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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 168 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				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
55.1.d.a	$55$	$1$	55.d	55.d	$2$	$1$	$1$	$0.027$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q-q^{4}-q^{5}+q^{9}-q^{11}+q^{16}+q^{20}+\cdots$
80.1.h.a	$80$	$1$	80.h	20.d	$2$	$1$	$1$	$0.040$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q-q^{5}-q^{9}+q^{25}+2q^{29}-2q^{41}+\cdots$
95.1.d.a	$95$	$1$	95.d	95.d	$2$	$1$	$1$	$0.047$	$\Q$	$D_{2}$	$\Q(\sqrt{-19}) $, $\Q(\sqrt{-95}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q-q^{4}+q^{5}-q^{9}-2q^{11}+q^{16}+q^{19}+\cdots$
145.1.f.a	$145$	$1$	145.f	145.f	$4$	$2$	$1$	$0.072$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{4}-iq^{5}+iq^{9}+(-1-i)q^{11}+\cdots$
155.1.c.a	$155$	$1$	155.c	155.c	$2$	$1$	$1$	$0.077$	$\Q$	$D_{2}$	$\Q(\sqrt{-31}) $, $\Q(\sqrt{-155}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+q^{4}-q^{5}-q^{9}+q^{16}-2q^{19}-q^{20}+\cdots$
225.1.g.a	$225$	$1$	225.g	5.c	$4$	$2$	$1$	$0.112$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-15}) $	$\Q(\sqrt{5}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{4}-q^{16}-iq^{19}-q^{31}+iq^{49}+\cdots$
275.1.c.a	$275$	$1$	275.c	11.b	$2$	$1$	$1$	$0.137$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}-q^{9}-q^{11}+q^{16}-2q^{31}+\cdots$
295.1.d.a	$295$	$1$	295.d	295.d	$2$	$1$	$1$	$0.147$	$\Q$	$D_{2}$	$\Q(\sqrt{-59}) $, $\Q(\sqrt{-295}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q-q^{4}+q^{5}+q^{9}+q^{16}-2q^{19}-q^{20}+\cdots$
320.1.h.a	$320$	$1$	320.h	20.d	$2$	$1$	$1$	$0.160$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+q^{5}-q^{9}+q^{25}-2q^{29}-2q^{41}+\cdots$
355.1.c.a	$355$	$1$	355.c	355.c	$2$	$1$	$1$	$0.177$	$\Q$	$D_{2}$	$\Q(\sqrt{-71}) $, $\Q(\sqrt{-355}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+q^{4}-q^{5}+q^{9}+q^{16}-2q^{19}-q^{20}+\cdots$
380.1.o.a	$380$	$1$	380.o	95.h	$6$	$2$	$1$	$0.190$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{9}+q^{11}+\zeta_{6}^{2}q^{19}+\cdots$
395.1.c.a	$395$	$1$	395.c	395.c	$2$	$1$	$1$	$0.197$	$\Q$	$D_{2}$	$\Q(\sqrt{-79}) $, $\Q(\sqrt{-395}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+q^{4}+q^{5}-q^{9}-2q^{11}+q^{16}-2q^{19}+\cdots$
400.1.b.a	$400$	$1$	400.b	4.b	$2$	$1$	$1$	$0.200$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{9}-2q^{29}-2q^{41}+q^{49}-2q^{61}+\cdots$
475.1.c.a	$475$	$1$	475.c	19.b	$2$	$1$	$1$	$0.237$	$\Q$	$D_{2}$	$\Q(\sqrt{-19}) $, $\Q(\sqrt{-95}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}+q^{9}-2q^{11}+q^{16}-q^{19}+\cdots$
495.1.h.a	$495$	$1$	495.h	55.d	$2$	$1$	$1$	$0.247$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q-q^{4}+q^{5}+q^{11}+q^{16}-q^{20}+q^{25}+\cdots$
505.1.g.a	$505$	$1$	505.g	505.g	$4$	$2$	$1$	$0.252$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+iq^{4}+q^{5}+iq^{9}+(-1-i)q^{11}+\cdots$
605.1.h.a	$605$	$1$	605.h	55.h	$10$	$4$	$1$	$0.302$	$\Q(\zeta_{10})$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{5}) $		$16$	$0$	$0$	$0$	$1$	$0$	$1$		$q+\zeta_{10}^{3}q^{4}+\zeta_{10}q^{5}+\zeta_{10}^{4}q^{9}-\zeta_{10}q^{16}+\cdots$
620.1.q.a	$620$	$1$	620.q	155.i	$6$	$2$	$1$	$0.309$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+\zeta_{6}q^{5}+\zeta_{6}q^{9}+(-1+\zeta_{6}^{2})q^{11}+\cdots$
655.1.d.b	$655$	$1$	655.d	655.d	$2$	$1$	$1$	$0.327$	$\Q$	$D_{2}$	$\Q(\sqrt{-131}) $, $\Q(\sqrt{-655}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q-q^{4}-q^{5}+q^{9}+2q^{11}+q^{16}+q^{20}+\cdots$
695.1.d.b	$695$	$1$	695.d	695.d	$2$	$1$	$1$	$0.347$	$\Q$	$D_{2}$	$\Q(\sqrt{-139}) $, $\Q(\sqrt{-695}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q-q^{4}+q^{5}-q^{9}+2q^{11}+q^{16}-q^{20}+\cdots$
695.1.h.a	$695$	$1$	695.h	695.h	$6$	$2$	$1$	$0.347$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q-\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{9}+\zeta_{6}q^{11}+\cdots$
720.1.j.a	$720$	$1$	720.j	20.d	$2$	$1$	$1$	$0.359$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+q^{5}+q^{25}-2q^{29}+2q^{41}-q^{49}+\cdots$
725.1.g.a	$725$	$1$	725.g	29.c	$4$	$2$	$1$	$0.362$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{4}-iq^{9}+(-1-i)q^{11}-q^{16}+\cdots$
755.1.c.b	$755$	$1$	755.c	755.c	$2$	$1$	$1$	$0.377$	$\Q$	$D_{2}$	$\Q(\sqrt{-151}) $, $\Q(\sqrt{-755}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+q^{4}-q^{5}-q^{9}+2q^{11}+q^{16}+2q^{19}+\cdots$
755.1.k.a	$755$	$1$	755.k	755.k	$6$	$2$	$1$	$0.377$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}-q^{9}+\zeta_{6}q^{11}+\cdots$
775.1.d.a	$775$	$1$	775.d	31.b	$2$	$1$	$1$	$0.387$	$\Q$	$D_{2}$	$\Q(\sqrt{-31}) $, $\Q(\sqrt{-155}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{4}+q^{9}+q^{16}+2q^{19}-q^{31}+\cdots$
855.1.g.a	$855$	$1$	855.g	95.d	$2$	$1$	$1$	$0.427$	$\Q$	$D_{2}$	$\Q(\sqrt{-19}) $, $\Q(\sqrt{-95}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q-q^{4}-q^{5}+2q^{11}+q^{16}+q^{19}+\cdots$
880.1.i.a	$880$	$1$	880.i	55.d	$2$	$1$	$1$	$0.439$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q-q^{5}+q^{9}+q^{11}+q^{25}+2q^{31}+\cdots$
895.1.d.a	$895$	$1$	895.d	895.d	$2$	$1$	$1$	$0.447$	$\Q$	$D_{2}$	$\Q(\sqrt{-179}) $, $\Q(\sqrt{-895}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q-q^{4}+q^{5}+q^{9}+q^{16}-2q^{19}-q^{20}+\cdots$
905.1.g.a	$905$	$1$	905.g	905.g	$4$	$2$	$1$	$0.452$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+iq^{4}+q^{5}+q^{9}-iq^{11}-q^{16}+\cdots$
955.1.c.a	$955$	$1$	955.c	955.c	$2$	$1$	$1$	$0.477$	$\Q$	$D_{2}$	$\Q(\sqrt{-191}) $, $\Q(\sqrt{-955}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+q^{4}-q^{5}+q^{9}+q^{16}-q^{20}+q^{25}+\cdots$
995.1.c.a	$995$	$1$	995.c	995.c	$2$	$1$	$1$	$0.497$	$\Q$	$D_{2}$	$\Q(\sqrt{-199}) $, $\Q(\sqrt{-995}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+q^{4}+q^{5}-q^{9}+q^{16}+q^{20}+q^{25}+\cdots$
995.1.i.a	$995$	$1$	995.i	995.i	$6$	$2$	$1$	$0.497$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+\zeta_{6}^{2}q^{4}+q^{5}-\zeta_{6}^{2}q^{9}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{11}+\cdots$
995.1.p.a	$995$	$1$	995.p	995.p	$18$	$6$	$1$	$0.497$	$\Q(\zeta_{18})$	$D_{18}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$-3$	$0$	$1$		$q-\zeta_{18}^{5}q^{4}-\zeta_{18}^{3}q^{5}-\zeta_{18}^{2}q^{9}+\cdots$
1025.1.f.a	$1025$	$1$	1025.f	205.f	$4$	$2$	$1$	$0.512$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{4}+q^{9}+(1+i)q^{11}-q^{16}+(-1+\cdots)q^{19}+\cdots$
1025.1.i.a	$1025$	$1$	1025.i	205.i	$4$	$2$	$1$	$0.512$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{4}-q^{9}+(1-i)q^{11}-q^{16}+(1+\cdots)q^{19}+\cdots$
1055.1.d.b	$1055$	$1$	1055.d	1055.d	$2$	$1$	$1$	$0.527$	$\Q$	$D_{2}$	$\Q(\sqrt{-211}) $, $\Q(\sqrt{-1055}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q-q^{4}-q^{5}-q^{9}+2q^{11}+q^{16}+2q^{19}+\cdots$
1055.1.m.a	$1055$	$1$	1055.m	1055.m	$10$	$4$	$1$	$0.527$	$\Q(\zeta_{10})$	$D_{10}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+\zeta_{10}q^{4}+\zeta_{10}q^{5}+\zeta_{10}^{3}q^{9}+(-\zeta_{10}^{3}+\cdots)q^{11}+\cdots$
1145.1.g.a	$1145$	$1$	1145.g	1145.g	$4$	$2$	$1$	$0.571$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{4}-iq^{5}+q^{9}-q^{16}-q^{20}+\cdots$
1195.1.c.a	$1195$	$1$	1195.c	1195.c	$2$	$1$	$1$	$0.596$	$\Q$	$D_{2}$	$\Q(\sqrt{-239}) $, $\Q(\sqrt{-1195}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+q^{4}+q^{5}+q^{9}-2q^{11}+q^{16}+q^{20}+\cdots$
1225.1.g.a	$1225$	$1$	1225.g	5.c	$4$	$2$	$1$	$0.611$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-35}) $	$\Q(\sqrt{5}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{4}+iq^{9}+q^{11}-q^{16}-iq^{29}+\cdots$
1225.1.q.a	$1225$	$1$	1225.q	35.l	$12$	$4$	$1$	$0.611$	$\Q(\zeta_{12})$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-35}) $	$\Q(\sqrt{5}) $		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{12}q^{4}-\zeta_{12}^{5}q^{9}+\zeta_{12}^{4}q^{11}+\cdots$
1255.1.d.b	$1255$	$1$	1255.d	1255.d	$2$	$1$	$1$	$0.626$	$\Q$	$D_{2}$	$\Q(\sqrt{-251}) $, $\Q(\sqrt{-1255}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q-q^{4}-q^{5}+q^{9}+q^{16}+q^{20}+q^{25}+\cdots$
1280.1.e.a	$1280$	$1$	1280.e	40.e	$2$	$2$	$2$	$0.639$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{5}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{5}+q^{9}-q^{25}-iq^{29}+q^{41}+\cdots$
1305.1.l.a	$1305$	$1$	1305.l	145.f	$4$	$2$	$1$	$0.651$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{4}-iq^{5}+(1-i)q^{11}-q^{16}+\cdots$
1355.1.c.b	$1355$	$1$	1355.c	1355.c	$2$	$1$	$1$	$0.676$	$\Q$	$D_{2}$	$\Q(\sqrt{-271}) $, $\Q(\sqrt{-1355}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+q^{4}-q^{5}-q^{9}+2q^{11}+q^{16}-q^{20}+\cdots$
1375.1.q.a	$1375$	$1$	1375.q	55.h	$10$	$4$	$1$	$0.686$	$\Q(\zeta_{10})$	$D_{10}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{10}^{4}q^{4}+\zeta_{10}^{2}q^{9}-\zeta_{10}^{4}q^{11}+\cdots$
1375.1.x.a	$1375$	$1$	1375.x	11.d	$10$	$4$	$1$	$0.686$	$\Q(\zeta_{10})$	$D_{10}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{10}^{3}q^{4}-\zeta_{10}^{4}q^{9}+\zeta_{10}^{3}q^{11}+\cdots$
1395.1.b.a	$1395$	$1$	1395.b	155.c	$2$	$1$	$1$	$0.696$	$\Q$	$D_{2}$	$\Q(\sqrt{-31}) $, $\Q(\sqrt{-155}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+q^{4}+q^{5}+q^{16}-2q^{19}+q^{20}+\cdots$
1475.1.c.a	$1475$	$1$	1475.c	59.b	$2$	$1$	$1$	$0.736$	$\Q$	$D_{2}$	$\Q(\sqrt{-59}) $, $\Q(\sqrt{-295}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}-q^{9}+q^{16}+2q^{19}+2q^{29}+\cdots$

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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.