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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 60 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
2704.1.c.a	$2704$	$1$	2704.c	52.b	$2$	$2$	$2$	$1.349$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{5}+q^{9}+q^{17}+(-1+\cdots)q^{25}+\cdots$
2704.1.d.a	$2704$	$1$	2704.d	4.b	$2$	$1$	$1$	$1.349$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-13}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+q^{9}+2q^{17}-q^{25}-2q^{29}+q^{49}+\cdots$
2704.1.d.b	$2704$	$1$	2704.d	4.b	$2$	$2$	$2$	$1.349$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{5}+q^{9}-q^{17}+2q^{25}+q^{29}+\cdots$
2704.1.y.a	$2704$	$1$	2704.y	52.i	$6$	$2$	$1$	$1.349$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{5}+\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{17}+\cdots$
2704.1.y.b	$2704$	$1$	2704.y	52.i	$6$	$2$	$1$	$1.349$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-13}) $	$\Q(\sqrt{13}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{9}-\zeta_{6}^{2}q^{17}+q^{25}+\zeta_{6}q^{29}+\cdots$
2704.1.bb.a	$2704$	$1$	2704.bb	52.j	$6$	$2$	$1$	$1.349$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-13}) $	$\Q(\sqrt{13}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{6}q^{9}-\zeta_{6}q^{17}-q^{25}-\zeta_{6}^{2}q^{29}+\cdots$
2704.1.bb.b	$2704$	$1$	2704.bb	52.j	$6$	$4$	$2$	$1.349$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$3$		$q+(\zeta_{12}-\zeta_{12}^{5})q^{5}+\zeta_{12}^{4}q^{9}-\zeta_{12}^{4}q^{17}+\cdots$
2704.1.bu.a	$2704$	$1$	2704.bu	676.p	$26$	$12$	$1$	$1.349$	$\Q(\zeta_{26})$	$D_{26}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{26}^{4}+\zeta_{26}^{5})q^{5}-\zeta_{26}^{7}q^{9}+\zeta_{26}^{5}q^{13}+\cdots$
2704.1.cm.a	$2704$	$1$	2704.cm	676.u	$78$	$24$	$1$	$1.349$	$\Q(\zeta_{39})$	$D_{78}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{78}^{29}-\zeta_{78}^{31})q^{5}+\zeta_{78}^{38}q^{9}+\cdots$
2704.2.a.a	$2704$	$2$	2704.a	1.a	$1$	$1$	$1$	$21.592$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-2q^{5}+q^{7}+6q^{9}-5q^{11}+\cdots$
2704.2.a.b	$2704$	$2$	2704.a	1.a	$1$	$1$	$1$	$21.592$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+2q^{5}-q^{7}+6q^{9}+5q^{11}+\cdots$
2704.2.a.c	$2704$	$2$	2704.a	1.a	$1$	$1$	$1$	$21.592$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}-q^{7}-2q^{9}+q^{11}+2q^{15}+\cdots$
2704.2.a.d	$2704$	$2$	2704.a	1.a	$1$	$1$	$1$	$21.592$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$1$	$5$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+5q^{7}-2q^{9}-2q^{11}+\cdots$
2704.2.a.e	$2704$	$2$	2704.a	1.a	$1$	$1$	$1$	$21.592$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+q^{7}-2q^{9}-q^{11}-2q^{15}+\cdots$
2704.2.a.f	$2704$	$2$	2704.a	1.a	$1$	$1$	$1$	$21.592$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}-q^{7}-2q^{9}+6q^{11}+\cdots$
2704.2.a.g	$2704$	$2$	2704.a	1.a	$1$	$1$	$1$	$21.592$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-2q^{7}-3q^{9}-2q^{11}+6q^{17}+\cdots$
2704.2.a.h	$2704$	$2$	2704.a	1.a	$1$	$1$	$1$	$21.592$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-4q^{7}-3q^{9}-4q^{11}+3q^{17}+\cdots$
2704.2.a.i	$2704$	$2$	2704.a	1.a	$1$	$1$	$1$	$21.592$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+4q^{7}-3q^{9}+4q^{11}+3q^{17}+\cdots$
2704.2.a.j	$2704$	$2$	2704.a	1.a	$1$	$1$	$1$	$21.592$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-3$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}+3q^{7}-2q^{9}-3q^{15}+\cdots$
2704.2.a.k	$2704$	$2$	2704.a	1.a	$1$	$1$	$1$	$21.592$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}-3q^{7}-2q^{9}+3q^{15}+\cdots$
2704.2.a.l	$2704$	$2$	2704.a	1.a	$1$	$1$	$1$	$21.592$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-3q^{5}+4q^{7}+q^{9}-6q^{15}+\cdots$
2704.2.a.m	$2704$	$2$	2704.a	1.a	$1$	$1$	$1$	$21.592$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$3$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+3q^{5}-4q^{7}+q^{9}+6q^{15}+\cdots$
2704.2.a.n	$2704$	$2$	2704.a	1.a	$1$	$1$	$1$	$21.592$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+q^{5}+q^{7}+6q^{9}-2q^{11}+\cdots$
2704.2.a.o	$2704$	$2$	2704.a	1.a	$1$	$2$	$2$	$21.592$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$2$	$1$	$0$	$-4$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-\beta q^{5}+q^{9}+2\beta q^{15}+3q^{17}+\cdots$
2704.2.a.p	$2704$	$2$	2704.a	1.a	$1$	$2$	$2$	$21.592$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-2+\beta )q^{5}-\beta q^{7}+(1+\beta )q^{9}+\cdots$
2704.2.a.q	$2704$	$2$	2704.a	1.a	$1$	$2$	$2$	$21.592$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-1-\beta )q^{5}+\beta q^{7}+(1+\beta )q^{9}+\cdots$
2704.2.a.r	$2704$	$2$	2704.a	1.a	$1$	$2$	$2$	$21.592$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(1+\beta )q^{5}-\beta q^{7}+(1+\beta )q^{9}+\cdots$
2704.2.a.s	$2704$	$2$	2704.a	1.a	$1$	$2$	$2$	$21.592$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-1$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-\beta q^{5}+(-2-\beta )q^{7}+(1+\beta )q^{9}+\cdots$
2704.2.a.t	$2704$	$2$	2704.a	1.a	$1$	$2$	$2$	$21.592$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$1$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+\beta q^{5}+(2+\beta )q^{7}+(1+\beta )q^{9}+\cdots$
2704.2.a.u	$2704$	$2$	2704.a	1.a	$1$	$2$	$2$	$21.592$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$2$	$1$	$0$	$2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-\beta q^{7}-2q^{9}+3\beta q^{11}-3q^{17}+\cdots$
2704.2.a.v	$2704$	$2$	2704.a	1.a	$1$	$3$	$3$	$21.592$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}+\beta _{2})q^{3}-2\beta _{1}q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots$
2704.2.a.w	$2704$	$2$	2704.a	1.a	$1$	$3$	$3$	$21.592$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}+\beta _{2})q^{3}+2\beta _{1}q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots$
2704.2.a.x	$2704$	$2$	2704.a	1.a	$1$	$3$	$3$	$21.592$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-8$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-2\beta _{1}+\beta _{2})q^{3}+(-3-\beta _{2})q^{5}+\cdots$
2704.2.a.y	$2704$	$2$	2704.a	1.a	$1$	$3$	$3$	$21.592$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$8$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-2\beta _{1}+\beta _{2})q^{3}+(3+\beta _{2})q^{5}+(2+\cdots)q^{7}+\cdots$
2704.2.a.z	$2704$	$2$	2704.a	1.a	$1$	$3$	$3$	$21.592$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-4$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(-1-\beta _{1})q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots$
2704.2.a.ba	$2704$	$2$	2704.a	1.a	$1$	$3$	$3$	$21.592$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$4$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(1+\beta _{1})q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots$
2704.2.a.bb	$2704$	$2$	2704.a	1.a	$1$	$3$	$3$	$21.592$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$1$	$0$	$4$	$-4$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{3}+(-1-\beta _{1})q^{5}+\beta _{1}q^{7}+\cdots$
2704.2.a.bc	$2704$	$2$	2704.a	1.a	$1$	$3$	$3$	$21.592$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$0$	$0$	$4$	$4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{3}+(1+\beta _{1})q^{5}-\beta _{1}q^{7}+\cdots$
2704.2.a.bd	$2704$	$2$	2704.a	1.a	$1$	$4$	$4$	$21.592$	4.4.13968.1	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1-\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots$
2704.2.a.be	$2704$	$2$	2704.a	1.a	$1$	$4$	$4$	$21.592$	4.4.13968.1	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1+\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots$
2704.2.a.bf	$2704$	$2$	2704.a	1.a	$1$	$6$	$6$	$21.592$	6.6.3728753.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1}-\beta _{2}-\beta _{5})q^{3}+(-\beta _{1}+\cdots)q^{5}+\cdots$
2704.2.a.bg	$2704$	$2$	2704.a	1.a	$1$	$6$	$6$	$21.592$	6.6.3728753.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$2$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1}-\beta _{2}-\beta _{5})q^{3}+(\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots$
2704.2.f.a	$2704$	$2$	2704.f	13.b	$2$	$2$	$2$	$21.592$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$1$	$0$	$-6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-3q^{3}+2iq^{5}+iq^{7}+6q^{9}-5iq^{11}+\cdots$
2704.2.f.b	$2704$	$2$	2704.f	13.b	$2$	$2$	$2$	$21.592$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-4$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-2q^{3}-\zeta_{6}q^{5}+q^{9}+2\zeta_{6}q^{15}-3q^{17}+\cdots$
2704.2.f.c	$2704$	$2$	2704.f	13.b	$2$	$2$	$2$	$21.592$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+2iq^{5}-iq^{7}-2q^{9}+iq^{11}+\cdots$
2704.2.f.d	$2704$	$2$	2704.f	13.b	$2$	$2$	$2$	$21.592$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}-3iq^{5}-iq^{7}-2q^{9}+6iq^{11}+\cdots$
2704.2.f.e	$2704$	$2$	2704.f	13.b	$2$	$2$	$2$	$21.592$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}-iq^{5}+5iq^{7}-2q^{9}-2iq^{11}+\cdots$
2704.2.f.f	$2704$	$2$	2704.f	13.b	$2$	$2$	$2$	$21.592$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{5}+iq^{7}-3q^{9}+iq^{11}-6q^{17}+\cdots$
2704.2.f.g	$2704$	$2$	2704.f	13.b	$2$	$2$	$2$	$21.592$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$1$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{5}-4iq^{7}-3q^{9}-4iq^{11}-3q^{17}+\cdots$
2704.2.f.h	$2704$	$2$	2704.f	13.b	$2$	$2$	$2$	$21.592$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}-\zeta_{6}q^{7}-2q^{9}+3\zeta_{6}q^{11}+3q^{17}+\cdots$

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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.