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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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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
1596.1.y.a	$1596$	$1$	1596.y	399.n	$6$	$2$	$1$	$0.797$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-1$		$1$		$q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{13}+\cdots$
1596.1.y.b	$1596$	$1$	1596.y	399.n	$6$	$2$	$1$	$0.797$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$2$		$1$		$q+\zeta_{6}^{2}q^{3}+q^{7}-\zeta_{6}q^{9}+\zeta_{6}^{2}q^{13}+\cdots$
1596.1.bo.a	$1596$	$1$	1596.bo	399.r	$6$	$2$	$1$	$0.797$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-2$	$0$	$2$		$1$		$q-q^{3}+q^{7}+q^{9}-\zeta_{6}q^{13}+\zeta_{6}q^{19}+\cdots$
1596.1.bo.b	$1596$	$1$	1596.bo	399.r	$6$	$2$	$1$	$0.797$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$2$	$0$	$-1$		$1$		$q+q^{3}-\zeta_{6}q^{7}+q^{9}-\zeta_{6}q^{13}+q^{19}+\cdots$
1596.1.bs.a	$1596$	$1$	1596.bs	399.s	$6$	$2$	$1$	$0.797$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-1$		$1$		$q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+q^{13}+\cdots$
1596.1.bs.b	$1596$	$1$	1596.bs	399.s	$6$	$2$	$1$	$0.797$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-1$		$1$		$q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}-q^{13}+\cdots$
1596.1.bw.a	$1596$	$1$	1596.bw	1596.aw	$6$	$2$	$1$	$0.797$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$-1$	$-1$	$1$	$2$		$1$		$q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots$
1596.1.bw.b	$1596$	$1$	1596.bw	1596.aw	$6$	$2$	$1$	$0.797$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$-1$	$1$	$-1$	$-2$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\cdots$
1596.1.bw.c	$1596$	$1$	1596.bw	1596.aw	$6$	$2$	$1$	$0.797$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$1$	$-1$	$-1$	$2$		$1$		$q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\cdots$
1596.1.bw.d	$1596$	$1$	1596.bw	1596.aw	$6$	$2$	$1$	$0.797$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$1$	$1$	$1$	$-2$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots$
1596.1.cl.a	$1596$	$1$	1596.cl	399.ai	$6$	$2$	$1$	$0.797$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$2$	$0$	$-1$		$1$		$q+q^{3}+\zeta_{6}^{2}q^{7}+q^{9}-\zeta_{6}^{2}q^{13}+q^{19}+\cdots$
1596.1.cl.b	$1596$	$1$	1596.cl	399.ai	$6$	$2$	$1$	$0.797$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$2$	$0$	$2$		$1$		$q+q^{3}+q^{7}+q^{9}+\zeta_{6}^{2}q^{13}+\zeta_{6}^{2}q^{19}+\cdots$
1596.1.cy.a	$1596$	$1$	1596.cy	399.an	$6$	$2$	$1$	$0.797$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$2$		$1$		$q+\zeta_{6}^{2}q^{3}+q^{7}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{13}+\cdots$
1596.1.cy.b	$1596$	$1$	1596.cy	399.an	$6$	$2$	$1$	$0.797$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-1$		$1$		$q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{13}+\cdots$
1596.1.dg.a	$1596$	$1$	1596.dg	399.ba	$18$	$6$	$1$	$0.797$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{7}q^{3}+\zeta_{18}^{8}q^{7}-\zeta_{18}^{5}q^{9}+\cdots$
1596.1.dh.a	$1596$	$1$	1596.dh	399.as	$18$	$6$	$1$	$0.797$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{8}q^{3}+\zeta_{18}^{4}q^{7}-\zeta_{18}^{7}q^{9}+\cdots$
1596.1.dt.a	$1596$	$1$	1596.dt	1596.ct	$18$	$6$	$1$	$0.797$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$0$	$0$	$-3$	$-3$		$1$		$q-\zeta_{18}^{7}q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+(-\zeta_{18}^{3}+\cdots)q^{5}+\cdots$
1596.1.dt.b	$1596$	$1$	1596.dt	1596.ct	$18$	$6$	$1$	$0.797$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$0$	$0$	$-3$	$3$		$1$		$q+\zeta_{18}^{7}q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+(-\zeta_{18}^{3}+\cdots)q^{5}+\cdots$
1596.1.dt.c	$1596$	$1$	1596.dt	1596.ct	$18$	$6$	$1$	$0.797$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$0$	$0$	$3$	$-3$		$1$		$q+\zeta_{18}^{7}q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+(\zeta_{18}^{3}+\cdots)q^{5}+\cdots$
1596.1.dt.d	$1596$	$1$	1596.dt	1596.ct	$18$	$6$	$1$	$0.797$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$0$	$0$	$3$	$3$		$1$		$q-\zeta_{18}^{7}q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+(\zeta_{18}^{3}+\cdots)q^{5}+\cdots$
1596.1.ef.a	$1596$	$1$	1596.ef	399.ax	$18$	$6$	$1$	$0.797$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{5}q^{3}-\zeta_{18}^{7}q^{7}-\zeta_{18}q^{9}+(\zeta_{18}^{2}+\cdots)q^{13}+\cdots$
1596.1.ef.b	$1596$	$1$	1596.ef	399.ax	$18$	$6$	$1$	$0.797$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{5}q^{3}+\zeta_{18}^{8}q^{7}-\zeta_{18}q^{9}+(-\zeta_{18}^{2}+\cdots)q^{13}+\cdots$
1596.1.en.a	$1596$	$1$	1596.en	399.bh	$18$	$6$	$1$	$0.797$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{7}q^{3}-\zeta_{18}^{7}q^{7}-\zeta_{18}^{5}q^{9}+\cdots$
1596.1.eq.a	$1596$	$1$	1596.eq	399.ay	$18$	$6$	$1$	$0.797$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{5}q^{3}-\zeta_{18}^{5}q^{7}-\zeta_{18}q^{9}+(-1+\cdots)q^{13}+\cdots$
1596.2.a.a	$1596$	$2$	1596.a	1.a	$1$	$1$	$1$	$12.744$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-2q^{11}+6q^{13}+\cdots$
1596.2.a.b	$1596$	$2$	1596.a	1.a	$1$	$1$	$1$	$12.744$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots$
1596.2.a.c	$1596$	$2$	1596.a	1.a	$1$	$1$	$1$	$12.744$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots$
1596.2.a.d	$1596$	$2$	1596.a	1.a	$1$	$1$	$1$	$12.744$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots$
1596.2.a.e	$1596$	$2$	1596.a	1.a	$1$	$1$	$1$	$12.744$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}-q^{7}+q^{9}+6q^{11}+2q^{13}+\cdots$
1596.2.a.f	$1596$	$2$	1596.a	1.a	$1$	$2$	$2$	$12.744$	$\Q(\sqrt{7}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1+\beta )q^{5}-q^{7}+q^{9}-2\beta q^{11}+\cdots$
1596.2.a.g	$1596$	$2$	1596.a	1.a	$1$	$2$	$2$	$12.744$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-2$	$2$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta )q^{5}+q^{7}+q^{9}-2q^{11}+\cdots$
1596.2.a.h	$1596$	$2$	1596.a	1.a	$1$	$2$	$2$	$12.744$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}+q^{7}+q^{9}+2q^{11}+2\beta q^{13}+\cdots$
1596.2.a.i	$1596$	$2$	1596.a	1.a	$1$	$2$	$2$	$12.744$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1+\beta )q^{5}-q^{7}+q^{9}-2\beta q^{11}+\cdots$
1596.2.a.j	$1596$	$2$	1596.a	1.a	$1$	$3$	$3$	$12.744$	3.3.1016.1	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$0$	$3$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{2}q^{5}+q^{7}+q^{9}+2q^{11}+\cdots$
1596.2.b.a	$1596$	$2$	1596.b	57.d	$2$	$2$	$2$	$12.744$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta )q^{3}+\beta q^{5}+q^{7}+(-1-2\beta )q^{9}+\cdots$
1596.2.b.b	$1596$	$2$	1596.b	57.d	$2$	$2$	$2$	$12.744$	$\Q(\sqrt{-2}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta )q^{3}+\beta q^{5}+q^{7}+(-1-2\beta )q^{9}+\cdots$
1596.2.b.c	$1596$	$2$	1596.b	57.d	$2$	$8$	$8$	$12.744$	8.0.207360000.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-8$		$2^{8}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}-\beta _{3}q^{5}-q^{7}-3q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots$
1596.2.b.d	$1596$	$2$	1596.b	57.d	$2$	$12$	$12$	$12.744$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-12$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+\beta _{10}q^{5}-q^{7}+(1+\beta _{2})q^{9}+\cdots$
1596.2.b.e	$1596$	$2$	1596.b	57.d	$2$	$16$	$16$	$12.744$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$16$		$2^{8}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+\beta _{7}q^{5}+q^{7}+(1+\beta _{2})q^{9}+\cdots$
1596.2.i.a	$1596$	$2$	1596.i	133.c	$2$	$14$	$14$	$12.744$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-14$	$0$	$-1$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}-\beta _{10}q^{5}+\beta _{11}q^{7}+q^{9}+\beta _{1}q^{11}+\cdots$
1596.2.i.b	$1596$	$2$	1596.i	133.c	$2$	$14$	$14$	$12.744$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$14$	$0$	$-1$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}-\beta _{10}q^{5}+\beta _{11}q^{7}+q^{9}+\beta _{1}q^{11}+\cdots$
1596.2.j.a	$1596$	$2$	1596.j	21.c	$2$	$48$	$48$	$12.744$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{2}]$
1596.2.q.a	$1596$	$2$	1596.q	133.g	$3$	$2$	$1$	$12.744$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$-3$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-q^{3}-3\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+q^{9}+\cdots$
1596.2.q.b	$1596$	$2$	1596.q	133.g	$3$	$2$	$1$	$12.744$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$0$	$2$	$-4$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{3}-4\zeta_{6}q^{5}+(-2+3\zeta_{6})q^{7}+q^{9}+\cdots$
1596.2.q.c	$1596$	$2$	1596.q	133.g	$3$	$2$	$1$	$12.744$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$-1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{3}-\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+q^{9}+\cdots$
1596.2.q.d	$1596$	$2$	1596.q	133.g	$3$	$2$	$1$	$12.744$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{3}+\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+q^{9}+\cdots$
1596.2.q.e	$1596$	$2$	1596.q	133.g	$3$	$18$	$9$	$12.744$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$18$	$5$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{3}+(1+\beta _{1}-\beta _{2}+\beta _{4})q^{5}+(-\beta _{9}+\cdots)q^{7}+\cdots$
1596.2.q.f	$1596$	$2$	1596.q	133.g	$3$	$26$	$13$	$12.744$		$_{}$	None	None		$2$	$0$	$0$	$-26$	$4$	$-6$			$\mathrm{SU}(2)[C_{3}]$
1596.2.r.a	$1596$	$2$	1596.r	7.c	$3$	$2$	$1$	$12.744$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$-2$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots$
1596.2.r.b	$1596$	$2$	1596.r	7.c	$3$	$2$	$1$	$12.744$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$0$	$-1$	$-1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-2+3\zeta_{6})q^{7}+\cdots$

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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.