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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 7241 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
1001.1.y.a	$1001$	$1$	1001.y	1001.y	$6$	$2$	$1$	$0.500$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-143}) $	None		$4$	$0$	$-1$	$1$	$0$	$1$	$1$		$q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-q^{6}+\zeta_{6}q^{7}-q^{8}+\cdots$
1001.1.y.b	$1001$	$1$	1001.y	1001.y	$6$	$2$	$1$	$0.500$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-143}) $	None		$4$	$0$	$1$	$1$	$0$	$-1$	$1$		$q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}+q^{6}-\zeta_{6}q^{7}+q^{8}+\cdots$
1003.1.b.b	$1003$	$1$	1003.b	1003.b	$2$	$2$	$2$	$0.501$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$2$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{3}+q^{4}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{5}+\cdots$
1003.1.f.a	$1003$	$1$	1003.f	1003.f	$4$	$2$	$1$	$0.501$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$-2$	$-2$	$-2$	$1$		$q+(-1+i)q^{3}-q^{4}+(-1+i)q^{5}+\cdots$
1007.1.d.c	$1007$	$1$	1007.d	1007.d	$2$	$2$	$2$	$0.503$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-1007}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$-1$	$1$		$q+(-1+\beta )q^{2}-\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots$
1007.1.d.d	$1007$	$1$	1007.d	1007.d	$2$	$2$	$2$	$0.503$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-1007}) $	None	✓	$2$	$0$	$1$	$1$	$0$	$-1$	$1$		$q+(1-\beta )q^{2}+\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots$
1008.1.u.a	$1008$	$1$	1008.u	112.l	$4$	$2$	$1$	$0.503$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}+iq^{7}-q^{8}+(1-i)q^{11}+\cdots$
1008.1.u.b	$1008$	$1$	1008.u	112.l	$4$	$2$	$1$	$0.503$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{2}-q^{4}-iq^{7}-iq^{8}+(1-i+\cdots)q^{11}+\cdots$
1008.1.u.c	$1008$	$1$	1008.u	112.l	$4$	$2$	$1$	$0.503$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}+iq^{7}+q^{8}+(-1+i+\cdots)q^{11}+\cdots$
1008.1.cd.a	$1008$	$1$	1008.cd	28.g	$6$	$2$	$1$	$0.503$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-1$	$1$		$q+\zeta_{6}^{2}q^{7}+q^{13}+(1+\zeta_{6})q^{19}+\zeta_{6}q^{25}+\cdots$
1008.1.cd.b	$1008$	$1$	1008.cd	28.g	$6$	$2$	$1$	$0.503$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$1$	$1$		$q-\zeta_{6}^{2}q^{7}+q^{13}+(-1-\zeta_{6})q^{19}+\cdots$
1008.1.cg.a	$1008$	$1$	1008.cg	7.d	$6$	$2$	$1$	$0.503$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-1$	$1$		$q-\zeta_{6}q^{7}+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+(1-\zeta_{6}^{2}+\cdots)q^{19}+\cdots$
1011.1.c.d	$1011$	$1$	1011.c	1011.c	$2$	$2$	$2$	$0.505$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-1011}) $	None	✓	$4$	$0$	$0$	$-2$	$0$	$-2$	$1$		$q-q^{3}+q^{4}-\beta q^{5}-q^{7}+q^{9}-q^{12}+\cdots$
1011.1.f.a	$1011$	$1$	1011.f	1011.f	$4$	$2$	$1$	$0.505$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}+q^{4}-q^{9}-iq^{12}+q^{16}+\cdots$
1015.1.f.c	$1015$	$1$	1015.f	1015.f	$2$	$2$	$2$	$0.507$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-1015}) $	None	✓	$4$	$0$	$0$	$0$	$-2$	$2$	$1$		$q-\beta q^{2}+q^{4}-q^{5}+q^{7}+q^{9}+\beta q^{10}+\cdots$
1015.1.f.d	$1015$	$1$	1015.f	1015.f	$2$	$2$	$2$	$0.507$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-1015}) $	None	✓	$4$	$0$	$0$	$0$	$2$	$-2$	$1$		$q-\beta q^{2}+q^{4}+q^{5}-q^{7}+q^{9}-\beta q^{10}+\cdots$
1016.1.h.b	$1016$	$1$	1016.h	1016.h	$2$	$2$	$2$	$0.507$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-254}) $	None	✓	$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+q^{2}-\beta q^{3}+q^{4}+\beta q^{5}-\beta q^{6}+q^{8}+\cdots$
1023.1.g.c	$1023$	$1$	1023.g	1023.g	$2$	$2$	$2$	$0.511$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-1023}) $	None	✓	$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-\beta q^{2}-q^{3}+q^{4}+\beta q^{6}+q^{9}+q^{11}+\cdots$
1023.1.g.d	$1023$	$1$	1023.g	1023.g	$2$	$2$	$2$	$0.511$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-1023}) $	None	✓	$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q-\beta q^{2}+q^{3}+q^{4}-\beta q^{6}+q^{9}-q^{11}+\cdots$
1023.1.u.a	$1023$	$1$	1023.u	1023.u	$6$	$2$	$1$	$0.511$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-1$	$-3$	$0$	$1$		$q+\zeta_{6}^{2}q^{3}-q^{4}+(-1+\zeta_{6}^{2})q^{5}-\zeta_{6}q^{9}+\cdots$
1023.1.u.b	$1023$	$1$	1023.u	1023.u	$6$	$2$	$1$	$0.511$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$1$	$3$	$0$	$1$		$q-\zeta_{6}^{2}q^{3}-q^{4}+(1-\zeta_{6}^{2})q^{5}-\zeta_{6}q^{9}+\cdots$
1024.1.c.a	$1024$	$1$	1024.c	4.b	$2$	$2$	$2$	$0.511$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta q^{5}+q^{9}+\beta q^{13}+q^{25}+\beta q^{29}+\cdots$
1024.1.d.a	$1024$	$1$	1024.d	8.d	$2$	$2$	$2$	$0.511$	$\Q(\sqrt{-2}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta q^{5}-q^{9}-\beta q^{13}-q^{25}-\beta q^{29}+\cdots$
1024.1.f.a	$1024$	$1$	1024.f	16.f	$4$	$2$	$1$	$0.511$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q+(-1-i)q^{3}+iq^{9}+(1-i)q^{11}+\cdots$
1024.1.f.b	$1024$	$1$	1024.f	16.f	$4$	$2$	$1$	$0.511$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{2}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{9}+q^{17}-iq^{25}+iq^{41}-q^{49}+\cdots$
1024.1.f.c	$1024$	$1$	1024.f	16.f	$4$	$2$	$1$	$0.511$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+(1+i)q^{3}+iq^{9}+(-1+i)q^{11}+\cdots$
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}) $		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{4}-q^{9}+(1-i)q^{11}-q^{16}+(1+\cdots)q^{19}+\cdots$
1027.1.o.a	$1027$	$1$	1027.o	1027.o	$6$	$2$	$1$	$0.513$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$1$	$0$	$-2$	$0$	$1$		$q-\zeta_{6}^{2}q^{2}-q^{5}+q^{8}-\zeta_{6}q^{9}+\zeta_{6}^{2}q^{10}+\cdots$
1027.1.s.a	$1027$	$1$	1027.s	1027.s	$6$	$2$	$1$	$0.513$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$3$	$0$	$0$	$0$	$1$		$q+(1-\zeta_{6}^{2})q^{2}+(1-\zeta_{6}-\zeta_{6}^{2})q^{4}+\cdots$
1027.1.u.a	$1027$	$1$	1027.u	1027.u	$6$	$2$	$1$	$0.513$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{13}) $		$4$	$0$	$0$	$3$	$0$	$0$	$1$		$q+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+(1+\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{9}+\cdots$
1028.1.d.b	$1028$	$1$	1028.d	1028.d	$2$	$2$	$2$	$0.513$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{257}) $		$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{8}-q^{9}+(\zeta_{6}+\cdots)q^{11}+\cdots$
1028.1.d.c	$1028$	$1$	1028.d	1028.d	$2$	$2$	$2$	$0.513$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-257}) $	None	✓	$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+q^{2}-\beta q^{3}+q^{4}-\beta q^{6}+\beta q^{7}+q^{8}+\cdots$
1028.1.e.a	$1028$	$1$	1028.e	1028.e	$4$	$2$	$1$	$0.513$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$2$	$0$	$-2$	$0$	$1$		$q+q^{2}+q^{4}+(-1+i)q^{5}+q^{8}+iq^{9}+\cdots$
1031.1.b.a	$1031$	$1$	1031.b	1031.b	$2$	$2$	$2$	$0.515$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-1031}) $	None	✓	$2$	$0$	$-1$	$4$	$-1$	$0$	$1$		$q+(-1+\beta )q^{2}+2q^{3}+(1-\beta )q^{4}+(-1+\cdots)q^{5}+\cdots$
1032.1.bb.a	$1032$	$1$	1032.bb	1032.ab	$6$	$2$	$1$	$0.515$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-2$	$-1$	$0$	$0$	$1$		$q-q^{2}+\zeta_{6}^{2}q^{3}+q^{4}-\zeta_{6}^{2}q^{6}-q^{8}+\cdots$
1032.1.bb.b	$1032$	$1$	1032.bb	1032.ab	$6$	$2$	$1$	$0.515$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$2$	$1$	$0$	$0$	$1$		$q+q^{2}-\zeta_{6}^{2}q^{3}+q^{4}-\zeta_{6}^{2}q^{6}+q^{8}+\cdots$
1036.1.e.c	$1036$	$1$	1036.e	259.b	$2$	$2$	$2$	$0.517$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-259}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-\beta q^{5}-q^{7}+q^{9}+q^{11}+\beta q^{13}+\cdots$
1036.1.e.d	$1036$	$1$	1036.e	259.b	$2$	$2$	$2$	$0.517$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{37}) $		$4$	$0$	$0$	$0$	$0$	$1$	$1$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{3}+\zeta_{6}q^{7}+(-1-\zeta_{6}+\cdots)q^{9}+\cdots$
1036.1.n.a	$1036$	$1$	1036.n	1036.n	$4$	$2$	$1$	$0.517$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}+iq^{7}-q^{8}+q^{9}-iq^{14}+\cdots$
1036.1.n.b	$1036$	$1$	1036.n	1036.n	$4$	$2$	$1$	$0.517$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{2}-q^{4}-iq^{7}-iq^{8}+q^{9}+q^{14}+\cdots$
1040.1.l.a	$1040$	$1$	1040.l	260.g	$2$	$2$	$2$	$0.519$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-65}) $	None	✓	$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-\beta q^{3}-q^{5}+q^{9}-\beta q^{11}+q^{13}+\cdots$
1040.1.l.b	$1040$	$1$	1040.l	260.g	$2$	$2$	$2$	$0.519$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-65}) $	None	✓	$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q-\beta q^{3}+q^{5}+q^{9}+\beta q^{11}-q^{13}+\cdots$
1040.1.bf.a	$1040$	$1$	1040.bf	260.l	$4$	$2$	$1$	$0.519$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{5}-iq^{9}-iq^{13}+(-1+i)q^{17}+\cdots$
1040.1.ce.a	$1040$	$1$	1040.ce	260.s	$4$	$2$	$1$	$0.519$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-q^{5}-iq^{9}+q^{13}+(1-i)q^{17}+q^{25}+\cdots$
1040.1.cx.a	$1040$	$1$	1040.cx	260.v	$6$	$2$	$1$	$0.519$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{9}-\zeta_{6}q^{13}+(1+\zeta_{6}+\cdots)q^{17}+\cdots$
1040.1.cx.b	$1040$	$1$	1040.cx	260.v	$6$	$2$	$1$	$0.519$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q-\zeta_{6}^{2}q^{5}-\zeta_{6}^{2}q^{9}+\zeta_{6}q^{13}+(-1+\cdots)q^{17}+\cdots$
1043.1.c.b	$1043$	$1$	1043.c	1043.c	$2$	$2$	$2$	$0.521$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-1043}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-\beta q^{3}+q^{4}-q^{7}+q^{9}-\beta q^{12}+\beta q^{13}+\cdots$
1044.1.g.c	$1044$	$1$	1044.g	116.d	$2$	$2$	$2$	$0.521$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-87}) $	$\Q(\sqrt{87}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-q^{4}+iq^{8}+q^{13}+q^{16}+\cdots$
1045.1.k.a	$1045$	$1$	1045.k	1045.k	$4$	$2$	$1$	$0.522$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{209}) $		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q+(-1-i)q^{2}+iq^{4}-iq^{5}-q^{8}+\cdots$

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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.