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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
119.1.d.a	$119$	$1$	119.d	119.d	$2$	$2$	$2$	$0.059$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-119}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$2$	$1$		$q+(-1+\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots$
119.1.d.b	$119$	$1$	119.d	119.d	$2$	$2$	$2$	$0.059$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-119}) $	None	✓	$2$	$0$	$-1$	$1$	$1$	$-2$	$1$		$q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(1-\beta )q^{4}+\cdots$
595.1.b.a	$595$	$1$	595.b	595.b	$2$	$2$	$2$	$0.297$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-35}) $, $\Q(\sqrt{-119}) $	$\Q(\sqrt{85}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}+q^{4}+iq^{5}-iq^{7}-3q^{9}+\cdots$
595.1.b.b	$595$	$1$	595.b	595.b	$2$	$8$	$8$	$0.297$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-119}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{20}^{2}+\zeta_{20}^{8})q^{2}+(-\zeta_{20}^{3}-\zeta_{20}^{7}+\cdots)q^{3}+\cdots$
833.1.h.a	$833$	$1$	833.h	119.h	$6$	$4$	$2$	$0.416$	$\Q(\sqrt{-3}, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$1$	$-1$	$-1$	$0$	$1$		$q+(-\beta _{1}-\beta _{2})q^{2}-\beta _{1}q^{3}-\beta _{1}q^{4}+\cdots$
833.1.h.b	$833$	$1$	833.h	119.h	$6$	$4$	$2$	$0.416$	$\Q(\sqrt{-3}, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$1$	$1$	$1$	$0$	$1$		$q+(\beta _{1}+\beta _{2}-\beta _{3})q^{2}+(1-\beta _{1}+\beta _{3})q^{3}+\cdots$
952.1.e.a	$952$	$1$	952.e	952.e	$2$	$1$	$1$	$0.475$	$\Q$	$D_{2}$	$\Q(\sqrt{-119}) $, $\Q(\sqrt{-238}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q-q^{2}+q^{4}-q^{7}-q^{8}+q^{9}+q^{14}+\cdots$
952.1.e.b	$952$	$1$	952.e	952.e	$2$	$1$	$1$	$0.475$	$\Q$	$D_{2}$	$\Q(\sqrt{-119}) $, $\Q(\sqrt{-238}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$-1$	$0$	$0$	$1$	$1$		$q-q^{2}+q^{4}+q^{7}-q^{8}+q^{9}-q^{14}+\cdots$
952.1.e.c	$952$	$1$	952.e	952.e	$2$	$4$	$4$	$0.475$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$1$	$0$	$0$	$4$	$1$		$q+\zeta_{10}q^{2}+(\zeta_{10}+\zeta_{10}^{4})q^{3}+\zeta_{10}^{2}q^{4}+\cdots$
952.1.e.d	$952$	$1$	952.e	952.e	$2$	$4$	$4$	$0.475$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$1$	$0$	$0$	$-4$	$1$		$q-\zeta_{10}^{4}q^{2}+(\zeta_{10}+\zeta_{10}^{4})q^{3}-\zeta_{10}^{3}q^{4}+\cdots$
1071.1.h.a	$1071$	$1$	1071.h	119.d	$2$	$2$	$2$	$0.534$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-119}) $	None	✓	$2$	$0$	$1$	$0$	$-1$	$-2$	$1$		$q+\beta q^{2}+\beta q^{4}+(-1+\beta )q^{5}-q^{7}+\cdots$
1071.1.h.b	$1071$	$1$	1071.h	119.d	$2$	$2$	$2$	$0.534$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-119}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$2$	$1$		$q+\beta q^{2}+\beta q^{4}+(1-\beta )q^{5}+q^{7}+q^{8}+\cdots$
1071.1.x.a	$1071$	$1$	1071.x	1071.x	$6$	$2$	$1$	$0.534$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$1$	$-1$	$1$	$-1$	$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}+\zeta_{6}q^{5}-q^{6}+\zeta_{6}^{2}q^{7}+\cdots$
1071.1.x.b	$1071$	$1$	1071.x	1071.x	$6$	$2$	$1$	$0.534$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$1$	$1$	$-1$	$1$	$1$		$q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{5}+q^{6}-\zeta_{6}^{2}q^{7}+\cdots$
1071.1.x.c	$1071$	$1$	1071.x	1071.x	$6$	$8$	$4$	$0.534$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$-1$	$-1$	$1$	$4$	$1$		$q+(-\zeta_{30}-\zeta_{30}^{9})q^{2}+\zeta_{30}q^{3}+(\zeta_{30}^{2}+\cdots)q^{4}+\cdots$
1071.1.x.d	$1071$	$1$	1071.x	1071.x	$6$	$8$	$4$	$0.534$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$-1$	$1$	$-1$	$-4$	$1$		$q+(-\zeta_{30}^{3}-\zeta_{30}^{7})q^{2}-\zeta_{30}^{7}q^{3}+\cdots$
1428.1.b.a	$1428$	$1$	1428.b	1428.b	$2$	$2$	$2$	$0.713$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-21}) $, $\Q(\sqrt{-119}) $	$\Q(\sqrt{51}) $		$8$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-q^{2}-iq^{3}+q^{4}+iq^{5}+iq^{6}+iq^{7}+\cdots$
1428.1.b.b	$1428$	$1$	1428.b	1428.b	$2$	$2$	$2$	$0.713$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-21}) $, $\Q(\sqrt{-119}) $	$\Q(\sqrt{51}) $		$8$	$0$	$2$	$0$	$0$	$0$	$1$		$q+q^{2}-iq^{3}+q^{4}-iq^{5}-iq^{6}+iq^{7}+\cdots$
1428.1.b.e	$1428$	$1$	1428.b	1428.b	$2$	$8$	$8$	$0.713$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-119}) $	None		$8$	$0$	$-2$	$0$	$0$	$0$	$1$		$q+\zeta_{20}^{4}q^{2}-\zeta_{20}q^{3}+\zeta_{20}^{8}q^{4}+(\zeta_{20}^{3}+\cdots)q^{5}+\cdots$
1428.1.b.f	$1428$	$1$	1428.b	1428.b	$2$	$8$	$8$	$0.713$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-119}) $	None		$8$	$0$	$2$	$0$	$0$	$0$	$1$		$q+\zeta_{20}^{6}q^{2}-\zeta_{20}q^{3}-\zeta_{20}^{2}q^{4}+(-\zeta_{20}^{3}+\cdots)q^{5}+\cdots$
1785.1.bk.a	$1785$	$1$	1785.bk	1785.ak	$4$	$4$	$2$	$0.891$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-119}) $	None		$8$	$0$	$-4$	$0$	$0$	$0$	$1$		$q+(-1-\zeta_{8}^{2})q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}+\cdots$
1785.1.bk.b	$1785$	$1$	1785.bk	1785.ak	$4$	$4$	$2$	$0.891$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-119}) $	None		$8$	$0$	$4$	$0$	$0$	$0$	$1$		$q+(1+\zeta_{8}^{2})q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}+\cdots$
1785.1.bk.c	$1785$	$1$	1785.bk	1785.ak	$4$	$16$	$8$	$0.891$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-119}) $	None		$8$	$0$	$-4$	$0$	$0$	$0$	$1$		$q+(-\zeta_{40}^{14}+\zeta_{40}^{16})q^{2}-\zeta_{40}^{11}q^{3}+\cdots$
1785.1.bk.d	$1785$	$1$	1785.bk	1785.ak	$4$	$16$	$8$	$0.891$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-119}) $	None		$8$	$0$	$4$	$0$	$0$	$0$	$1$		$q+(\zeta_{40}^{4}+\zeta_{40}^{6})q^{2}-\zeta_{40}^{11}q^{3}+(\zeta_{40}^{8}+\cdots)q^{4}+\cdots$
1904.1.n.a	$1904$	$1$	1904.n	119.d	$2$	$2$	$2$	$0.950$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-119}) $	None	✓	$2$	$0$	$0$	$-1$	$1$	$2$	$1$		$q-\beta q^{3}+(1-\beta )q^{5}+q^{7}+\beta q^{9}+q^{15}+\cdots$
1904.1.n.b	$1904$	$1$	1904.n	119.d	$2$	$2$	$2$	$0.950$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-119}) $	None	✓	$2$	$0$	$0$	$1$	$-1$	$-2$	$1$		$q+\beta q^{3}+(-1+\beta )q^{5}-q^{7}+\beta q^{9}+\cdots$
1904.1.bg.a	$1904$	$1$	1904.bg	1904.ag	$4$	$2$	$1$	$0.950$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$0$	$-2$	$-2$	$0$	$1$		$q-iq^{2}+(-1+i)q^{3}-q^{4}+(-1-i+\cdots)q^{5}+\cdots$
1904.1.bg.b	$1904$	$1$	1904.bg	1904.ag	$4$	$2$	$1$	$0.950$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$0$	$2$	$2$	$0$	$1$		$q-iq^{2}+(1-i)q^{3}-q^{4}+(1+i)q^{5}+\cdots$
1904.1.bg.c	$1904$	$1$	1904.bg	1904.ag	$4$	$8$	$4$	$0.950$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$0$	$-2$	$-2$	$0$	$1$		$q-\zeta_{20}^{9}q^{2}+(-\zeta_{20}+\zeta_{20}^{4})q^{3}-\zeta_{20}^{8}q^{4}+\cdots$
1904.1.bg.d	$1904$	$1$	1904.bg	1904.ag	$4$	$8$	$4$	$0.950$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$0$	$2$	$2$	$0$	$1$		$q-\zeta_{20}q^{2}+(\zeta_{20}^{6}+\zeta_{20}^{9})q^{3}+\zeta_{20}^{2}q^{4}+\cdots$
2023.1.c.e	$2023$	$1$	2023.c	7.b	$2$	$4$	$4$	$1.010$	$\Q(i, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q-\beta _{2}q^{2}-\beta _{1}q^{3}-\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots$
2023.1.f.b	$2023$	$1$	2023.f	119.f	$4$	$8$	$4$	$1.010$	8.0.40960000.1	$D_{5}$	$\Q(\sqrt{-119}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\beta _{4}-\beta _{5})q^{2}+(-\beta _{6}+\beta _{7})q^{3}+(-1+\cdots)q^{4}+\cdots$
2023.1.l.b	$2023$	$1$	2023.l	119.l	$8$	$16$	$4$	$1.010$	16.0.$\cdots$.1	$D_{5}$	$\Q(\sqrt{-119}) $	None		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{12}q^{2}-\beta _{1}q^{3}-\beta _{8}q^{4}+(-\beta _{10}+\cdots)q^{5}+\cdots$
2380.1.bi.a	$2380$	$1$	2380.bi	2380.ai	$4$	$4$	$2$	$1.188$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-119}) $	None		$8$	$0$	$-4$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-\zeta_{8}q^{5}+\zeta_{8}^{3}q^{7}-q^{8}+\cdots$
2380.1.bi.b	$2380$	$1$	2380.bi	2380.ai	$4$	$4$	$2$	$1.188$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-119}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}q^{5}-\zeta_{8}^{3}q^{7}+\cdots$
2380.1.bi.c	$2380$	$1$	2380.bi	2380.ai	$4$	$16$	$8$	$1.188$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-119}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{40}^{2}q^{2}+(\zeta_{40}^{13}+\zeta_{40}^{17})q^{3}+\cdots$
2380.1.bi.d	$2380$	$1$	2380.bi	2380.ai	$4$	$16$	$8$	$1.188$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-119}) $	None		$8$	$0$	$4$	$0$	$0$	$0$	$1$		$q-\zeta_{40}^{8}q^{2}+(\zeta_{40}^{13}+\zeta_{40}^{17})q^{3}+\cdots$
2499.1.e.a	$2499$	$1$	2499.e	51.c	$2$	$1$	$1$	$1.247$	$\Q$	$D_{2}$	$\Q(\sqrt{-51}) $, $\Q(\sqrt{-119}) $	$\Q(\sqrt{21}) $	✓	$4$	$0$	$0$	$-1$	$2$	$0$	$1$		$q-q^{3}+q^{4}+2q^{5}+q^{9}-q^{12}-2q^{15}+\cdots$
2499.1.e.b	$2499$	$1$	2499.e	51.c	$2$	$1$	$1$	$1.247$	$\Q$	$D_{2}$	$\Q(\sqrt{-51}) $, $\Q(\sqrt{-119}) $	$\Q(\sqrt{21}) $	✓	$4$	$0$	$0$	$1$	$-2$	$0$	$1$		$q+q^{3}+q^{4}-2q^{5}+q^{9}+q^{12}-2q^{15}+\cdots$
2499.1.e.e	$2499$	$1$	2499.e	51.c	$2$	$4$	$4$	$1.247$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$0$	$-1$	$2$	$0$	$1$		$q+(\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{3}+(-1+\cdots)q^{4}+\cdots$
2499.1.e.f	$2499$	$1$	2499.e	51.c	$2$	$4$	$4$	$1.247$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$0$	$1$	$-2$	$0$	$1$		$q+(\zeta_{10}+\zeta_{10}^{4})q^{2}+\zeta_{10}q^{3}+(-1+\cdots)q^{4}+\cdots$
2499.1.q.a	$2499$	$1$	2499.q	357.q	$6$	$2$	$1$	$1.247$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-51}) $, $\Q(\sqrt{-119}) $	$\Q(\sqrt{21}) $		$8$	$0$	$0$	$-1$	$2$	$0$	$1$		$q-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}+\cdots$
2499.1.q.b	$2499$	$1$	2499.q	357.q	$6$	$2$	$1$	$1.247$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-51}) $, $\Q(\sqrt{-119}) $	$\Q(\sqrt{21}) $		$8$	$0$	$0$	$1$	$-2$	$0$	$1$		$q+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}+\cdots$
2499.1.q.e	$2499$	$1$	2499.q	357.q	$6$	$8$	$4$	$1.247$	$\Q(\zeta_{15})$	$D_{10}$	$\Q(\sqrt{-119}) $	None		$8$	$0$	$0$	$-1$	$2$	$0$	$1$		$q+(\zeta_{30}^{11}+\zeta_{30}^{14})q^{2}+\zeta_{30}q^{3}+(-\zeta_{30}^{7}+\cdots)q^{4}+\cdots$
2499.1.q.f	$2499$	$1$	2499.q	357.q	$6$	$8$	$4$	$1.247$	$\Q(\zeta_{15})$	$D_{10}$	$\Q(\sqrt{-119}) $	None		$8$	$0$	$0$	$1$	$-2$	$0$	$1$		$q+(-\zeta_{30}^{2}+\zeta_{30}^{8})q^{2}-\zeta_{30}^{7}q^{3}+\cdots$
2856.1.bd.i	$2856$	$1$	2856.bd	2856.ad	$2$	$2$	$2$	$1.425$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-119}) $, $\Q(\sqrt{-42}) $	$\Q(\sqrt{102}) $		$8$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-q^{2}-iq^{3}+q^{4}+iq^{6}+iq^{7}-q^{8}+\cdots$
2856.1.bd.j	$2856$	$1$	2856.bd	2856.ad	$2$	$2$	$2$	$1.425$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-119}) $, $\Q(\sqrt{-42}) $	$\Q(\sqrt{102}) $		$8$	$0$	$2$	$0$	$0$	$0$	$1$		$q+q^{2}-iq^{3}+q^{4}-iq^{6}-iq^{7}+q^{8}+\cdots$
2856.1.bd.k	$2856$	$1$	2856.bd	2856.ad	$2$	$8$	$8$	$1.425$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-119}) $	None		$8$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-\zeta_{20}^{6}q^{2}-\zeta_{20}q^{3}-\zeta_{20}^{2}q^{4}+(\zeta_{20}^{3}+\cdots)q^{5}+\cdots$
2856.1.bd.l	$2856$	$1$	2856.bd	2856.ad	$2$	$8$	$8$	$1.425$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-119}) $	None		$8$	$0$	$2$	$0$	$0$	$0$	$1$		$q-\zeta_{20}^{4}q^{2}-\zeta_{20}q^{3}+\zeta_{20}^{8}q^{4}+(-\zeta_{20}^{3}+\cdots)q^{5}+\cdots$
2975.1.b.a	$2975$	$1$	2975.b	595.b	$2$	$4$	$4$	$1.485$	$\Q(i, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}-\beta _{1}q^{3}+\beta _{2}q^{4}+(-1+\beta _{2}+\cdots)q^{6}+\cdots$

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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.