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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 88 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				Fricke sign	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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
3380.1.g.a	$3380$	$1$	3380.g	260.g	$2$	$2$	$2$	$1.687$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$-1$	$0$		$1$		$q-q^{2}+q^{4}+\zeta_{6}^{2}q^{5}-q^{8}-q^{9}-\zeta_{6}^{2}q^{10}+\cdots$
3380.1.g.b	$3380$	$1$	3380.g	260.g	$2$	$2$	$2$	$1.687$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$2$	$0$	$1$	$0$		$1$		$q+q^{2}+q^{4}-\zeta_{6}^{2}q^{5}+q^{8}-q^{9}-\zeta_{6}^{2}q^{10}+\cdots$
3380.1.g.c	$3380$	$1$	3380.g	260.g	$2$	$6$	$6$	$1.687$	6.0.153664.1	$D_{7}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+\beta _{5}q^{2}-\beta _{4}q^{3}-q^{4}+\beta _{5}q^{5}-\beta _{1}q^{6}+\cdots$
3380.1.g.d	$3380$	$1$	3380.g	260.g	$2$	$6$	$6$	$1.687$	6.0.153664.1	$D_{7}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+\beta _{5}q^{2}+\beta _{4}q^{3}-q^{4}-\beta _{5}q^{5}+\beta _{1}q^{6}+\cdots$
3380.1.h.a	$3380$	$1$	3380.h	20.d	$2$	$2$	$2$	$1.687$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-65}) $	$\Q(\sqrt{65}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+iq^{2}-q^{4}-iq^{5}-iq^{8}-q^{9}+q^{10}+\cdots$
3380.1.h.b	$3380$	$1$	3380.h	20.d	$2$	$3$	$3$	$1.687$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-5}) $	None	✓	$2$	$0$	$-3$	$-1$	$-3$	$1$		$1$		$q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
3380.1.h.c	$3380$	$1$	3380.h	20.d	$2$	$3$	$3$	$1.687$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-5}) $	None	✓	$2$	$0$	$-3$	$1$	$3$	$1$		$1$		$q-q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
3380.1.h.d	$3380$	$1$	3380.h	20.d	$2$	$3$	$3$	$1.687$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-5}) $	None	✓	$2$	$0$	$3$	$-1$	$3$	$-1$		$1$		$q+q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
3380.1.h.e	$3380$	$1$	3380.h	20.d	$2$	$3$	$3$	$1.687$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-5}) $	None	✓	$2$	$0$	$3$	$1$	$-3$	$-1$		$1$		$q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
3380.1.h.f	$3380$	$1$	3380.h	20.d	$2$	$4$	$4$	$1.687$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{3}q^{2}-q^{4}-\zeta_{12}q^{5}+\zeta_{12}^{3}q^{8}+\cdots$
3380.1.l.a	$3380$	$1$	3380.l	260.l	$4$	$2$	$1$	$1.687$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-iq^{2}-q^{4}-q^{5}+iq^{8}+iq^{9}+iq^{10}+\cdots$
3380.1.l.b	$3380$	$1$	3380.l	260.l	$4$	$4$	$2$	$1.687$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\zeta_{12}^{3}q^{2}-q^{4}-\zeta_{12}^{2}q^{5}+\zeta_{12}^{3}q^{8}+\cdots$
3380.1.l.c	$3380$	$1$	3380.l	260.l	$4$	$4$	$2$	$1.687$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\zeta_{12}^{3}q^{2}-q^{4}+\zeta_{12}^{2}q^{5}+\zeta_{12}^{3}q^{8}+\cdots$
3380.1.s.a	$3380$	$1$	3380.s	260.s	$4$	$2$	$1$	$1.687$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}-iq^{5}+q^{8}+iq^{9}-iq^{10}+\cdots$
3380.1.s.b	$3380$	$1$	3380.s	260.s	$4$	$4$	$2$	$1.687$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-4$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-\zeta_{12}q^{5}-q^{8}+\zeta_{12}^{3}q^{9}+\cdots$
3380.1.s.c	$3380$	$1$	3380.s	260.s	$4$	$4$	$2$	$1.687$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$4$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+\zeta_{12}^{5}q^{5}+q^{8}+\zeta_{12}^{3}q^{9}+\cdots$
3380.1.v.a	$3380$	$1$	3380.v	260.v	$6$	$4$	$2$	$1.687$	$\Q(\zeta_{12})$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-65}) $	$\Q(\sqrt{65}) $		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}-\zeta_{12}^{3}q^{8}+\cdots$
3380.1.v.b	$3380$	$1$	3380.v	260.v	$6$	$4$	$2$	$1.687$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}q^{5}+\zeta_{12}^{3}q^{8}+\cdots$
3380.1.v.c	$3380$	$1$	3380.v	260.v	$6$	$4$	$2$	$1.687$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{5}-\zeta_{12}^{3}q^{8}+\cdots$
3380.1.v.d	$3380$	$1$	3380.v	260.v	$6$	$6$	$3$	$1.687$	6.0.64827.1	$D_{7}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$-3$	$-1$	$-6$	$1$		$1$		$q-\beta _{5}q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3}-\beta _{4}-\beta _{5})q^{3}+\cdots$
3380.1.v.e	$3380$	$1$	3380.v	260.v	$6$	$6$	$3$	$1.687$	6.0.64827.1	$D_{7}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$-3$	$1$	$6$	$1$		$1$		$q-\beta _{5}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{3}+\cdots$
3380.1.v.f	$3380$	$1$	3380.v	260.v	$6$	$6$	$3$	$1.687$	6.0.64827.1	$D_{7}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$3$	$-1$	$6$	$-1$		$1$		$q+\beta _{5}q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3}-\beta _{4}-\beta _{5})q^{3}+\cdots$
3380.1.v.g	$3380$	$1$	3380.v	260.v	$6$	$6$	$3$	$1.687$	6.0.64827.1	$D_{7}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$3$	$1$	$-6$	$-1$		$1$		$q+\beta _{5}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{3}+\cdots$
3380.1.w.a	$3380$	$1$	3380.w	260.w	$6$	$2$	$1$	$1.687$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-65}) $	$\Q(\sqrt{65}) $		$8$	$0$	$-1$	$0$	$-2$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{5}+q^{8}+\zeta_{6}q^{9}+\cdots$
3380.1.w.b	$3380$	$1$	3380.w	260.w	$6$	$2$	$1$	$1.687$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$1$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+q^{8}+\zeta_{6}q^{9}+\cdots$
3380.1.w.c	$3380$	$1$	3380.w	260.w	$6$	$2$	$1$	$1.687$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$-1$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}-q^{8}+\cdots$
3380.1.w.d	$3380$	$1$	3380.w	260.w	$6$	$2$	$1$	$1.687$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-65}) $	$\Q(\sqrt{65}) $		$8$	$0$	$1$	$0$	$2$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{5}-q^{8}+\zeta_{6}q^{9}+\cdots$
3380.1.w.e	$3380$	$1$	3380.w	260.w	$6$	$12$	$6$	$1.687$	12.0.$\cdots$.1	$D_{7}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+\beta _{10}q^{2}+(-1+\beta _{3}+\beta _{5}-\beta _{9})q^{3}+\cdots$
3380.1.w.f	$3380$	$1$	3380.w	260.w	$6$	$12$	$6$	$1.687$	12.0.$\cdots$.1	$D_{7}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$2$	$0$	$0$		$1$		$q-\beta _{6}q^{2}-\beta _{9}q^{3}+\beta _{7}q^{4}+(\beta _{6}-\beta _{10}+\cdots)q^{5}+\cdots$
3380.1.be.a	$3380$	$1$	3380.be	260.ae	$12$	$4$	$1$	$1.687$	$\Q(\zeta_{12})$	$D_{4}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}-\zeta_{12}^{3}q^{5}+\cdots$
3380.1.be.b	$3380$	$1$	3380.be	260.ae	$12$	$4$	$1$	$1.687$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+\zeta_{12}^{5}q^{5}+\cdots$
3380.1.be.c	$3380$	$1$	3380.be	260.ae	$12$	$4$	$1$	$1.687$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+\zeta_{12}q^{5}+q^{8}+\cdots$
3380.1.be.d	$3380$	$1$	3380.be	260.ae	$12$	$4$	$1$	$1.687$	$\Q(\zeta_{12})$	$D_{4}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$2$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+\zeta_{12}^{3}q^{5}+\cdots$
3380.1.be.e	$3380$	$1$	3380.be	260.ae	$12$	$4$	$1$	$1.687$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}-\zeta_{12}q^{5}-q^{8}+\cdots$
3380.1.bl.a	$3380$	$1$	3380.bl	260.al	$12$	$4$	$1$	$1.687$	$\Q(\zeta_{12})$	$D_{4}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$-4$	$0$		$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-q^{5}+\zeta_{12}^{3}q^{8}+\cdots$
3380.1.bl.b	$3380$	$1$	3380.bl	260.al	$12$	$4$	$1$	$1.687$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{2}q^{5}+\cdots$
3380.1.bl.c	$3380$	$1$	3380.bl	260.al	$12$	$4$	$1$	$1.687$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{4}q^{5}+\cdots$
3380.1.bl.d	$3380$	$1$	3380.bl	260.al	$12$	$4$	$1$	$1.687$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{2}q^{5}+\cdots$
3380.1.bl.e	$3380$	$1$	3380.bl	260.al	$12$	$4$	$1$	$1.687$	$\Q(\zeta_{12})$	$D_{4}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$4$	$0$		$1$		$q-\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+q^{5}-\zeta_{12}^{3}q^{8}+\cdots$
3380.1.bq.a	$3380$	$1$	3380.bq	3380.aq	$26$	$12$	$1$	$1.687$	$\Q(\zeta_{26})$	$D_{26}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$1$	$0$		$1$		$q+\zeta_{26}^{10}q^{2}-\zeta_{26}^{7}q^{4}-\zeta_{26}^{2}q^{5}+\cdots$
3380.1.bq.b	$3380$	$1$	3380.bq	3380.aq	$26$	$12$	$1$	$1.687$	$\Q(\zeta_{26})$	$D_{26}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$-1$	$0$		$1$		$q-\zeta_{26}^{10}q^{2}-\zeta_{26}^{7}q^{4}-\zeta_{26}^{9}q^{5}+\cdots$
3380.1.bz.a	$3380$	$1$	3380.bz	3380.az	$52$	$24$	$1$	$1.687$	$\Q(\zeta_{52})$	$D_{52}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q-\zeta_{52}^{16}q^{2}-\zeta_{52}^{6}q^{4}+\zeta_{52}^{11}q^{5}+\cdots$
3380.1.cg.a	$3380$	$1$	3380.cg	3380.bg	$52$	$24$	$1$	$1.687$	$\Q(\zeta_{52})$	$D_{52}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+\zeta_{52}^{23}q^{2}-\zeta_{52}^{20}q^{4}-\zeta_{52}^{22}q^{5}+\cdots$
3380.1.co.a	$3380$	$1$	3380.co	3380.bo	$78$	$24$	$1$	$1.687$	$\Q(\zeta_{39})$	$D_{78}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$1$	$0$		$1$		$q+\zeta_{78}^{17}q^{2}+\zeta_{78}^{34}q^{4}-\zeta_{78}q^{5}+\cdots$
3380.1.co.b	$3380$	$1$	3380.co	3380.bo	$78$	$24$	$1$	$1.687$	$\Q(\zeta_{39})$	$D_{78}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$-1$	$0$		$1$		$q-\zeta_{78}^{17}q^{2}+\zeta_{78}^{34}q^{4}-\zeta_{78}^{32}q^{5}+\cdots$
3380.1.cs.a	$3380$	$1$	3380.cs	3380.bs	$156$	$48$	$1$	$1.687$	$\Q(\zeta_{156})$	$D_{156}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\zeta_{156}^{41}q^{2}-\zeta_{156}^{4}q^{4}-\zeta_{156}^{46}q^{5}+\cdots$
3380.1.cz.a	$3380$	$1$	3380.cz	3380.bz	$156$	$48$	$1$	$1.687$	$\Q(\zeta_{156})$	$D_{156}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q+\zeta_{156}^{46}q^{2}-\zeta_{156}^{14}q^{4}-\zeta_{156}^{43}q^{5}+\cdots$
3380.2.a.a	$3380$	$2$	3380.a	1.a	$1$	$1$	$1$	$26.989$	$\Q$	$_{}$	None	None	✓	$1$	$2$	$0$	$-3$	$-1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{5}-3q^{7}+6q^{9}-3q^{11}+\cdots$
3380.2.a.b	$3380$	$2$	3380.a	1.a	$1$	$1$	$1$	$26.989$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+q^{5}+3q^{7}+6q^{9}+3q^{11}+\cdots$
3380.2.a.c	$3380$	$2$	3380.a	1.a	$1$	$1$	$1$	$26.989$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}-2q^{7}+q^{9}-2q^{15}+\cdots$

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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.