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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 118 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
83.1.b.a	$83$	$1$	83.b	83.b	$2$	$1$	$1$	$0.041$	$\Q$	$D_{3}$	$\Q(\sqrt{-83}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$-1$	$1$		$q-q^{3}+q^{4}-q^{7}-q^{11}-q^{12}+q^{16}+\cdots$
332.1.d.a	$332$	$1$	332.d	83.b	$2$	$3$	$3$	$0.166$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-83}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{7}+(1+\beta _{2})q^{9}+\cdots$
581.1.g.b	$581$	$1$	581.g	581.g	$6$	$6$	$3$	$0.290$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}-\zeta_{18}^{5})q^{3}-\zeta_{18}^{3}q^{4}+\zeta_{18}^{8}q^{7}+\cdots$
747.1.c.a	$747$	$1$	747.c	83.b	$2$	$1$	$1$	$0.373$	$\Q$	$D_{3}$	$\Q(\sqrt{-83}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$-1$	$1$		$q+q^{4}-q^{7}+q^{11}+q^{16}+q^{17}-2q^{23}+\cdots$
747.1.g.a	$747$	$1$	747.g	747.g	$6$	$6$	$3$	$0.373$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{8}q^{3}-\zeta_{18}^{3}q^{4}+(\zeta_{18}^{4}+\zeta_{18}^{8}+\cdots)q^{7}+\cdots$
913.1.h.a	$913$	$1$	913.h	913.h	$10$	$4$	$1$	$0.456$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$3$	$0$	$3$	$1$		$q+(1+\zeta_{10}^{4})q^{3}-\zeta_{10}^{3}q^{4}+(1-\zeta_{10}+\cdots)q^{7}+\cdots$
913.1.h.b	$913$	$1$	913.h	913.h	$10$	$8$	$2$	$0.456$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$-3$	$0$	$-3$	$1$		$q+(\zeta_{30}^{2}+\zeta_{30}^{10})q^{3}-\zeta_{30}^{9}q^{4}+(\zeta_{30}^{8}+\cdots)q^{7}+\cdots$
1328.1.g.a	$1328$	$1$	1328.g	83.b	$2$	$1$	$1$	$0.663$	$\Q$	$D_{3}$	$\Q(\sqrt{-83}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$1$	$1$		$q+q^{3}+q^{7}+q^{11}-q^{17}+q^{21}-2q^{23}+\cdots$
1328.1.g.b	$1328$	$1$	1328.g	83.b	$2$	$3$	$3$	$0.663$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-83}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+(1+\beta _{2})q^{9}+\cdots$
1411.1.b.a	$1411$	$1$	1411.b	1411.b	$2$	$1$	$1$	$0.704$	$\Q$	$D_{2}$	$\Q(\sqrt{-83}) $, $\Q(\sqrt{-1411}) $	$\Q(\sqrt{17}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}+q^{9}+q^{16}-q^{17}-q^{25}+q^{36}+\cdots$
1411.1.b.b	$1411$	$1$	1411.b	1411.b	$2$	$2$	$2$	$0.704$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{3}+q^{4}+(\zeta_{6}+\zeta_{6}^{2})q^{7}+\cdots$
1411.1.f.a	$1411$	$1$	1411.f	1411.f	$4$	$2$	$1$	$0.704$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$-2$	$0$	$2$	$1$		$q+(-1-i)q^{3}-q^{4}+(1-i)q^{7}+iq^{9}+\cdots$
1411.1.f.b	$1411$	$1$	1411.f	1411.f	$4$	$4$	$2$	$0.704$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$2$	$0$	$-2$	$1$		$q+(-\zeta_{12}+\zeta_{12}^{2})q^{3}-q^{4}+(-\zeta_{12}+\cdots)q^{7}+\cdots$
1411.1.h.a	$1411$	$1$	1411.h	1411.h	$8$	$4$	$1$	$0.704$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$0$	$0$	$-4$	$1$		$q+(-\zeta_{8}+\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+(-1+\cdots)q^{7}+\cdots$
1411.1.h.b	$1411$	$1$	1411.h	1411.h	$8$	$8$	$2$	$0.704$	$\Q(\zeta_{24})$	$D_{24}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$0$	$0$	$4$	$1$		$q+(-\zeta_{24}+\zeta_{24}^{2})q^{3}-\zeta_{24}^{6}q^{4}+(\zeta_{24}+\cdots)q^{7}+\cdots$
1743.1.f.c	$1743$	$1$	1743.f	1743.f	$2$	$1$	$1$	$0.870$	$\Q$	$D_{2}$	$\Q(\sqrt{-83}) $, $\Q(\sqrt{-1743}) $	$\Q(\sqrt{21}) $	✓	$4$	$0$	$0$	$-1$	$0$	$-1$	$1$		$q-q^{3}-q^{4}-q^{7}+q^{9}+q^{12}+q^{16}+\cdots$
1743.1.f.d	$1743$	$1$	1743.f	1743.f	$2$	$1$	$1$	$0.870$	$\Q$	$D_{2}$	$\Q(\sqrt{-83}) $, $\Q(\sqrt{-1743}) $	$\Q(\sqrt{21}) $	✓	$4$	$0$	$0$	$1$	$0$	$-1$	$1$		$q+q^{3}-q^{4}-q^{7}+q^{9}-q^{12}+q^{16}+\cdots$
1743.1.f.h	$1743$	$1$	1743.f	1743.f	$2$	$2$	$2$	$0.870$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$-1$	$0$	$1$	$1$		$q+\zeta_{6}^{2}q^{3}-q^{4}-\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots$
1743.1.f.i	$1743$	$1$	1743.f	1743.f	$2$	$2$	$2$	$0.870$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$1$	$0$	$1$	$1$		$q-\zeta_{6}^{2}q^{3}-q^{4}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+(\zeta_{6}+\cdots)q^{11}+\cdots$
1743.1.l.a	$1743$	$1$	1743.l	1743.l	$6$	$6$	$3$	$0.870$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{4}q^{3}-\zeta_{18}^{6}q^{4}+\zeta_{18}q^{7}+\zeta_{18}^{8}q^{9}+\cdots$
1743.1.l.b	$1743$	$1$	1743.l	1743.l	$6$	$6$	$3$	$0.870$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{2}q^{3}-\zeta_{18}^{6}q^{4}+\zeta_{18}^{7}q^{7}+\cdots$
1909.1.h.a	$1909$	$1$	1909.h	1909.h	$22$	$10$	$1$	$0.953$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$9$	$0$	$-2$	$1$		$q+(1+\zeta_{22}^{2})q^{3}-\zeta_{22}^{3}q^{4}+(-\zeta_{22}^{3}+\cdots)q^{7}+\cdots$
1909.1.h.b	$1909$	$1$	1909.h	1909.h	$22$	$20$	$2$	$0.953$	$\Q(\zeta_{33})$	$D_{33}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$-9$	$0$	$2$	$11$		$q+(-\zeta_{66}-\zeta_{66}^{11})q^{3}+\zeta_{66}^{18}q^{4}+\cdots$
2075.1.c.a	$2075$	$1$	2075.c	83.b	$2$	$1$	$1$	$1.036$	$\Q$	$D_{3}$	$\Q(\sqrt{-83}) $	None	✓	$2$	$0$	$0$	$-2$	$0$	$1$	$1$		$q-2q^{3}+q^{4}+q^{7}+3q^{9}-q^{11}-2q^{12}+\cdots$
2075.1.c.b	$2075$	$1$	2075.c	83.b	$2$	$1$	$1$	$1.036$	$\Q$	$D_{3}$	$\Q(\sqrt{-83}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$-1$	$1$		$q-q^{3}+q^{4}-q^{7}-q^{11}-q^{12}+q^{16}+\cdots$
2075.1.c.c	$2075$	$1$	2075.c	83.b	$2$	$1$	$1$	$1.036$	$\Q$	$D_{3}$	$\Q(\sqrt{-83}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$2$	$1$		$q-q^{3}+q^{4}+2q^{7}+2q^{11}-q^{12}+\cdots$
2075.1.c.d	$2075$	$1$	2075.c	83.b	$2$	$1$	$1$	$1.036$	$\Q$	$D_{3}$	$\Q(\sqrt{-83}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$-2$	$1$		$q+q^{3}+q^{4}-2q^{7}+2q^{11}+q^{12}+\cdots$
2075.1.c.e	$2075$	$1$	2075.c	83.b	$2$	$1$	$1$	$1.036$	$\Q$	$D_{3}$	$\Q(\sqrt{-83}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$1$	$1$		$q+q^{3}+q^{4}+q^{7}-q^{11}+q^{12}+q^{16}+\cdots$
2075.1.c.f	$2075$	$1$	2075.c	83.b	$2$	$1$	$1$	$1.036$	$\Q$	$D_{3}$	$\Q(\sqrt{-83}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$1$	$1$		$q+q^{3}+q^{4}+q^{7}-q^{11}+q^{12}+q^{16}+\cdots$
2075.1.c.g	$2075$	$1$	2075.c	83.b	$2$	$1$	$1$	$1.036$	$\Q$	$D_{3}$	$\Q(\sqrt{-83}) $	None	✓	$2$	$0$	$0$	$2$	$0$	$-1$	$1$		$q+2q^{3}+q^{4}-q^{7}+3q^{9}-q^{11}+2q^{12}+\cdots$
2075.1.d.a	$2075$	$1$	2075.d	415.d	$2$	$2$	$2$	$1.036$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}-q^{4}-iq^{7}-3q^{9}-q^{11}+\cdots$
2075.1.d.b	$2075$	$1$	2075.d	415.d	$2$	$2$	$2$	$1.036$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}-q^{4}+iq^{7}-q^{11}+iq^{12}+\cdots$
2075.1.d.c	$2075$	$1$	2075.d	415.d	$2$	$2$	$2$	$1.036$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{3}-q^{4}-iq^{7}-q^{11}-iq^{12}+\cdots$
2075.1.d.d	$2075$	$1$	2075.d	415.d	$2$	$2$	$2$	$1.036$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}-q^{4}-iq^{7}+q^{11}+iq^{12}+\cdots$
2241.1.g.a	$2241$	$1$	2241.g	747.g	$6$	$6$	$3$	$1.118$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$3$		$q+\zeta_{18}^{6}q^{4}+(-\zeta_{18}^{7}+\zeta_{18}^{8})q^{7}+\cdots$
2241.1.k.a	$2241$	$1$	2241.k	2241.k	$18$	$18$	$3$	$1.118$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{54}^{17}q^{3}-\zeta_{54}^{21}q^{4}+(\zeta_{54}^{4}+\zeta_{54}^{8}+\cdots)q^{7}+\cdots$
2324.1.k.a	$2324$	$1$	2324.k	581.g	$6$	$2$	$1$	$1.160$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$-2$	$0$	$2$	$1$		$q-\zeta_{6}q^{3}+q^{7}+3\zeta_{6}^{2}q^{9}+\zeta_{6}q^{11}+\cdots$
2324.1.k.b	$2324$	$1$	2324.k	581.g	$6$	$2$	$1$	$1.160$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$1$	$0$	$-1$	$1$		$q+\zeta_{6}q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{11}+\zeta_{6}q^{17}+\cdots$
2324.1.k.c	$2324$	$1$	2324.k	581.g	$6$	$2$	$1$	$1.160$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$1$	$0$	$-1$	$1$		$q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{7}+\zeta_{6}q^{11}+\zeta_{6}q^{17}+\cdots$
2324.1.k.e	$2324$	$1$	2324.k	581.g	$6$	$6$	$3$	$1.160$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{3}+\zeta_{18}^{8}q^{7}+(-\zeta_{18}^{3}+\cdots)q^{9}+\cdots$
2407.1.d.a	$2407$	$1$	2407.d	2407.d	$2$	$1$	$1$	$1.201$	$\Q$	$D_{2}$	$\Q(\sqrt{-83}) $, $\Q(\sqrt{-2407}) $	$\Q(\sqrt{29}) $	✓	$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q-q^{4}+2q^{7}+q^{9}+q^{16}-2q^{23}+\cdots$
2407.1.d.c	$2407$	$1$	2407.d	2407.d	$2$	$2$	$2$	$1.201$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{3}-q^{4}-q^{7}+(-1-\zeta_{6}+\cdots)q^{9}+\cdots$
2407.1.h.a	$2407$	$1$	2407.h	2407.h	$14$	$6$	$1$	$1.201$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$0$	$0$	$5$	$1$		$q+\zeta_{14}^{5}q^{4}+(1+\zeta_{14}^{4})q^{7}+\zeta_{14}^{4}q^{9}+\cdots$
2407.1.h.b	$2407$	$1$	2407.h	2407.h	$14$	$12$	$2$	$1.201$	$\Q(\zeta_{21})$	$D_{42}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$0$	$0$	$-5$	$1$		$q+(-\zeta_{42}^{4}-\zeta_{42}^{11})q^{3}+\zeta_{42}^{3}q^{4}+\cdots$
2407.1.i.a	$2407$	$1$	2407.i	2407.i	$14$	$6$	$1$	$1.201$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$-2$	$0$	$5$	$1$		$q-\zeta_{14}q^{3}+\zeta_{14}^{6}q^{4}+(1+\zeta_{14}^{2})q^{7}+\cdots$
2407.1.i.b	$2407$	$1$	2407.i	2407.i	$14$	$12$	$2$	$1.201$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$2$	$0$	$-5$	$1$		$q+\zeta_{42}^{9}q^{3}+\zeta_{42}^{12}q^{4}+(\zeta_{42}^{4}+\zeta_{42}^{14}+\cdots)q^{7}+\cdots$
2573.1.g.a	$2573$	$1$	2573.g	2573.g	$6$	$6$	$3$	$1.284$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{3}+q^{4}+(-\zeta_{18}+\cdots)q^{7}+\cdots$
2573.1.k.a	$2573$	$1$	2573.k	2573.k	$10$	$4$	$1$	$1.284$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$3$	$0$	$-2$	$1$		$q+(1+\zeta_{10}^{2})q^{3}-\zeta_{10}^{3}q^{4}+(\zeta_{10}^{2}+\cdots)q^{7}+\cdots$
2573.1.k.b	$2573$	$1$	2573.k	2573.k	$10$	$8$	$2$	$1.284$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$-3$	$0$	$2$	$1$		$q+(\zeta_{30}^{10}-\zeta_{30}^{11})q^{3}-\zeta_{30}^{9}q^{4}+\cdots$
2573.1.p.a	$2573$	$1$	2573.p	2573.p	$30$	$24$	$3$	$1.284$	$\Q(\zeta_{45})$	$D_{45}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{90}^{25}-\zeta_{90}^{41})q^{3}-\zeta_{90}^{9}q^{4}+\cdots$

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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.