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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 190 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
2496.1.b.a	$2496$	$1$	2496.b	312.b	$2$	$2$	$2$	$1.246$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-26}) $	$\Q(\sqrt{78}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+iq^{3}-iq^{7}-q^{9}-q^{13}+2q^{21}+\cdots$
2496.1.b.b	$2496$	$1$	2496.b	312.b	$2$	$2$	$2$	$1.246$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-26}) $	$\Q(\sqrt{78}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{3}-iq^{7}-q^{9}+q^{13}-2q^{21}+\cdots$
2496.1.b.c	$2496$	$1$	2496.b	312.b	$2$	$4$	$4$	$1.246$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-26}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{3}+(\zeta_{12}^{2}+\zeta_{12}^{4})q^{5}-\zeta_{12}^{3}q^{7}+\cdots$
2496.1.b.d	$2496$	$1$	2496.b	312.b	$2$	$4$	$4$	$1.246$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-26}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{3}+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{5}+\cdots$
2496.1.l.a	$2496$	$1$	2496.l	39.d	$2$	$1$	$1$	$1.246$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-q^{3}+q^{9}+q^{13}-q^{25}-q^{27}-q^{39}+\cdots$
2496.1.l.b	$2496$	$1$	2496.l	39.d	$2$	$1$	$1$	$1.246$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q+q^{3}+q^{9}+q^{13}-q^{25}+q^{27}+q^{39}+\cdots$
2496.1.l.c	$2496$	$1$	2496.l	39.d	$2$	$4$	$4$	$1.246$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{39}) $		$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q+\zeta_{8}^{2}q^{3}+(-\zeta_{8}+\zeta_{8}^{3})q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots$
2496.1.bd.a	$2496$	$1$	2496.bd	156.l	$4$	$2$	$1$	$1.246$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+iq^{3}+(-1-i)q^{7}-q^{9}+iq^{13}+\cdots$
2496.1.bd.b	$2496$	$1$	2496.bd	156.l	$4$	$2$	$1$	$1.246$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-iq^{3}+(1+i)q^{7}-q^{9}+iq^{13}+(1+\cdots)q^{19}+\cdots$
2496.1.be.a	$2496$	$1$	2496.be	312.w	$4$	$2$	$1$	$1.246$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-2$	$0$	$-2$		$1$		$q-q^{3}+(-1-i)q^{7}+q^{9}+iq^{13}+\cdots$
2496.1.be.b	$2496$	$1$	2496.be	312.w	$4$	$2$	$1$	$1.246$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-2$	$0$	$2$		$1$		$q-q^{3}+(1+i)q^{7}+q^{9}-iq^{13}+(1+\cdots)q^{19}+\cdots$
2496.1.be.c	$2496$	$1$	2496.be	312.w	$4$	$2$	$1$	$1.246$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$2$	$0$	$-2$		$1$		$q+q^{3}+(-1-i)q^{7}+q^{9}-iq^{13}+\cdots$
2496.1.be.d	$2496$	$1$	2496.be	312.w	$4$	$2$	$1$	$1.246$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$2$	$0$	$2$		$1$		$q+q^{3}+(1+i)q^{7}+q^{9}+iq^{13}+(-1+\cdots)q^{19}+\cdots$
2496.1.bi.a	$2496$	$1$	2496.bi	624.ai	$4$	$8$	$4$	$1.246$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q+\zeta_{16}^{2}q^{3}+(-\zeta_{16}+\zeta_{16}^{3})q^{5}+\zeta_{16}^{4}q^{9}+\cdots$
2496.1.bs.a	$2496$	$1$	2496.bs	39.i	$6$	$2$	$1$	$1.246$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-1$		$1$		$q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}-\zeta_{6}^{2}q^{13}+\cdots$
2496.1.bs.b	$2496$	$1$	2496.bs	39.i	$6$	$2$	$1$	$1.246$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$1$		$1$		$q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}-\zeta_{6}^{2}q^{13}+\cdots$
2496.1.bs.c	$2496$	$1$	2496.bs	39.i	$6$	$8$	$4$	$1.246$	$\Q(\zeta_{24})$	$S_{4}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{11}q^{3}-\zeta_{24}^{6}q^{5}+(-\zeta_{24}-\zeta_{24}^{7}+\cdots)q^{7}+\cdots$
2496.1.bw.a	$2496$	$1$	2496.bw	312.ag	$6$	$4$	$2$	$1.246$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{5}q^{3}+\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}+\zeta_{12}^{4}q^{13}+\cdots$
2496.1.bw.b	$2496$	$1$	2496.bw	312.ag	$6$	$4$	$2$	$1.246$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{5}q^{3}-\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}-\zeta_{12}^{4}q^{13}+\cdots$
2496.1.bx.a	$2496$	$1$	2496.bx	312.ah	$6$	$4$	$2$	$1.246$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}q^{3}+(\zeta_{12}+\zeta_{12}^{3})q^{7}+\zeta_{12}^{2}q^{9}+\cdots$
2496.1.bx.b	$2496$	$1$	2496.bx	312.ah	$6$	$4$	$2$	$1.246$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}q^{3}+(-\zeta_{12}-\zeta_{12}^{3})q^{7}+\zeta_{12}^{2}q^{9}+\cdots$
2496.1.cb.a	$2496$	$1$	2496.cb	39.h	$6$	$2$	$1$	$1.246$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-3$		$1$		$q+\zeta_{6}^{2}q^{3}+(-1+\zeta_{6}^{2})q^{7}-\zeta_{6}q^{9}+\cdots$
2496.1.cb.b	$2496$	$1$	2496.cb	39.h	$6$	$2$	$1$	$1.246$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$3$		$1$		$q-\zeta_{6}^{2}q^{3}+(1-\zeta_{6}^{2})q^{7}-\zeta_{6}q^{9}-\zeta_{6}q^{13}+\cdots$
2496.1.de.a	$2496$	$1$	2496.de	312.aq	$12$	$4$	$1$	$1.246$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-2$	$0$	$-4$		$1$		$q-\zeta_{12}^{2}q^{3}+(-1+\zeta_{12}^{5})q^{7}+\zeta_{12}^{4}q^{9}+\cdots$
2496.1.de.b	$2496$	$1$	2496.de	312.aq	$12$	$4$	$1$	$1.246$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-2$	$0$	$4$		$1$		$q-\zeta_{12}^{2}q^{3}+(1-\zeta_{12}^{5})q^{7}+\zeta_{12}^{4}q^{9}+\cdots$
2496.1.de.c	$2496$	$1$	2496.de	312.aq	$12$	$4$	$1$	$1.246$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$2$	$0$	$-4$		$1$		$q+\zeta_{12}^{2}q^{3}+(-1+\zeta_{12}^{5})q^{7}+\zeta_{12}^{4}q^{9}+\cdots$
2496.1.de.d	$2496$	$1$	2496.de	312.aq	$12$	$4$	$1$	$1.246$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$2$	$0$	$4$		$1$		$q+\zeta_{12}^{2}q^{3}+(1-\zeta_{12}^{5})q^{7}+\zeta_{12}^{4}q^{9}+\cdots$
2496.1.df.a	$2496$	$1$	2496.df	156.v	$12$	$4$	$1$	$1.246$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\zeta_{12}q^{3}+(-\zeta_{12}^{3}+\zeta_{12}^{4})q^{7}+\zeta_{12}^{2}q^{9}+\cdots$
2496.1.df.b	$2496$	$1$	2496.df	156.v	$12$	$4$	$1$	$1.246$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+\zeta_{12}q^{3}+(\zeta_{12}^{3}-\zeta_{12}^{4})q^{7}+\zeta_{12}^{2}q^{9}+\cdots$
2496.1.eh.a	$2496$	$1$	2496.eh	2496.dh	$16$	$32$	$4$	$1.246$	$\Q(\zeta_{64})$	$D_{32}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{64}^{27}q^{2}-\zeta_{64}^{26}q^{3}-\zeta_{64}^{22}q^{4}+\cdots$
2496.2.a.a	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{5}+q^{9}-2q^{11}+q^{13}+\cdots$
2496.2.a.b	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots$
2496.2.a.c	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+q^{9}-q^{13}+2q^{15}+\cdots$
2496.2.a.d	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+2q^{7}+q^{9}+2q^{11}+\cdots$
2496.2.a.e	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots$
2496.2.a.f	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}+q^{9}+4q^{11}-q^{13}+\cdots$
2496.2.a.g	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}-6q^{11}+q^{13}+2q^{17}+\cdots$
2496.2.a.h	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}+q^{9}-q^{13}-6q^{17}+\cdots$
2496.2.a.i	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}+q^{9}-q^{13}+2q^{17}+\cdots$
2496.2.a.j	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{7}+q^{9}-2q^{11}+q^{13}+\cdots$
2496.2.a.k	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}-4q^{7}+q^{9}-q^{13}-2q^{15}+\cdots$
2496.2.a.l	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+q^{9}+4q^{11}-q^{13}+\cdots$
2496.2.a.m	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+2q^{7}+q^{9}+6q^{11}+\cdots$
2496.2.a.n	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{5}-4q^{7}+q^{9}+2q^{11}+\cdots$
2496.2.a.o	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{5}+2q^{7}+q^{9}-4q^{11}+\cdots$
2496.2.a.p	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{5}+q^{9}+2q^{11}+q^{13}+\cdots$
2496.2.a.q	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots$
2496.2.a.r	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-2q^{7}+q^{9}-2q^{11}+\cdots$
2496.2.a.s	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{9}-q^{13}-2q^{15}+\cdots$
2496.2.a.t	$2496$	$2$	2496.a	1.a	$1$	$1$	$1$	$19.931$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots$

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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.