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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 66 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
144.1.g.a	$144$	$1$	144.g	4.b	$2$	$1$	$1$	$0.072$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-1}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-2q^{13}-q^{25}+2q^{37}+q^{49}+2q^{61}+\cdots$
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}) $	✓	$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
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}) $		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}-q^{6}+\cdots$
384.1.h.a	$384$	$1$	384.h	24.h	$2$	$1$	$1$	$0.192$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-q^{3}+q^{9}+2q^{11}-q^{25}-q^{27}+\cdots$
384.1.h.b	$384$	$1$	384.h	24.h	$2$	$1$	$1$	$0.192$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{9}-2q^{11}-q^{25}+q^{27}+\cdots$
468.1.e.a	$468$	$1$	468.e	52.b	$2$	$1$	$1$	$0.234$	$\Q$	$D_{2}$	$\Q(\sqrt{-39}) $, $\Q(\sqrt{-13}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-q^{8}+2q^{11}-q^{13}+q^{16}+\cdots$
468.1.e.b	$468$	$1$	468.e	52.b	$2$	$1$	$1$	$0.234$	$\Q$	$D_{2}$	$\Q(\sqrt{-39}) $, $\Q(\sqrt{-13}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}+q^{8}-2q^{11}-q^{13}+q^{16}+\cdots$
528.1.g.a	$528$	$1$	528.g	132.d	$2$	$1$	$1$	$0.264$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-33}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-q^{3}+q^{9}+q^{11}+2q^{23}+q^{25}+\cdots$
528.1.g.b	$528$	$1$	528.g	132.d	$2$	$1$	$1$	$0.264$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-33}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{9}-q^{11}-2q^{23}+q^{25}+\cdots$
564.1.f.a	$564$	$1$	564.f	564.f	$2$	$1$	$1$	$0.281$	$\Q$	$D_{2}$	$\Q(\sqrt{-47}) $, $\Q(\sqrt{-141}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$-1$	$1$	$0$	$0$	$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
564.1.f.b	$564$	$1$	564.f	564.f	$2$	$1$	$1$	$0.281$	$\Q$	$D_{2}$	$\Q(\sqrt{-47}) $, $\Q(\sqrt{-141}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
576.1.g.a	$576$	$1$	576.g	4.b	$2$	$1$	$1$	$0.287$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-1}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+2q^{13}-q^{25}-2q^{37}+q^{49}-2q^{61}+\cdots$
768.1.e.c	$768$	$1$	768.e	3.b	$2$	$2$	$2$	$0.383$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{3}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}-q^{9}-iq^{11}+q^{25}+iq^{27}+\cdots$
852.1.d.a	$852$	$1$	852.d	852.d	$2$	$1$	$1$	$0.425$	$\Q$	$D_{2}$	$\Q(\sqrt{-71}) $, $\Q(\sqrt{-213}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$-1$	$1$	$0$	$0$	$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
852.1.d.b	$852$	$1$	852.d	852.d	$2$	$1$	$1$	$0.425$	$\Q$	$D_{2}$	$\Q(\sqrt{-71}) $, $\Q(\sqrt{-213}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
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}) $		$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q-\zeta_{10}^{2}q^{2}+\zeta_{10}^{2}q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
1296.1.o.b	$1296$	$1$	1296.o	36.f	$6$	$2$	$1$	$0.647$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-1}) $	$\Q(\sqrt{3}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{13}+\zeta_{6}q^{25}+q^{37}+\zeta_{6}^{2}q^{49}+\cdots$
1332.1.b.a	$1332$	$1$	1332.b	148.b	$2$	$1$	$1$	$0.665$	$\Q$	$D_{2}$	$\Q(\sqrt{-111}) $, $\Q(\sqrt{-37}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-q^{8}+q^{16}+2q^{23}+q^{25}+\cdots$
1332.1.b.b	$1332$	$1$	1332.b	148.b	$2$	$1$	$1$	$0.665$	$\Q$	$D_{2}$	$\Q(\sqrt{-111}) $, $\Q(\sqrt{-37}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}+q^{8}+q^{16}-2q^{23}+q^{25}+\cdots$
1404.1.q.a	$1404$	$1$	1404.q	52.i	$6$	$2$	$1$	$0.701$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{3}) $		$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{8}+\zeta_{6}^{2}q^{11}+\cdots$
1404.1.q.b	$1404$	$1$	1404.q	52.i	$6$	$2$	$1$	$0.701$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{3}) $		$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}-\zeta_{6}^{2}q^{11}+\cdots$
1716.1.m.a	$1716$	$1$	1716.m	1716.m	$2$	$1$	$1$	$0.856$	$\Q$	$D_{2}$	$\Q(\sqrt{-143}) $, $\Q(\sqrt{-429}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
1716.1.m.b	$1716$	$1$	1716.m	1716.m	$2$	$1$	$1$	$0.856$	$\Q$	$D_{2}$	$\Q(\sqrt{-143}) $, $\Q(\sqrt{-429}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$-1$	$1$	$0$	$0$	$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
1716.1.m.c	$1716$	$1$	1716.m	1716.m	$2$	$1$	$1$	$0.856$	$\Q$	$D_{2}$	$\Q(\sqrt{-143}) $, $\Q(\sqrt{-429}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
1716.1.m.d	$1716$	$1$	1716.m	1716.m	$2$	$1$	$1$	$0.856$	$\Q$	$D_{2}$	$\Q(\sqrt{-143}) $, $\Q(\sqrt{-429}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$1$	$1$	$0$	$0$	$1$		$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
1764.1.g.c	$1764$	$1$	1764.g	4.b	$2$	$2$	$2$	$0.880$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{3}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-q^{4}+iq^{8}+iq^{11}+q^{16}+\cdots$
1764.1.y.c	$1764$	$1$	1764.y	28.g	$6$	$4$	$2$	$0.880$	$\Q(\zeta_{12})$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{3}) $		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{8}+\zeta_{12}^{5}q^{11}+\cdots$
2004.1.g.a	$2004$	$1$	2004.g	2004.g	$2$	$1$	$1$	$1.000$	$\Q$	$D_{2}$	$\Q(\sqrt{-167}) $, $\Q(\sqrt{-501}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
2004.1.g.b	$2004$	$1$	2004.g	2004.g	$2$	$1$	$1$	$1.000$	$\Q$	$D_{2}$	$\Q(\sqrt{-167}) $, $\Q(\sqrt{-501}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$1$	$1$	$0$	$0$	$1$		$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
2112.1.g.a	$2112$	$1$	2112.g	132.d	$2$	$1$	$1$	$1.054$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-33}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-q^{3}+q^{9}+q^{11}-2q^{23}+q^{25}+\cdots$
2112.1.g.b	$2112$	$1$	2112.g	132.d	$2$	$1$	$1$	$1.054$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-33}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{9}-q^{11}+2q^{23}+q^{25}+\cdots$
2196.1.h.a	$2196$	$1$	2196.h	244.c	$2$	$1$	$1$	$1.096$	$\Q$	$D_{2}$	$\Q(\sqrt{-183}) $, $\Q(\sqrt{-61}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-q^{8}+2q^{11}+2q^{13}+\cdots$
2196.1.h.c	$2196$	$1$	2196.h	244.c	$2$	$1$	$1$	$1.096$	$\Q$	$D_{2}$	$\Q(\sqrt{-183}) $, $\Q(\sqrt{-61}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}+q^{8}-2q^{11}+2q^{13}+\cdots$
2292.1.e.a	$2292$	$1$	2292.e	2292.e	$2$	$1$	$1$	$1.144$	$\Q$	$D_{2}$	$\Q(\sqrt{-191}) $, $\Q(\sqrt{-573}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
2292.1.e.b	$2292$	$1$	2292.e	2292.e	$2$	$1$	$1$	$1.144$	$\Q$	$D_{2}$	$\Q(\sqrt{-191}) $, $\Q(\sqrt{-573}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$1$	$1$	$0$	$0$	$1$		$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
2304.1.b.a	$2304$	$1$	2304.b	8.d	$2$	$2$	$2$	$1.150$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-1}) $	$\Q(\sqrt{3}) $		$8$	$0$	$0$	$0$	$0$	$0$	$2$		$q-iq^{13}+q^{25}-iq^{37}+q^{49}+iq^{61}+\cdots$
2628.1.p.b	$2628$	$1$	2628.p	292.g	$4$	$2$	$1$	$1.312$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{3}) $		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{2}-q^{4}-iq^{8}+(-1+i)q^{11}+\cdots$
2628.1.p.c	$2628$	$1$	2628.p	292.g	$4$	$2$	$1$	$1.312$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{3}) $		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-q^{4}+iq^{8}+(1-i)q^{11}+(-1+\cdots)q^{13}+\cdots$
2700.1.m.a	$2700$	$1$	2700.m	60.l	$4$	$8$	$4$	$1.347$	$\Q(\zeta_{24})$	$D_{6}$	None	$\Q(\sqrt{3}) $		$16$	$0$	$0$	$0$	$0$	$0$	$2^{4}$		$q-\zeta_{24}^{9}q^{2}-\zeta_{24}^{6}q^{4}-\zeta_{24}^{3}q^{8}+\cdots$
2832.1.b.a	$2832$	$1$	2832.b	708.b	$2$	$1$	$1$	$1.413$	$\Q$	$D_{2}$	$\Q(\sqrt{-59}) $, $\Q(\sqrt{-177}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-q^{3}+q^{9}+q^{25}-q^{27}+q^{49}+q^{59}+\cdots$
2832.1.b.b	$2832$	$1$	2832.b	708.b	$2$	$1$	$1$	$1.413$	$\Q$	$D_{2}$	$\Q(\sqrt{-59}) $, $\Q(\sqrt{-177}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{9}+q^{25}+q^{27}+q^{49}-q^{59}+\cdots$
2868.1.e.a	$2868$	$1$	2868.e	2868.e	$2$	$1$	$1$	$1.431$	$\Q$	$D_{2}$	$\Q(\sqrt{-239}) $, $\Q(\sqrt{-717}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
2868.1.e.b	$2868$	$1$	2868.e	2868.e	$2$	$1$	$1$	$1.431$	$\Q$	$D_{2}$	$\Q(\sqrt{-239}) $, $\Q(\sqrt{-717}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$1$	$1$	$0$	$0$	$1$		$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
3072.1.i.f	$3072$	$1$	3072.i	48.i	$4$	$4$	$2$	$1.533$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{3}) $		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{3}q^{3}-\zeta_{8}^{2}q^{9}-\zeta_{8}q^{11}-\zeta_{8}^{2}q^{25}+\cdots$
3156.1.h.a	$3156$	$1$	3156.h	3156.h	$2$	$1$	$1$	$1.575$	$\Q$	$D_{2}$	$\Q(\sqrt{-263}) $, $\Q(\sqrt{-789}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
3156.1.h.b	$3156$	$1$	3156.h	3156.h	$2$	$1$	$1$	$1.575$	$\Q$	$D_{2}$	$\Q(\sqrt{-263}) $, $\Q(\sqrt{-789}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$1$	$1$	$0$	$0$	$1$		$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
3492.1.p.a	$3492$	$1$	3492.p	388.g	$4$	$2$	$1$	$1.743$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{3}) $		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-q^{8}+(1+i)q^{13}+q^{16}+\cdots$
3492.1.p.c	$3492$	$1$	3492.p	388.g	$4$	$2$	$1$	$1.743$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{3}) $		$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}+q^{8}+(1+i)q^{13}+q^{16}+\cdots$

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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.