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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
167.1.b.a	$167$	$1$	167.b	167.b	$2$	$5$	$5$	$0.083$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-167}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$-1$		$1$		$q+\beta _{4}q^{2}+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4})q^{3}+\cdots$
271.1.b.a	$271$	$1$	271.b	271.b	$2$	$5$	$5$	$0.135$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-271}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$-1$		$1$		$q+\beta _{4}q^{2}+(1-\beta _{3})q^{4}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
591.1.d.a	$591$	$1$	591.d	591.d	$2$	$5$	$5$	$0.295$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-591}) $	None	✓	$2$	$0$	$-1$	$5$	$-1$	$-1$		$1$		$q+\beta _{4}q^{2}+q^{3}+(1-\beta _{3})q^{4}+\beta _{2}q^{5}+\cdots$
591.1.d.b	$591$	$1$	591.d	591.d	$2$	$5$	$5$	$0.295$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-591}) $	None	✓	$2$	$0$	$1$	$-5$	$1$	$-1$		$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}-q^{3}+\cdots$
623.1.d.a	$623$	$1$	623.d	623.d	$2$	$5$	$5$	$0.311$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-623}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$5$		$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4})q^{2}+\beta _{4}q^{3}+\cdots$
623.1.d.b	$623$	$1$	623.d	623.d	$2$	$5$	$5$	$0.311$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-623}) $	None	✓	$2$	$0$	$-1$	$1$	$0$	$-5$		$1$		$q+\beta _{2}q^{2}+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{3}+\cdots$
659.1.b.a	$659$	$1$	659.b	659.b	$2$	$5$	$5$	$0.329$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-659}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$0$		$1$		$q+\beta _{4}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots$
767.1.d.a	$767$	$1$	767.d	767.d	$2$	$5$	$5$	$0.383$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-767}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$0$		$1$		$q+\beta _{4}q^{2}+\beta _{2}q^{3}+(1-\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots$
767.1.d.b	$767$	$1$	767.d	767.d	$2$	$5$	$5$	$0.383$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-767}) $	None	✓	$2$	$0$	$1$	$-1$	$0$	$0$		$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}-\beta _{3}q^{3}+\cdots$
839.1.b.b	$839$	$1$	839.b	839.b	$2$	$5$	$5$	$0.419$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-839}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$-1$		$1$		$q+\beta _{4}q^{2}+\beta _{4}q^{3}+(1-\beta _{3})q^{4}+\beta _{2}q^{5}+\cdots$
871.1.d.a	$871$	$1$	871.d	871.d	$2$	$5$	$5$	$0.435$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-871}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$-1$		$1$		$q+\beta _{4}q^{2}+(1-\beta _{3})q^{4}-\beta _{3}q^{5}+\beta _{2}q^{7}+\cdots$
871.1.d.b	$871$	$1$	871.d	871.d	$2$	$5$	$5$	$0.435$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-871}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$1$		$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
879.1.d.a	$879$	$1$	879.d	879.d	$2$	$5$	$5$	$0.439$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-879}) $	None	✓	$2$	$0$	$-1$	$5$	$-1$	$0$		$1$		$q+\beta _{4}q^{2}+q^{3}+(1-\beta _{3})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
879.1.d.b	$879$	$1$	879.d	879.d	$2$	$5$	$5$	$0.439$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-879}) $	None	✓	$2$	$0$	$1$	$-5$	$1$	$0$		$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}-q^{3}+\cdots$
967.1.b.a	$967$	$1$	967.b	967.b	$2$	$5$	$5$	$0.483$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-967}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$0$		$1$		$q+\beta _{4}q^{2}+(1-\beta _{3})q^{4}+(-\beta _{1}+\beta _{4})q^{8}+\cdots$
119.2.a.b	$119$	$2$	119.a	1.a	$1$	$5$	$5$	$0.950$	5.5.453749.1	$_{}$	None	None	✓	$1$	$0$	$2$	$-2$	$0$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(2-\beta _{3}+\cdots)q^{4}+\cdots$
157.2.a.a	$157$	$2$	157.a	1.a	$1$	$5$	$5$	$1.254$	5.5.24217.1	$_{}$	None	None	✓	$1$	$1$	$-5$	$-7$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{3})q^{2}+(-1-\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots$
159.2.a.b	$159$	$2$	159.a	1.a	$1$	$5$	$5$	$1.270$	5.5.1054013.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-5$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{3})q^{2}-q^{3}+(2-\beta _{4})q^{4}+\cdots$
161.2.a.d	$161$	$2$	161.a	1.a	$1$	$5$	$5$	$1.286$	5.5.2147108.1	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$-4$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(2+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
163.2.a.b	$163$	$2$	163.a	1.a	$1$	$5$	$5$	$1.302$	5.5.65657.1	$_{}$	None	None	✓	$1$	$1$	$-5$	$-5$	$-9$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2}+\beta _{3})q^{2}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots$
181.2.a.a	$181$	$2$	181.a	1.a	$1$	$5$	$5$	$1.445$	5.5.24217.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$-5$	$-5$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+\cdots$
185.2.a.d	$185$	$2$	185.a	1.a	$1$	$5$	$5$	$1.477$	5.5.368464.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$5$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}-\beta _{3}q^{3}+(2-\beta _{1}-\beta _{4})q^{4}+\cdots$
185.2.a.e	$185$	$2$	185.a	1.a	$1$	$5$	$5$	$1.477$	5.5.973904.1	$_{}$	None	None	✓	$1$	$0$	$2$	$3$	$-5$	$11$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{2}+(1-\beta _{1})q^{3}+(2+\beta _{3})q^{4}+\cdots$
193.2.a.b	$193$	$2$	193.a	1.a	$1$	$5$	$5$	$1.541$	5.5.70601.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$-5$	$-8$	$-10$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{2}+(-1+\beta _{2}-\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
197.2.a.b	$197$	$2$	197.a	1.a	$1$	$5$	$5$	$1.573$	5.5.24217.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-8$	$-4$	$-10$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{2})q^{2}+(-2+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots$
201.2.a.e	$201$	$2$	201.a	1.a	$1$	$5$	$5$	$1.605$	5.5.1025428.1	$_{}$	None	None	✓	$1$	$0$	$0$	$5$	$-3$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{4})q^{5}+\cdots$
203.2.a.g	$203$	$2$	203.a	1.a	$1$	$5$	$5$	$1.621$	5.5.2626356.1	$_{}$	None	None	✓	$1$	$0$	$2$	$-2$	$5$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{4}q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
209.2.a.c	$209$	$2$	209.a	1.a	$1$	$5$	$5$	$1.669$	5.5.246832.1	$_{}$	None	None	✓	$1$	$0$	$2$	$1$	$-5$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+\beta _{3}q^{3}+(\beta _{1}+\beta _{2}+\beta _{3}+\beta _{4})q^{4}+\cdots$
215.2.a.c	$215$	$2$	215.a	1.a	$1$	$5$	$5$	$1.717$	5.5.1933097.1	$_{}$	None	None	✓	$1$	$0$	$2$	$-1$	$5$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(2+\beta _{2}+\cdots)q^{4}+\cdots$
217.2.a.d	$217$	$2$	217.a	1.a	$1$	$5$	$5$	$1.733$	5.5.138136.1	$_{}$	None	None	✓	$1$	$0$	$3$	$3$	$0$	$-5$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{4})q^{2}+(1-\beta _{2})q^{3}+(2+\beta _{3}+\cdots)q^{4}+\cdots$
235.2.a.d	$235$	$2$	235.a	1.a	$1$	$5$	$5$	$1.876$	5.5.106069.1	$_{}$	None	None	✓	$1$	$1$	$-4$	$-5$	$-5$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{4})q^{2}+(-1+\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots$
247.2.a.d	$247$	$2$	247.a	1.a	$1$	$5$	$5$	$1.972$	5.5.2655049.1	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(2+\beta _{2})q^{4}+\cdots$
247.2.a.e	$247$	$2$	247.a	1.a	$1$	$5$	$5$	$1.972$	5.5.288565.1	$_{}$	None	None	✓	$1$	$0$	$4$	$3$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-\beta _{2})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
249.2.a.e	$249$	$2$	249.a	1.a	$1$	$5$	$5$	$1.988$	5.5.368464.1	$_{}$	None	None	✓	$1$	$0$	$-3$	$-5$	$-2$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
253.2.a.c	$253$	$2$	253.a	1.a	$1$	$5$	$5$	$2.020$	5.5.170701.1	$_{}$	None	None	✓	$1$	$1$	$-4$	$-5$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(-1-\beta _{1}-\beta _{2})q^{3}+\cdots$
254.2.a.f	$254$	$2$	254.a	1.a	$1$	$5$	$5$	$2.028$	5.5.2949696.1	$_{}$	None	None	✓	$1$	$0$	$-5$	$-2$	$-1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{4}q^{5}+\beta _{1}q^{6}+\cdots$
263.2.a.a	$263$	$2$	263.a	1.a	$1$	$5$	$5$	$2.100$	5.5.24217.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$-5$	$-3$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(-1+\beta _{3})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
269.2.a.b	$269$	$2$	269.a	1.a	$1$	$5$	$5$	$2.148$	5.5.65657.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$-5$	$-4$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(-1+\beta _{2}+\beta _{3})q^{3}+\beta _{1}q^{4}+\cdots$
274.2.a.e	$274$	$2$	274.a	1.a	$1$	$5$	$5$	$2.188$	5.5.401584.1	$_{}$	None	None	✓	$1$	$0$	$5$	$2$	$5$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(\beta _{1}-\beta _{2}+\beta _{4})q^{3}+q^{4}+(1+\cdots)q^{5}+\cdots$
278.2.a.e	$278$	$2$	278.a	1.a	$1$	$5$	$5$	$2.220$	5.5.617176.1	$_{}$	None	None	✓	$1$	$0$	$5$	$1$	$-2$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{3}q^{3}+q^{4}+\beta _{4}q^{5}+\beta _{3}q^{6}+\cdots$
287.2.a.e	$287$	$2$	287.a	1.a	$1$	$5$	$5$	$2.292$	5.5.633117.1	$_{}$	None	None	✓	$1$	$0$	$-1$	$4$	$-5$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1-\beta _{1})q^{3}+(1+\beta _{2})q^{4}+\cdots$
298.2.a.e	$298$	$2$	298.a	1.a	$1$	$5$	$5$	$2.380$	5.5.617176.1	$_{}$	None	None	✓	$1$	$0$	$5$	$1$	$5$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{3}q^{3}+q^{4}+(1+\beta _{1})q^{5}+\beta _{3}q^{6}+\cdots$
301.2.a.b	$301$	$2$	301.a	1.a	$1$	$5$	$5$	$2.403$	5.5.81509.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-6$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{2}+(-1-\beta _{3}-\beta _{4})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots$
301.2.a.c	$301$	$2$	301.a	1.a	$1$	$5$	$5$	$2.403$	5.5.301909.1	$_{}$	None	None	✓	$1$	$0$	$1$	$5$	$4$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots$
309.2.a.c	$309$	$2$	309.a	1.a	$1$	$5$	$5$	$2.467$	5.5.81509.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$-5$	$-5$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}-q^{3}+(-\beta _{3}-\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots$
323.2.a.d	$323$	$2$	323.a	1.a	$1$	$5$	$5$	$2.579$	5.5.106069.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$-3$	$-3$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(-1-\beta _{3})q^{3}+(1+\cdots)q^{4}+\cdots$
326.2.a.d	$326$	$2$	326.a	1.a	$1$	$5$	$5$	$2.603$	5.5.482689.1	$_{}$	None	None	✓	$1$	$0$	$-5$	$3$	$9$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{2})q^{3}+q^{4}+(2+\beta _{3})q^{5}+\cdots$
329.2.a.f	$329$	$2$	329.a	1.a	$1$	$5$	$5$	$2.627$	5.5.1032140.1	$_{}$	None	None	✓	$1$	$0$	$1$	$2$	$-4$	$-5$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{2}+\beta _{2}q^{3}+(3-\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
339.2.a.g	$339$	$2$	339.a	1.a	$1$	$5$	$5$	$2.707$	5.5.265504.1	$_{}$	None	None	✓	$1$	$0$	$0$	$5$	$3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots$
339.2.a.h	$339$	$2$	339.a	1.a	$1$	$5$	$5$	$2.707$	5.5.1882484.1	$_{}$	None	None	✓	$1$	$0$	$1$	$-5$	$-2$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2}-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots$

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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.