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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 163 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
2340.1.i.a	$2340$	$1$	2340.i	260.g	$2$	$1$	$1$	$1.168$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-65}) $	$\Q(\sqrt{65}) $	✓	$4$	$0$	$-1$	$0$	$1$	$0$		$1$		$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-q^{13}+\cdots$
2340.1.i.b	$2340$	$1$	2340.i	260.g	$2$	$1$	$1$	$1.168$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-65}) $	$\Q(\sqrt{65}) $	✓	$4$	$0$	$1$	$0$	$-1$	$0$		$1$		$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+q^{13}+\cdots$
2340.1.i.c	$2340$	$1$	2340.i	260.g	$2$	$4$	$4$	$1.168$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}q^{5}-\zeta_{8}^{3}q^{8}+\cdots$
2340.1.i.d	$2340$	$1$	2340.i	260.g	$2$	$4$	$4$	$1.168$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{5}+\zeta_{8}q^{8}+\cdots$
2340.1.v.a	$2340$	$1$	2340.v	260.l	$4$	$2$	$1$	$1.168$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-iq^{2}-q^{4}-q^{5}+iq^{8}+iq^{10}+\cdots$
2340.1.v.b	$2340$	$1$	2340.v	260.l	$4$	$2$	$1$	$1.168$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+iq^{2}-q^{4}-q^{5}-iq^{8}-iq^{10}+\cdots$
2340.1.v.c	$2340$	$1$	2340.v	260.l	$4$	$2$	$1$	$1.168$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-iq^{2}-q^{4}+q^{5}+iq^{8}-iq^{10}+\cdots$
2340.1.z.a	$2340$	$1$	2340.z	780.w	$4$	$4$	$2$	$1.168$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}-\zeta_{8}q^{8}+\cdots$
2340.1.z.b	$2340$	$1$	2340.z	780.w	$4$	$4$	$2$	$1.168$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{5}+\zeta_{8}q^{8}+\cdots$
2340.1.be.a	$2340$	$1$	2340.be	780.ab	$4$	$4$	$2$	$1.168$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{5}-\zeta_{8}q^{8}+\cdots$
2340.1.be.b	$2340$	$1$	2340.be	780.ab	$4$	$4$	$2$	$1.168$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}-\zeta_{8}q^{8}+\cdots$
2340.1.bo.a	$2340$	$1$	2340.bo	260.s	$4$	$2$	$1$	$1.168$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}+iq^{5}-q^{8}-iq^{10}-q^{13}+\cdots$
2340.1.bo.b	$2340$	$1$	2340.bo	260.s	$4$	$2$	$1$	$1.168$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}-iq^{5}+q^{8}-iq^{10}-q^{13}+\cdots$
2340.1.bo.c	$2340$	$1$	2340.bo	260.s	$4$	$2$	$1$	$1.168$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+iq^{5}+q^{8}+iq^{10}+iq^{13}+\cdots$
2340.1.cq.a	$2340$	$1$	2340.cq	260.v	$6$	$4$	$2$	$1.168$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}q^{5}-\zeta_{12}^{3}q^{8}+\cdots$
2340.1.cq.b	$2340$	$1$	2340.cq	260.v	$6$	$4$	$2$	$1.168$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{5}q^{5}+\cdots$
2340.1.db.a	$2340$	$1$	2340.db	2340.cb	$6$	$2$	$1$	$1.168$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-65}) $	None		$4$	$0$	$-1$	$-2$	$-1$	$0$		$1$		$q-\zeta_{6}q^{2}-q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+\cdots$
2340.1.db.b	$2340$	$1$	2340.db	2340.cb	$6$	$2$	$1$	$1.168$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-65}) $	None		$4$	$0$	$-1$	$2$	$-1$	$0$		$1$		$q-\zeta_{6}q^{2}+q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+\cdots$
2340.1.db.c	$2340$	$1$	2340.db	2340.cb	$6$	$2$	$1$	$1.168$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-65}) $	None		$4$	$0$	$1$	$-2$	$1$	$0$		$1$		$q+\zeta_{6}q^{2}-q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+\cdots$
2340.1.db.d	$2340$	$1$	2340.db	2340.cb	$6$	$2$	$1$	$1.168$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-65}) $	None		$4$	$0$	$1$	$2$	$1$	$0$		$1$		$q+\zeta_{6}q^{2}+q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+\cdots$
2340.1.db.e	$2340$	$1$	2340.db	2340.cb	$6$	$4$	$2$	$1.168$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-65}) $	None		$8$	$0$	$-2$	$0$	$2$	$0$		$1$		$q+\zeta_{12}^{4}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{2}q^{4}+\cdots$
2340.1.db.f	$2340$	$1$	2340.db	2340.cb	$6$	$4$	$2$	$1.168$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-65}) $	None		$8$	$0$	$2$	$0$	$-2$	$0$		$1$		$q-\zeta_{12}^{4}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{2}q^{4}+\cdots$
2340.1.dd.a	$2340$	$1$	2340.dd	260.w	$6$	$2$	$1$	$1.168$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$1$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+q^{8}-q^{10}+\cdots$
2340.1.dd.b	$2340$	$1$	2340.dd	260.w	$6$	$2$	$1$	$1.168$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$-1$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}-q^{8}+\cdots$
2340.1.em.a	$2340$	$1$	2340.em	260.ae	$12$	$4$	$1$	$1.168$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+\zeta_{12}^{5}q^{5}+\cdots$
2340.1.em.b	$2340$	$1$	2340.em	260.ae	$12$	$4$	$1$	$1.168$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}-\zeta_{12}q^{5}+q^{8}+\cdots$
2340.1.em.c	$2340$	$1$	2340.em	260.ae	$12$	$4$	$1$	$1.168$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+\zeta_{12}q^{5}-q^{8}+\cdots$
2340.1.ex.a	$2340$	$1$	2340.ex	780.bj	$12$	$8$	$2$	$1.168$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}-\zeta_{24}q^{5}+\zeta_{24}^{3}q^{8}+\cdots$
2340.1.ex.b	$2340$	$1$	2340.ex	780.bj	$12$	$8$	$2$	$1.168$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{5}q^{5}-\zeta_{24}^{3}q^{8}+\cdots$
2340.1.ga.a	$2340$	$1$	2340.ga	780.br	$12$	$8$	$2$	$1.168$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}-\zeta_{24}^{11}q^{5}+\cdots$
2340.1.ga.b	$2340$	$1$	2340.ga	780.br	$12$	$8$	$2$	$1.168$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}-\zeta_{24}^{7}q^{5}+\cdots$
2340.1.gi.a	$2340$	$1$	2340.gi	585.cb	$12$	$4$	$1$	$1.168$	$\Q(\zeta_{12})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}q^{3}+\zeta_{12}q^{5}+\zeta_{12}^{2}q^{9}-\zeta_{12}q^{13}+\cdots$
2340.1.gi.b	$2340$	$1$	2340.gi	585.cb	$12$	$4$	$1$	$1.168$	$\Q(\zeta_{12})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\zeta_{12}q^{3}-\zeta_{12}^{4}q^{5}+\zeta_{12}^{2}q^{9}+\zeta_{12}q^{13}+\cdots$
2340.1.gu.a	$2340$	$1$	2340.gu	780.bw	$12$	$8$	$2$	$1.168$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}-\zeta_{24}^{7}q^{5}+\cdots$
2340.1.gu.b	$2340$	$1$	2340.gu	780.bw	$12$	$8$	$2$	$1.168$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}-\zeta_{24}^{11}q^{5}+\cdots$
2340.1.hj.a	$2340$	$1$	2340.hj	260.al	$12$	$4$	$1$	$1.168$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{4}q^{5}+\zeta_{12}^{3}q^{8}+\cdots$
2340.1.hj.b	$2340$	$1$	2340.hj	260.al	$12$	$4$	$1$	$1.168$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{4}q^{5}-\zeta_{12}^{3}q^{8}+\cdots$
2340.1.hj.c	$2340$	$1$	2340.hj	260.al	$12$	$4$	$1$	$1.168$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{2}q^{5}+\zeta_{12}^{3}q^{8}+\cdots$
2340.2.a.a	$2340$	$2$	2340.a	1.a	$1$	$1$	$1$	$18.685$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}+2q^{11}-q^{13}+2q^{17}+\cdots$
2340.2.a.b	$2340$	$2$	2340.a	1.a	$1$	$1$	$1$	$18.685$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-q^{7}+q^{11}-q^{13}+5q^{17}+\cdots$
2340.2.a.c	$2340$	$2$	2340.a	1.a	$1$	$1$	$1$	$18.685$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-6q^{11}+q^{13}+4q^{17}+4q^{19}+\cdots$
2340.2.a.d	$2340$	$2$	2340.a	1.a	$1$	$1$	$1$	$18.685$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+3q^{7}-q^{11}+q^{13}+3q^{17}+\cdots$
2340.2.a.e	$2340$	$2$	2340.a	1.a	$1$	$1$	$1$	$18.685$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}+6q^{11}-q^{13}+2q^{17}+\cdots$
2340.2.a.f	$2340$	$2$	2340.a	1.a	$1$	$1$	$1$	$18.685$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{7}-3q^{11}+q^{13}-3q^{17}+\cdots$
2340.2.a.g	$2340$	$2$	2340.a	1.a	$1$	$1$	$1$	$18.685$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{7}-q^{11}-q^{13}-5q^{17}+\cdots$
2340.2.a.h	$2340$	$2$	2340.a	1.a	$1$	$1$	$1$	$18.685$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+6q^{11}+q^{13}-4q^{17}+4q^{19}+\cdots$
2340.2.a.i	$2340$	$2$	2340.a	1.a	$1$	$1$	$1$	$18.685$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}-4q^{11}-q^{13}-2q^{17}+\cdots$
2340.2.a.j	$2340$	$2$	2340.a	1.a	$1$	$2$	$2$	$18.685$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+\beta q^{7}+(2-\beta )q^{11}+q^{13}+(-4+\cdots)q^{17}+\cdots$
2340.2.a.k	$2340$	$2$	2340.a	1.a	$1$	$2$	$2$	$18.685$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-2$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+(1+\beta )q^{7}+(-1-\beta )q^{11}-q^{13}+\cdots$
2340.2.a.l	$2340$	$2$	2340.a	1.a	$1$	$2$	$2$	$18.685$	$\Q(\sqrt{73}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-\beta q^{7}-\beta q^{11}-q^{13}+\beta q^{17}+\cdots$

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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.