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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 113 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
111.1.d.a	$111$	$1$	111.d	111.d	$2$	$1$	$1$	$0.055$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-111}) $	$\Q(\sqrt{37}) $	✓	$4$	$0$	$0$	$1$	$0$	$-2$	$1$		$q+q^{3}-q^{4}-2q^{7}+q^{9}-q^{12}+q^{16}+\cdots$
111.1.d.b	$111$	$1$	111.d	111.d	$2$	$2$	$2$	$0.055$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-111}) $	None	✓	$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-\beta q^{2}-q^{3}+q^{4}+\beta q^{5}+\beta q^{6}+q^{9}+\cdots$
555.1.b.a	$555$	$1$	555.b	555.b	$2$	$8$	$8$	$0.277$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-111}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{16}-\zeta_{16}^{7})q^{2}+\zeta_{16}^{4}q^{3}+(-1+\cdots)q^{4}+\cdots$
777.1.w.a	$777$	$1$	777.w	777.w	$6$	$2$	$1$	$0.388$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-111}) $	None		$4$	$0$	$-1$	$-1$	$2$	$2$	$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{5}+q^{6}+q^{7}+\cdots$
777.1.w.b	$777$	$1$	777.w	777.w	$6$	$2$	$1$	$0.388$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-111}) $	None		$4$	$0$	$1$	$-1$	$-2$	$2$	$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{5}-q^{6}+q^{7}+\cdots$
777.1.w.c	$777$	$1$	777.w	777.w	$6$	$4$	$2$	$0.388$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-111}) $	None		$8$	$0$	$0$	$-2$	$0$	$-4$	$3$		$q+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{2}-\zeta_{12}^{2}q^{3}+\cdots$
777.1.w.d	$777$	$1$	777.w	777.w	$6$	$8$	$4$	$0.388$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-111}) $	None		$8$	$0$	$0$	$4$	$0$	$0$	$1$		$q+(\zeta_{24}^{7}+\zeta_{24}^{9})q^{2}+\zeta_{24}^{4}q^{3}+(-\zeta_{24}^{2}+\cdots)q^{4}+\cdots$
888.1.i.e	$888$	$1$	888.i	888.i	$2$	$8$	$8$	$0.443$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-111}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{16}q^{2}-\zeta_{16}^{4}q^{3}+\zeta_{16}^{2}q^{4}+(\zeta_{16}^{3}+\cdots)q^{5}+\cdots$
999.1.d.a	$999$	$1$	999.d	111.d	$2$	$1$	$1$	$0.499$	$\Q$	$D_{3}$	$\Q(\sqrt{-111}) $	None	✓	$2$	$0$	$-2$	$0$	$1$	$-1$	$1$		$q-2q^{2}+3q^{4}+q^{5}-q^{7}-4q^{8}-2q^{10}+\cdots$
999.1.d.b	$999$	$1$	999.d	111.d	$2$	$1$	$1$	$0.499$	$\Q$	$D_{3}$	$\Q(\sqrt{-111}) $	None	✓	$2$	$0$	$2$	$0$	$-1$	$-1$	$1$		$q+2q^{2}+3q^{4}-q^{5}-q^{7}+4q^{8}-2q^{10}+\cdots$
999.1.d.c	$999$	$1$	999.d	111.d	$2$	$2$	$2$	$0.499$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-111}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q-q^{4}-\beta q^{5}+q^{7}+q^{16}+\beta q^{17}+\cdots$
999.1.d.d	$999$	$1$	999.d	111.d	$2$	$4$	$4$	$0.499$	$\Q(\zeta_{24})^+$	$D_{12}$	$\Q(\sqrt{-111}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\beta _{1}-\beta _{3})q^{2}+q^{4}-\beta _{1}q^{5}-\beta _{2}q^{7}+\cdots$
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}) $	✓	$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}+q^{8}+q^{16}-2q^{23}+q^{25}+\cdots$
1332.1.b.c	$1332$	$1$	1332.b	148.b	$2$	$2$	$2$	$0.665$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-111}) $	$\Q(\sqrt{111}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-q^{4}-iq^{5}+iq^{8}-2q^{10}+\cdots$
1332.1.b.d	$1332$	$1$	1332.b	148.b	$2$	$4$	$4$	$0.665$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-111}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots$
1665.1.t.a	$1665$	$1$	1665.t	185.h	$4$	$16$	$8$	$0.831$	$\Q(\zeta_{32})$	$D_{16}$	$\Q(\sqrt{-111}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{32}^{9}-\zeta_{32}^{15})q^{2}+(-\zeta_{32}^{2}+\cdots)q^{4}+\cdots$
1776.1.n.a	$1776$	$1$	1776.n	111.d	$2$	$1$	$1$	$0.886$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-111}) $	$\Q(\sqrt{37}) $	✓	$4$	$0$	$0$	$-1$	$0$	$2$	$1$		$q-q^{3}+2q^{7}+q^{9}-2q^{21}-q^{25}+\cdots$
1776.1.n.c	$1776$	$1$	1776.n	111.d	$2$	$2$	$2$	$0.886$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-111}) $	None	✓	$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+q^{3}-\beta q^{5}+q^{9}-\beta q^{15}+\beta q^{17}+\cdots$
1776.1.z.c	$1776$	$1$	1776.z	1776.z	$4$	$16$	$8$	$0.886$	$\Q(\zeta_{32})$	$D_{16}$	$\Q(\sqrt{-111}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{32}^{3}q^{2}+\zeta_{32}^{4}q^{3}+\zeta_{32}^{6}q^{4}+\cdots$
1887.1.g.e	$1887$	$1$	1887.g	1887.g	$2$	$8$	$8$	$0.942$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-111}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{16}^{3}-\zeta_{16}^{5})q^{2}-\zeta_{16}^{4}q^{3}+(1+\cdots)q^{4}+\cdots$
1887.1.j.a	$1887$	$1$	1887.j	1887.j	$4$	$16$	$8$	$0.942$	$\Q(\zeta_{32})$	$D_{16}$	$\Q(\sqrt{-111}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{32}^{7}-\zeta_{32}^{9})q^{2}-\zeta_{32}^{4}q^{3}+\cdots$
1887.1.bh.a	$1887$	$1$	1887.bh	1887.ah	$8$	$32$	$8$	$0.942$	$\Q(\zeta_{64})$	$D_{32}$	$\Q(\sqrt{-111}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{64}^{19}+\zeta_{64}^{29})q^{2}-\zeta_{64}^{4}q^{3}+\cdots$
2220.1.bf.a	$2220$	$1$	2220.bf	2220.af	$4$	$16$	$8$	$1.108$	$\Q(\zeta_{32})$	$D_{16}$	$\Q(\sqrt{-111}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{32}^{3}q^{2}-\zeta_{32}^{12}q^{3}+\zeta_{32}^{6}q^{4}+\cdots$
2220.1.bf.b	$2220$	$1$	2220.bf	2220.af	$4$	$16$	$8$	$1.108$	$\Q(\zeta_{32})$	$D_{16}$	$\Q(\sqrt{-111}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{32}^{3}q^{2}-\zeta_{32}^{4}q^{3}+\zeta_{32}^{6}q^{4}+\cdots$
2331.1.e.a	$2331$	$1$	2331.e	259.b	$2$	$1$	$1$	$1.163$	$\Q$	$D_{2}$	$\Q(\sqrt{-111}) $, $\Q(\sqrt{-259}) $	$\Q(\sqrt{21}) $	✓	$4$	$0$	$0$	$0$	$-2$	$-1$	$1$		$q+q^{4}-2q^{5}-q^{7}+q^{16}+2q^{17}+\cdots$
2331.1.e.e	$2331$	$1$	2331.e	259.b	$2$	$1$	$1$	$1.163$	$\Q$	$D_{2}$	$\Q(\sqrt{-111}) $, $\Q(\sqrt{-259}) $	$\Q(\sqrt{21}) $	✓	$4$	$0$	$0$	$0$	$2$	$-1$	$1$		$q+q^{4}+2q^{5}-q^{7}+q^{16}-2q^{17}+\cdots$
2331.1.e.f	$2331$	$1$	2331.e	259.b	$2$	$2$	$2$	$1.163$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-111}) $	$\Q(\sqrt{777}) $		$8$	$0$	$0$	$0$	$0$	$2$	$2$		$q-iq^{2}-3q^{4}+q^{7}+4iq^{8}-2iq^{14}+\cdots$
2331.1.e.g	$2331$	$1$	2331.e	259.b	$2$	$4$	$4$	$1.163$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-111}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}-q^{4}+(-\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{5}+\cdots$
2331.1.dd.a	$2331$	$1$	2331.dd	259.t	$6$	$2$	$1$	$1.163$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-111}) $	None		$4$	$0$	$-3$	$0$	$2$	$-2$	$1$		$q+(-1-\zeta_{6})q^{2}+(1+\zeta_{6}+\zeta_{6}^{2})q^{4}+\cdots$
2331.1.dd.b	$2331$	$1$	2331.dd	259.t	$6$	$2$	$1$	$1.163$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-111}) $	None		$4$	$0$	$3$	$0$	$-2$	$-2$	$1$		$q+(1+\zeta_{6})q^{2}+(1+\zeta_{6}+\zeta_{6}^{2})q^{4}+\zeta_{6}^{2}q^{5}+\cdots$
2331.1.dd.c	$2331$	$1$	2331.dd	259.t	$6$	$4$	$2$	$1.163$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-111}) $	None		$8$	$0$	$0$	$0$	$0$	$4$	$1$		$q+\zeta_{12}^{5}q^{2}+q^{7}-\zeta_{12}^{3}q^{8}+\zeta_{12}^{5}q^{14}+\cdots$
2331.1.dd.d	$2331$	$1$	2331.dd	259.t	$6$	$8$	$4$	$1.163$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-111}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{24}^{9}+\zeta_{24}^{11})q^{2}+(-\zeta_{24}^{6}-\zeta_{24}^{8}+\cdots)q^{4}+\cdots$
2553.1.bh.a	$2553$	$1$	2553.bh	2553.ah	$22$	$10$	$1$	$1.274$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-111}) $	None		$4$	$0$	$-2$	$-1$	$-2$	$-2$	$1$		$q+(-\zeta_{22}+\zeta_{22}^{2})q^{2}-\zeta_{22}q^{3}+(\zeta_{22}^{2}+\cdots)q^{4}+\cdots$
2553.1.bh.b	$2553$	$1$	2553.bh	2553.ah	$22$	$10$	$1$	$1.274$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-111}) $	None		$4$	$0$	$2$	$-1$	$2$	$-2$	$1$		$q+(\zeta_{22}-\zeta_{22}^{2})q^{2}-\zeta_{22}q^{3}+(\zeta_{22}^{2}+\cdots)q^{4}+\cdots$
2553.1.bh.c	$2553$	$1$	2553.bh	2553.ah	$22$	$20$	$2$	$1.274$	$\Q(\zeta_{44})$	$D_{22}$	$\Q(\sqrt{-111}) $	None		$8$	$0$	$0$	$-2$	$0$	$4$	$1$		$q+(-\zeta_{44}+\zeta_{44}^{17})q^{2}-\zeta_{44}^{6}q^{3}+\cdots$
2553.1.bh.d	$2553$	$1$	2553.bh	2553.ah	$22$	$40$	$4$	$1.274$	$\Q(\zeta_{88})$	$D_{44}$	$\Q(\sqrt{-111}) $	None		$8$	$0$	$0$	$4$	$0$	$0$	$1$		$q+(-\zeta_{88}^{7}-\zeta_{88}^{9})q^{2}+\zeta_{88}^{20}q^{3}+\cdots$
2664.1.m.c	$2664$	$1$	2664.m	296.h	$2$	$8$	$8$	$1.330$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-111}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{16}q^{2}+\zeta_{16}^{2}q^{4}+(-\zeta_{16}^{3}+\zeta_{16}^{5}+\cdots)q^{5}+\cdots$
2775.1.b.a	$2775$	$1$	2775.b	555.b	$2$	$2$	$2$	$1.385$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-111}) $	$\Q(\sqrt{37}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}+q^{4}-iq^{7}-q^{9}-iq^{12}+\cdots$
2775.1.b.b	$2775$	$1$	2775.b	555.b	$2$	$4$	$4$	$1.385$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-111}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\cdots$
2775.1.h.a	$2775$	$1$	2775.h	111.d	$2$	$1$	$1$	$1.385$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-111}) $	$\Q(\sqrt{37}) $	✓	$4$	$0$	$0$	$-1$	$0$	$2$	$1$		$q-q^{3}-q^{4}+2q^{7}+q^{9}+q^{12}+q^{16}+\cdots$
2775.1.h.b	$2775$	$1$	2775.h	111.d	$2$	$2$	$2$	$1.385$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-111}) $	None	✓	$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q-\beta q^{2}+q^{3}+q^{4}-\beta q^{6}+q^{9}+q^{12}+\cdots$
2775.1.h.c	$2775$	$1$	2775.h	111.d	$2$	$4$	$4$	$1.385$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-111}) $	None	✓	$4$	$0$	$0$	$-4$	$0$	$0$	$1$		$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
2775.1.h.d	$2775$	$1$	2775.h	111.d	$2$	$4$	$4$	$1.385$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-111}) $	None	✓	$4$	$0$	$0$	$4$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
2775.1.bg.a	$2775$	$1$	2775.bg	2775.ag	$10$	$4$	$1$	$1.385$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-111}) $	None		$4$	$0$	$-2$	$-1$	$-1$	$8$	$1$		$q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}-\zeta_{10}q^{3}+(-\zeta_{10}+\cdots)q^{4}+\cdots$
2775.1.bg.b	$2775$	$1$	2775.bg	2775.ag	$10$	$4$	$1$	$1.385$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-111}) $	None		$4$	$0$	$2$	$-1$	$1$	$8$	$1$		$q+(-\zeta_{10}^{2}-\zeta_{10}^{4})q^{2}-\zeta_{10}q^{3}+(-\zeta_{10}+\cdots)q^{4}+\cdots$
2775.1.bg.c	$2775$	$1$	2775.bg	2775.ag	$10$	$8$	$2$	$1.385$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-111}) $	None		$8$	$0$	$0$	$-2$	$0$	$-16$	$1$		$q+(-\zeta_{20}^{3}-\zeta_{20}^{9})q^{2}-\zeta_{20}^{2}q^{3}+\cdots$
2775.1.bg.d	$2775$	$1$	2775.bg	2775.ag	$10$	$16$	$4$	$1.385$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-111}) $	None		$8$	$0$	$0$	$4$	$0$	$0$	$1$		$q+(\zeta_{40}+\zeta_{40}^{7})q^{2}-\zeta_{40}^{8}q^{3}+(\zeta_{40}^{2}+\cdots)q^{4}+\cdots$
2775.1.bi.a	$2775$	$1$	2775.bi	2775.ai	$10$	$32$	$8$	$1.385$	$\Q(\zeta_{80})$	$D_{40}$	$\Q(\sqrt{-111}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{80}^{17}-\zeta_{80}^{31})q^{2}+\zeta_{80}^{28}q^{3}+\cdots$
2997.1.n.a	$2997$	$1$	2997.n	333.n	$6$	$2$	$1$	$1.496$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-111}) $	None		$4$	$0$	$-2$	$0$	$1$	$1$	$1$		$q+\zeta_{6}^{2}q^{2}-3\zeta_{6}q^{4}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+\cdots$

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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.