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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 1648 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
68.1.f.a	$68$	$1$	68.f	68.f	$4$	$2$	$1$	$0.034$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+iq^{2}-q^{4}+(-1-i)q^{5}-iq^{8}+\cdots$
95.1.d.b	$95$	$1$	95.d	95.d	$2$	$2$	$2$	$0.047$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-95}) $	None	✓	$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-\beta q^{2}+\beta q^{3}+q^{4}-q^{5}-2q^{6}+q^{9}+\cdots$
111.1.d.b	$111$	$1$	111.d	111.d	$2$	$2$	$2$	$0.055$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-111}) $	None	✓	$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-\beta q^{2}-q^{3}+q^{4}+\beta q^{5}+\beta q^{6}+q^{9}+\cdots$
112.1.l.a	$112$	$1$	112.l	112.l	$4$	$2$	$1$	$0.056$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{2}-q^{4}+iq^{7}-iq^{8}-iq^{9}+\cdots$
117.1.j.a	$117$	$1$	117.j	13.d	$4$	$2$	$1$	$0.058$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+iq^{4}+(-1-i)q^{7}-iq^{13}-q^{16}+\cdots$
136.1.j.a	$136$	$1$	136.j	136.j	$4$	$2$	$1$	$0.068$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-iq^{2}+(-1-i)q^{3}-q^{4}+(-1+i+\cdots)q^{6}+\cdots$
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}) $		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-iq^{4}-iq^{5}+(-1+i)q^{7}+iq^{9}+\cdots$
160.1.p.a	$160$	$1$	160.p	5.c	$4$	$2$	$1$	$0.080$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{5}+iq^{9}+(-1+i)q^{13}+(-1+\cdots)q^{17}+\cdots$
164.1.d.b	$164$	$1$	164.d	164.d	$2$	$2$	$2$	$0.082$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-41}) $	None	✓	$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}+\beta q^{7}-q^{8}+\cdots$
165.1.l.a	$165$	$1$	165.l	165.l	$4$	$2$	$1$	$0.082$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-q^{3}+iq^{4}+iq^{5}+q^{9}-iq^{11}+\cdots$
165.1.l.b	$165$	$1$	165.l	165.l	$4$	$2$	$1$	$0.082$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}+iq^{4}-iq^{5}-q^{9}+iq^{11}+\cdots$
180.1.m.a	$180$	$1$	180.m	60.l	$4$	$4$	$2$	$0.090$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{5}-\zeta_{8}q^{8}+\cdots$
183.1.d.b	$183$	$1$	183.d	183.d	$2$	$2$	$2$	$0.091$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-183}) $	None	✓	$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-\beta q^{2}-q^{3}+q^{4}+\beta q^{6}+q^{9}+\beta q^{11}+\cdots$
195.1.e.a	$195$	$1$	195.e	195.e	$2$	$4$	$4$	$0.097$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\cdots$
219.1.f.a	$219$	$1$	219.f	219.f	$4$	$2$	$1$	$0.109$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-iq^{3}+q^{4}+(-1+i)q^{7}-q^{9}-iq^{12}+\cdots$
240.1.bm.a	$240$	$1$	240.bm	240.am	$4$	$4$	$2$	$0.120$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{5}+\cdots$
248.1.g.b	$248$	$1$	248.g	248.g	$2$	$2$	$2$	$0.124$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-62}) $	None	✓	$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}-q^{8}+q^{9}+\cdots$
252.1.h.a	$252$	$1$	252.h	84.h	$2$	$4$	$4$	$0.126$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{2}q^{7}-\zeta_{8}^{3}q^{8}+\cdots$
255.1.i.a	$255$	$1$	255.i	255.i	$4$	$4$	$2$	$0.127$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+\zeta_{8}^{3}q^{3}-q^{4}+\cdots$
260.1.l.a	$260$	$1$	260.l	260.l	$4$	$2$	$1$	$0.130$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q-iq^{2}-q^{4}+q^{5}+iq^{8}-iq^{9}-iq^{10}+\cdots$
260.1.s.a	$260$	$1$	260.s	260.s	$4$	$2$	$1$	$0.130$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}+iq^{5}-q^{8}+iq^{9}-iq^{10}+\cdots$
272.1.g.a	$272$	$1$	272.g	68.d	$2$	$2$	$2$	$0.136$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-17}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta q^{3}+\beta q^{7}+q^{9}+\beta q^{11}-q^{17}+\cdots$
273.1.o.a	$273$	$1$	273.o	273.o	$4$	$2$	$1$	$0.136$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{3}+iq^{4}-iq^{7}-q^{9}-q^{12}+\cdots$
273.1.o.b	$273$	$1$	273.o	273.o	$4$	$2$	$1$	$0.136$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q-iq^{3}+iq^{4}+q^{7}-q^{9}+q^{12}-iq^{13}+\cdots$
280.1.c.a	$280$	$1$	280.c	280.c	$2$	$4$	$4$	$0.140$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-14}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}^{2}q^{2}+(-\zeta_{8}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots$
288.1.e.a	$288$	$1$	288.e	3.b	$2$	$2$	$2$	$0.144$	$\Q(\sqrt{-2}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta q^{5}+\beta q^{17}-q^{25}+\beta q^{29}-2q^{37}+\cdots$
291.1.g.a	$291$	$1$	291.g	291.g	$4$	$2$	$1$	$0.145$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q-iq^{3}-q^{4}+(1-i)q^{7}-q^{9}+iq^{12}+\cdots$
295.1.d.c	$295$	$1$	295.d	295.d	$2$	$2$	$2$	$0.147$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-295}) $	None	✓	$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-\beta q^{2}+q^{4}-q^{5}+q^{9}+\beta q^{10}+\beta q^{13}+\cdots$
299.1.c.b	$299$	$1$	299.c	299.c	$2$	$2$	$2$	$0.149$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-299}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}-\beta q^{5}+\beta q^{7}-q^{9}+\beta q^{11}+\cdots$
312.1.b.a	$312$	$1$	312.b	312.b	$2$	$4$	$4$	$0.156$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}-\zeta_{8}^{2}q^{3}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots$
320.1.p.a	$320$	$1$	320.p	5.c	$4$	$2$	$1$	$0.160$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{5}+iq^{9}+(1-i)q^{13}+(-1-i+\cdots)q^{17}+\cdots$
323.1.g.a	$323$	$1$	323.g	323.g	$4$	$2$	$1$	$0.161$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$2$	$-2$	$1$		$q-q^{4}+(1+i)q^{5}+(-1+i)q^{7}+iq^{9}+\cdots$
328.1.k.a	$328$	$1$	328.k	328.k	$4$	$2$	$1$	$0.164$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q-iq^{2}+(1-i)q^{3}-q^{4}+(-1-i+\cdots)q^{6}+\cdots$
333.1.i.a	$333$	$1$	333.i	37.d	$4$	$2$	$1$	$0.166$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{4}+(1-i)q^{13}-q^{16}+(-1+i+\cdots)q^{19}+\cdots$
360.1.u.a	$360$	$1$	360.u	40.i	$4$	$4$	$2$	$0.180$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-6}) $	None		$8$	$0$	$0$	$0$	$0$	$-4$	$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}+(-1+\cdots)q^{7}+\cdots$
368.1.k.a	$368$	$1$	368.k	368.k	$4$	$2$	$1$	$0.184$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q-iq^{2}+(1-i)q^{3}-q^{4}+(-1-i+\cdots)q^{6}+\cdots$
371.1.c.b	$371$	$1$	371.c	371.c	$2$	$2$	$2$	$0.185$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-371}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-\beta q^{3}+q^{4}+\beta q^{5}-q^{7}+q^{9}-\beta q^{12}+\cdots$
376.1.e.b	$376$	$1$	376.e	376.e	$2$	$2$	$2$	$0.188$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-94}) $	None	✓	$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-\beta q^{5}-q^{8}+q^{9}+\beta q^{10}+\cdots$
388.1.g.a	$388$	$1$	388.g	388.g	$4$	$2$	$1$	$0.194$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+iq^{2}-q^{4}+(1+i)q^{5}-iq^{8}-q^{9}+\cdots$
392.1.g.b	$392$	$1$	392.g	8.d	$2$	$2$	$2$	$0.196$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-2}) $	None	✓	$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}-q^{8}+q^{9}+\cdots$
392.1.k.b	$392$	$1$	392.k	56.k	$6$	$4$	$2$	$0.196$	$\Q(\sqrt{2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-2}) $	None		$8$	$0$	$2$	$0$	$0$	$0$	$1$		$q-\beta _{2}q^{2}-\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+\beta _{3}q^{6}+\cdots$
395.1.c.b	$395$	$1$	395.c	395.c	$2$	$2$	$2$	$0.197$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-395}) $	None	✓	$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-\beta q^{3}+q^{4}-q^{5}+\beta q^{7}+q^{9}-\beta q^{12}+\cdots$
396.1.d.a	$396$	$1$	396.d	132.d	$2$	$4$	$4$	$0.198$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{11}) $		$8$	$0$	$0$	$0$	$0$	$0$	$2$		$q+\zeta_{8}^{2}q^{2}-q^{4}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$
399.1.h.c	$399$	$1$	399.h	399.h	$2$	$2$	$2$	$0.199$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-399}) $	None	✓	$4$	$0$	$0$	$-2$	$0$	$-2$	$1$		$q-\beta q^{2}-q^{3}+q^{4}-\beta q^{5}+\beta q^{6}-q^{7}+\cdots$
399.1.h.d	$399$	$1$	399.h	399.h	$2$	$2$	$2$	$0.199$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-399}) $	None	✓	$4$	$0$	$0$	$2$	$0$	$-2$	$1$		$q-\beta q^{2}+q^{3}+q^{4}+\beta q^{5}-\beta q^{6}-q^{7}+\cdots$
407.1.d.b	$407$	$1$	407.d	407.d	$2$	$2$	$2$	$0.203$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-407}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta q^{2}+q^{4}-q^{9}+q^{11}+\beta q^{13}+\cdots$
416.1.t.a	$416$	$1$	416.t	13.d	$4$	$2$	$1$	$0.208$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+(1+i)q^{5}-q^{9}+iq^{13}-iq^{17}+\cdots$
435.1.b.a	$435$	$1$	435.b	435.b	$2$	$4$	$4$	$0.217$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{145}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-\zeta_{8}q^{3}-q^{4}+\zeta_{8}^{2}q^{5}+\cdots$
440.1.o.e	$440$	$1$	440.o	440.o	$2$	$4$	$4$	$0.220$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{2}q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots$

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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.