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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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
2027.1.b.a	$2027$	$1$	2027.b	2027.b	$2$	$5$	$5$	$1.012$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2027}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$0$	$1$		$q+\beta _{4}q^{3}+q^{4}+(1-\beta _{3})q^{9}+\beta _{4}q^{12}+\cdots$
2135.1.h.a	$2135$	$1$	2135.h	2135.h	$2$	$5$	$5$	$1.066$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2135}) $	None	✓	$2$	$0$	$-1$	$-1$	$5$	$5$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4})q^{2}+\beta _{4}q^{3}+\cdots$
2135.1.h.b	$2135$	$1$	2135.h	2135.h	$2$	$5$	$5$	$1.066$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2135}) $	None	✓	$2$	$0$	$-1$	$1$	$-5$	$5$	$1$		$q+\beta _{2}q^{2}+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{3}+\cdots$
2135.1.h.c	$2135$	$1$	2135.h	2135.h	$2$	$5$	$5$	$1.066$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2135}) $	None	✓	$2$	$0$	$1$	$-1$	$5$	$-5$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}+\beta _{4}q^{3}+\cdots$
2135.1.h.d	$2135$	$1$	2135.h	2135.h	$2$	$5$	$5$	$1.066$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2135}) $	None	✓	$2$	$0$	$1$	$1$	$-5$	$-5$	$1$		$q-\beta _{2}q^{2}+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{3}+\cdots$
2215.1.d.a	$2215$	$1$	2215.d	2215.d	$2$	$5$	$5$	$1.105$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2215}) $	None	✓	$2$	$0$	$-1$	$0$	$5$	$-1$	$1$		$q+\beta _{4}q^{2}+(1-\beta _{3})q^{4}+q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
2215.1.d.b	$2215$	$1$	2215.d	2215.d	$2$	$5$	$5$	$1.105$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2215}) $	None	✓	$2$	$0$	$1$	$0$	$-5$	$1$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
2216.1.h.a	$2216$	$1$	2216.h	2216.h	$2$	$5$	$5$	$1.106$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-554}) $	None	✓	$2$	$0$	$-5$	$-1$	$1$	$0$	$1$		$q-q^{2}+\beta _{4}q^{3}+q^{4}+(1-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
2216.1.h.b	$2216$	$1$	2216.h	2216.h	$2$	$5$	$5$	$1.106$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-554}) $	None	✓	$2$	$0$	$5$	$-1$	$-1$	$0$	$1$		$q+q^{2}+\beta _{4}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
2263.1.b.a	$2263$	$1$	2263.b	2263.b	$2$	$5$	$5$	$1.129$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2263}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$0$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4})q^{2}+(1+\cdots)q^{4}+\cdots$
2263.1.b.b	$2263$	$1$	2263.b	2263.b	$2$	$5$	$5$	$1.129$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2263}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$0$	$1$		$q+\beta _{2}q^{2}+(1+\beta _{4})q^{4}+(-1+\beta _{1}+\beta _{3}+\cdots)q^{8}+\cdots$
2267.1.b.a	$2267$	$1$	2267.b	2267.b	$2$	$5$	$5$	$1.131$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2267}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$-1$	$1$		$q+\beta _{4}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$
2271.1.d.b	$2271$	$1$	2271.d	2271.d	$2$	$5$	$5$	$1.133$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2271}) $	None	✓	$2$	$0$	$-1$	$5$	$-1$	$-1$	$1$		$q+\beta _{4}q^{2}+q^{3}+(1-\beta _{3})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
2271.1.d.c	$2271$	$1$	2271.d	2271.d	$2$	$5$	$5$	$1.133$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2271}) $	None	✓	$2$	$0$	$1$	$5$	$1$	$-1$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}+q^{3}+\cdots$
2423.1.b.b	$2423$	$1$	2423.b	2423.b	$2$	$5$	$5$	$1.209$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2423}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q+\beta _{4}q^{2}-\beta _{3}q^{3}+(1-\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots$
2435.1.c.a	$2435$	$1$	2435.c	2435.c	$2$	$5$	$5$	$1.215$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2435}) $	None	✓	$2$	$0$	$0$	$-1$	$5$	$-1$	$1$		$q+\beta _{4}q^{3}+q^{4}+q^{5}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
2435.1.c.b	$2435$	$1$	2435.c	2435.c	$2$	$5$	$5$	$1.215$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2435}) $	None	✓	$2$	$0$	$0$	$1$	$-5$	$1$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{3}+q^{4}+\cdots$
2439.1.d.b	$2439$	$1$	2439.d	271.b	$2$	$5$	$5$	$1.217$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-271}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$-1$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
2539.1.b.a	$2539$	$1$	2539.b	2539.b	$2$	$5$	$5$	$1.267$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2539}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$-1$	$1$		$q+q^{4}+\beta _{4}q^{5}-\beta _{1}q^{7}+q^{9}+\beta _{2}q^{13}+\cdots$
2567.1.d.b	$2567$	$1$	2567.d	2567.d	$2$	$5$	$5$	$1.281$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2567}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$-1$	$1$		$q+\beta _{2}q^{2}+\beta _{4}q^{3}+(1+\beta _{4})q^{4}+(-1+\cdots)q^{6}+\cdots$
2567.1.d.c	$2567$	$1$	2567.d	2567.d	$2$	$5$	$5$	$1.281$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2567}) $	None	✓	$2$	$0$	$-1$	$1$	$0$	$1$	$1$		$q-\beta _{3}q^{2}+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{3}+\cdots$
2623.1.d.a	$2623$	$1$	2623.d	2623.d	$2$	$5$	$5$	$1.309$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2623}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q+\beta _{4}q^{2}+(1-\beta _{3})q^{4}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
2623.1.d.b	$2623$	$1$	2623.d	2623.d	$2$	$5$	$5$	$1.309$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2623}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$1$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
2648.1.g.a	$2648$	$1$	2648.g	2648.g	$2$	$5$	$5$	$1.322$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-662}) $	None	✓	$2$	$0$	$-5$	$1$	$0$	$0$	$1$		$q-q^{2}+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{3}+\cdots$
2648.1.g.b	$2648$	$1$	2648.g	2648.g	$2$	$5$	$5$	$1.322$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-662}) $	None	✓	$2$	$0$	$5$	$-1$	$0$	$0$	$1$		$q+q^{2}+\beta _{4}q^{3}+q^{4}+\beta _{4}q^{6}+q^{8}+\cdots$
2672.1.g.a	$2672$	$1$	2672.g	167.b	$2$	$5$	$5$	$1.334$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-167}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$1$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{3}-\beta _{2}q^{7}+\cdots$
2731.1.b.a	$2731$	$1$	2731.b	2731.b	$2$	$5$	$5$	$1.363$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2731}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+q^{4}+\beta _{4}q^{5}+q^{9}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots$
2815.1.d.a	$2815$	$1$	2815.d	2815.d	$2$	$5$	$5$	$1.405$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2815}) $	None	✓	$2$	$0$	$-1$	$0$	$5$	$0$	$1$		$q+\beta _{4}q^{2}+(1-\beta _{3})q^{4}+q^{5}+(-\beta _{1}+\cdots)q^{8}+\cdots$
2815.1.d.b	$2815$	$1$	2815.d	2815.d	$2$	$5$	$5$	$1.405$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2815}) $	None	✓	$2$	$0$	$1$	$0$	$-5$	$0$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
2851.1.b.a	$2851$	$1$	2851.b	2851.b	$2$	$5$	$5$	$1.423$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2851}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+q^{4}+\beta _{4}q^{5}+q^{9}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots$
2863.1.b.c	$2863$	$1$	2863.b	2863.b	$2$	$5$	$5$	$1.429$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2863}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$-5$	$1$		$q+\beta _{4}q^{2}+(1-\beta _{3})q^{4}-q^{7}+(-\beta _{1}+\cdots)q^{8}+\cdots$
2863.1.b.d	$2863$	$1$	2863.b	2863.b	$2$	$5$	$5$	$1.429$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2863}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$5$	$1$		$q+\beta _{4}q^{2}+(1-\beta _{3})q^{4}+q^{7}+(-\beta _{1}+\cdots)q^{8}+\cdots$
2935.1.d.a	$2935$	$1$	2935.d	2935.d	$2$	$5$	$5$	$1.465$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2935}) $	None	✓	$2$	$0$	$-1$	$0$	$5$	$0$	$1$		$q+\beta _{4}q^{2}+(1-\beta _{3})q^{4}+q^{5}+(-\beta _{1}+\cdots)q^{8}+\cdots$
2935.1.d.b	$2935$	$1$	2935.d	2935.d	$2$	$5$	$5$	$1.465$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2935}) $	None	✓	$2$	$0$	$1$	$0$	$-5$	$0$	$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
2967.1.g.a	$2967$	$1$	2967.g	2967.g	$2$	$5$	$5$	$1.481$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2967}) $	None	✓	$2$	$0$	$-1$	$5$	$0$	$-1$	$1$		$q+\beta _{2}q^{2}+q^{3}+(1+\beta _{4})q^{4}+\beta _{2}q^{6}+\cdots$
2967.1.g.b	$2967$	$1$	2967.g	2967.g	$2$	$5$	$5$	$1.481$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2967}) $	None	✓	$2$	$0$	$-1$	$5$	$0$	$1$	$1$		$q-\beta _{3}q^{2}+q^{3}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4})q^{4}+\cdots$
2967.1.g.c	$2967$	$1$	2967.g	2967.g	$2$	$5$	$5$	$1.481$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2967}) $	None	✓	$2$	$0$	$1$	$-5$	$0$	$-1$	$1$		$q-\beta _{2}q^{2}-q^{3}+(1+\beta _{4})q^{4}+\beta _{2}q^{6}+\cdots$
2967.1.g.d	$2967$	$1$	2967.g	2967.g	$2$	$5$	$5$	$1.481$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2967}) $	None	✓	$2$	$0$	$1$	$-5$	$0$	$1$	$1$		$q+\beta _{3}q^{2}-q^{3}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4})q^{4}+\cdots$
2971.1.b.a	$2971$	$1$	2971.b	2971.b	$2$	$5$	$5$	$1.483$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-2971}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$-1$	$1$		$q+q^{4}+\beta _{4}q^{5}-\beta _{1}q^{7}+q^{9}+q^{16}+\cdots$
3032.1.g.a	$3032$	$1$	3032.g	3032.g	$2$	$5$	$5$	$1.513$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-758}) $	None	✓	$2$	$0$	$-5$	$1$	$0$	$0$	$1$		$q-q^{2}+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{3}+\cdots$
3032.1.g.b	$3032$	$1$	3032.g	3032.g	$2$	$5$	$5$	$1.513$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-758}) $	None	✓	$2$	$0$	$5$	$-1$	$0$	$0$	$1$		$q+q^{2}+\beta _{4}q^{3}+q^{4}+\beta _{4}q^{6}+q^{8}+\cdots$
3151.1.c.b	$3151$	$1$	3151.c	3151.c	$2$	$5$	$5$	$1.573$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-3151}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4})q^{2}+(1+\cdots)q^{4}+\cdots$
3151.1.c.c	$3151$	$1$	3151.c	3151.c	$2$	$5$	$5$	$1.573$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-3151}) $	None	✓	$2$	$0$	$-1$	$0$	$1$	$0$	$1$		$q+\beta _{2}q^{2}+(1+\beta _{4})q^{4}+(1-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
3203.1.b.b	$3203$	$1$	3203.b	3203.b	$2$	$5$	$5$	$1.599$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-3203}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$0$	$1$		$q+\beta _{4}q^{3}+q^{4}+(1-\beta _{3})q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots$
3316.1.c.a	$3316$	$1$	3316.c	3316.c	$2$	$5$	$5$	$1.655$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-829}) $	None	✓	$2$	$0$	$-5$	$0$	$-1$	$1$	$1$		$q-q^{2}+q^{4}+\beta _{4}q^{5}+(1-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
3316.1.c.b	$3316$	$1$	3316.c	3316.c	$2$	$5$	$5$	$1.655$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-829}) $	None	✓	$2$	$0$	$5$	$0$	$-1$	$-1$	$1$		$q+q^{2}+q^{4}+\beta _{4}q^{5}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
3347.1.b.a	$3347$	$1$	3347.b	3347.b	$2$	$5$	$5$	$1.670$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-3347}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$0$	$1$		$q+\beta _{4}q^{3}+q^{4}+(1-\beta _{3})q^{9}+\beta _{4}q^{12}+\cdots$
3416.1.p.b	$3416$	$1$	3416.p	3416.p	$2$	$5$	$5$	$1.705$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-854}) $	None	✓	$2$	$0$	$-5$	$-1$	$-1$	$-5$	$1$		$q-q^{2}+\beta _{4}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{4}q^{6}+\cdots$
3416.1.p.c	$3416$	$1$	3416.p	3416.p	$2$	$5$	$5$	$1.705$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-854}) $	None	✓	$2$	$0$	$-5$	$1$	$1$	$5$	$1$		$q-q^{2}+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{3}+\cdots$
3416.1.p.d	$3416$	$1$	3416.p	3416.p	$2$	$5$	$5$	$1.705$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-854}) $	None	✓	$2$	$0$	$5$	$-1$	$-1$	$5$	$1$		$q+q^{2}+\beta _{4}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{4}q^{6}+\cdots$

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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.