1.h.a	$444$	$1$	444.h	111.d	$2$	$2$	$2$	$0.222$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{37}) $		$4$	$0$	$0$	$-1$	$0$	$2$	$1$		$q+\zeta_{6}^{2}q^{3}+q^{7}-\zeta_{6}q^{9}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{11}+\cdots$
445.1.g.a	$445$	$1$	445.g	445.g	$4$	$2$	$1$	$0.222$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{89}) $		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q+(-1-i)q^{2}+iq^{4}-iq^{5}-q^{8}+\cdots$
468.1.z.a	$468$	$1$	468.z	117.n	$6$	$2$	$1$	$0.234$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{13}) $		$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{13}+(-\zeta_{6}+\cdots)q^{17}+\cdots$
505.1.g.a	$505$	$1$	505.g	505.g	$4$	$2$	$1$	$0.252$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+iq^{4}+q^{5}+iq^{9}+(-1-i)q^{11}+\cdots$
505.1.h.a	$505$	$1$	505.h	505.h	$4$	$2$	$1$	$0.252$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{101}) $		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+iq^{4}+q^{5}-iq^{9}+(-1+i)q^{13}+\cdots$
520.1.bg.a	$520$	$1$	520.bg	520.ag	$4$	$4$	$2$	$0.260$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{26}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}q^{5}-\zeta_{8}^{3}q^{8}+\cdots$
520.1.bo.a	$520$	$1$	520.bo	520.ao	$4$	$4$	$2$	$0.260$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{10}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{3}q^{2}+(-\zeta_{8}+\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots$
592.1.b.b	$592$	$1$	592.b	148.b	$2$	$2$	$2$	$0.295$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{37}) $		$4$	$0$	$0$	$0$	$0$	$0$	$2$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{3}+(\zeta_{6}+\zeta_{6}^{2})q^{7}+(-1+\cdots)q^{9}+\cdots$
616.1.z.a	$616$	$1$	616.z	616.z	$6$	$2$	$1$	$0.307$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{22}) $		$4$	$0$	$-1$	$-3$	$0$	$1$	$1$		$q-\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+\zeta_{6}^{2}q^{4}+\cdots$
616.1.z.b	$616$	$1$	616.z	616.z	$6$	$2$	$1$	$0.307$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{22}) $		$4$	$0$	$1$	$-3$	$0$	$-1$	$1$		$q+\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+\zeta_{6}^{2}q^{4}+\cdots$
620.1.q.a	$620$	$1$	620.q	155.i	$6$	$2$	$1$	$0.309$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+\zeta_{6}q^{5}+\zeta_{6}q^{9}+(-1+\zeta_{6}^{2})q^{11}+\cdots$
632.1.l.a	$632$	$1$	632.l	632.l	$6$	$2$	$1$	$0.315$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{2}) $		$4$	$0$	$-1$	$0$	$0$	$-3$	$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+(-1-\zeta_{6})q^{7}+\cdots$
656.1.m.a	$656$	$1$	656.m	656.m	$4$	$2$	$1$	$0.327$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{41}) $		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q-iq^{2}-q^{4}+(1+i)q^{5}+iq^{8}+iq^{9}+\cdots$
687.1.d.e	$687$	$1$	687.d	687.d	$2$	$2$	$2$	$0.343$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{229}) $		$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{3}-q^{4}+(-\zeta_{6}-\zeta_{6}^{2})q^{5}+\cdots$
689.1.g.a	$689$	$1$	689.g	689.g	$4$	$2$	$1$	$0.344$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{53}) $		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-iq^{4}+(-1-i)q^{7}+q^{9}+(1+i+\cdots)q^{11}+\cdots$
689.1.i.a	$689$	$1$	689.i	689.i	$4$	$2$	$1$	$0.344$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{13}) $		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+(1+i)q^{3}+iq^{4}+iq^{9}+(-1+i+\cdots)q^{12}+\cdots$
695.1.h.a	$695$	$1$	695.h	695.h	$6$	$2$	$1$	$0.347$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q-\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{9}+\zeta_{6}q^{11}+\cdots$
725.1.g.a	$725$	$1$	725.g	29.c	$4$	$2$	$1$	$0.362$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{4}-iq^{9}+(-1-i)q^{11}-q^{16}+\cdots$
725.1.h.a	$725$	$1$	725.h	145.h	$4$	$2$	$1$	$0.362$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{29}) $		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q-iq^{4}+(1-i)q^{7}+iq^{9}+(-1-i+\cdots)q^{13}+\cdots$
755.1.k.a	$755$	$1$	755.k	755.k	$6$	$2$	$1$	$0.377$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}-q^{9}+\zeta_{6}q^{11}+\cdots$
756.1.d.a	$756$	$1$	756.d	7.b	$2$	$2$	$2$	$0.377$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{21}) $		$4$	$0$	$0$	$0$	$0$	$-2$	$2$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{5}-q^{7}+(\zeta_{6}+\zeta_{6}^{2})q^{17}+\cdots$
765.1.v.a	$765$	$1$	765.v	765.v	$6$	$4$	$2$	$0.382$	$\Q(\zeta_{12})$	$D_{6}$	None	$\Q(\sqrt{85}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{4}+\zeta_{12}q^{5}+(-\zeta_{12}+\cdots)q^{7}+\cdots$
777.1.n.b	$777$	$1$	777.n	777.n	$4$	$2$	$1$	$0.388$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{21}) $		$4$	$0$	$0$	$0$	$-2$	$2$	$1$		$q+iq^{3}+iq^{4}+(-1+i)q^{5}+q^{7}+\cdots$
777.1.n.c	$777$	$1$	777.n	777.n	$4$	$2$	$1$	$0.388$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{21}) $		$4$	$0$	$0$	$0$	$2$	$2$	$1$		$q-iq^{3}+iq^{4}+(1-i)q^{5}+q^{7}-q^{9}+\cdots$
793.1.k.a	$793$	$1$	793.k	793.k	$4$	$2$	$1$	$0.396$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{13}) $		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{3}+iq^{4}-3q^{9}-2q^{12}+q^{13}+\cdots$
793.1.m.a	$793$	$1$	793.m	793.m	$4$	$2$	$1$	$0.396$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{61}) $		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+iq^{4}+(1+i)q^{5}-q^{9}+q^{13}-q^{16}+\cdots$
793.1.bn.a	$793$	$1$	793.bn	793.an	$12$	$4$	$1$	$0.396$	$\Q(\zeta_{12})$	$D_{12}$	None	$\Q(\sqrt{61}) $		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}q^{4}+(\zeta_{12}^{4}+\cdots)q^{5}+\cdots$
812.1.o.a	$812$	$1$	812.o	203.i	$6$	$2$	$1$	$0.405$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{29}) $		$4$	$0$	$0$	$0$	$-3$	$1$	$1$		$q+(-1-\zeta_{6})q^{5}+\zeta_{6}q^{7}-\zeta_{6}^{2}q^{9}+\cdots$
824.1.n.a	$824$	$1$	824.n	824.n	$6$	$2$	$1$	$0.411$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{2}) $		$4$	$0$	$1$	$0$	$0$	$-2$	$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{7}-q^{8}+\cdots$
837.1.d.a	$837$	$1$	837.d	31.b	$2$	$2$	$2$	$0.418$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{93}) $		$4$	$0$	$0$	$0$	$0$	$-2$	$2$		$q-q^{4}-q^{7}+(\zeta_{6}+\zeta_{6}^{2})q^{11}+q^{16}+\cdots$
852.1.o.a	$852$	$1$	852.o	852.o	$10$	$4$	$1$	$0.425$	$\Q(\zeta_{10})$	$D_{10}$	None	$\Q(\sqrt{3}) $		$4$	$0$	$-1$	$1$	$0$	$0$	$1$		$q+\zeta_{10}^{2}q^{2}-\zeta_{10}^{2}q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
852.1.o.b	$852$	$1$	852.o	852.o	$10$	$4$	$1$	$0.425$	$\Q(\zeta_{10})$	$D_{10}$	None	$\Q(\sqrt{3}) $		$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q-\zeta_{10}^{2}q^{2}+\zeta_{10}^{2}q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
897.1.m.b	$897$	$1$	897.m	897.m	$4$	$2$	$1$	$0.448$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{69}) $		$4$	$0$	$0$	$-2$	$-2$	$0$	$1$		$q-q^{3}-iq^{4}+(-1+i)q^{5}+q^{9}+(-1+\cdots)q^{11}+\cdots$
897.1.m.c	$897$	$1$	897.m	897.m	$4$	$2$	$1$	$0.448$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{69}) $		$4$	$0$	$0$	$-2$	$2$	$0$	$1$		$q-q^{3}-iq^{4}+(1-i)q^{5}+q^{9}+(1+i+\cdots)q^{11}+\cdots$
901.1.h.a	$901$	$1$	901.h	901.h	$4$	$2$	$1$	$0.450$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{17}) $		$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+(1+i)q^{2}+iq^{4}+q^{8}+iq^{9}+q^{16}+\cdots$
905.1.g.a	$905$	$1$	905.g	905.g	$4$	$2$	$1$	$0.452$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+iq^{4}+q^{5}+q^{9}-iq^{11}-q^{16}+\cdots$
905.1.h.a	$905$	$1$	905.h	905.h	$4$	$2$	$1$	$0.452$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{181}) $		$4$	$0$	$0$	$-2$	$-2$	$0$	$1$		$q+(-1+i)q^{3}+iq^{4}-q^{5}-iq^{9}+\cdots$
981.1.n.a	$981$	$1$	981.n	981.n	$6$	$2$	$1$	$0.490$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{109}) $		$4$	$0$	$0$	$1$	$3$	$-2$	$1$		$q-\zeta_{6}^{2}q^{3}+\zeta_{6}q^{4}+(1-\zeta_{6}^{2})q^{5}+\zeta_{6}^{2}q^{7}+\cdots$
984.1.m.e	$984$	$1$	984.m	984.m	$2$	$4$	$4$	$0.491$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{82}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}-\zeta_{8}^{3}q^{6}+\cdots$
995.1.i.a	$995$	$1$	995.i	995.i	$6$	$2$	$1$	$0.497$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+\zeta_{6}^{2}q^{4}+q^{5}-\zeta_{6}^{2}q^{9}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{11}+\cdots$
995.1.p.a	$995$	$1$	995.p	995.p	$18$	$6$	$1$	$0.497$	$\Q(\zeta_{18})$	$D_{18}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$-3$	$0$	$1$		$q-\zeta_{18}^{5}q^{4}-\zeta_{18}^{3}q^{5}-\zeta_{18}^{2}q^{9}+\cdots$
1025.1.f.a	$1025$	$1$	1025.f	205.f	$4$	$2$	$1$	$0.512$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{4}+q^{9}+(1+i)q^{11}-q^{16}+(-1+\cdots)q^{19}+\cdots$
1025.1.i.a	$1025$	$1$	1025.i	205.i	$4$	$2$	$1$	$0.512$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{4}-q^{9}+(1-i)q^{11}-q^{16}+(1+\cdots)q^{19}+\cdots$

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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.