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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 574 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
76.1.c.a	$76$	$1$	76.c	19.b	$2$	$1$	$1$	$0.038$	$\Q$	$D_{3}$	$\Q(\sqrt{-19}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$-1$	$1$		$q-q^{5}-q^{7}+q^{9}-q^{11}-q^{17}+q^{19}+\cdots$
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}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q-q^{4}+q^{5}-q^{9}-2q^{11}+q^{16}+q^{19}+\cdots$
133.1.r.a	$133$	$1$	133.r	133.r	$6$	$2$	$1$	$0.066$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$1$	$-1$	$1$		$q-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
171.1.c.a	$171$	$1$	171.c	19.b	$2$	$1$	$1$	$0.085$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-19}) $	$\Q(\sqrt{57}) $	✓	$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+q^{4}-2q^{7}+q^{16}-q^{19}-q^{25}+\cdots$
209.1.m.a	$209$	$1$	209.m	209.m	$10$	$4$	$1$	$0.104$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$3$	$1$		$q+\zeta_{10}^{4}q^{4}+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{5}+(1+\cdots)q^{7}+\cdots$
304.1.e.a	$304$	$1$	304.e	19.b	$2$	$1$	$1$	$0.152$	$\Q$	$D_{3}$	$\Q(\sqrt{-19}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$1$	$1$		$q-q^{5}+q^{7}+q^{9}+q^{11}-q^{17}-q^{19}+\cdots$
323.1.c.a	$323$	$1$	323.c	323.c	$2$	$1$	$1$	$0.161$	$\Q$	$D_{2}$	$\Q(\sqrt{-19}) $, $\Q(\sqrt{-323}) $	$\Q(\sqrt{17}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}-q^{9}+q^{16}-q^{17}-q^{19}+q^{25}+\cdots$
323.1.g.a	$323$	$1$	323.g	323.g	$4$	$2$	$1$	$0.161$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$2$	$-2$	$1$		$q-q^{4}+(1+i)q^{5}+(-1+i)q^{7}+iq^{9}+\cdots$
323.1.l.a	$323$	$1$	323.l	323.l	$8$	$4$	$1$	$0.161$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-4$	$0$	$1$		$q+\zeta_{8}^{2}q^{4}+(-1-\zeta_{8}^{3})q^{5}+(\zeta_{8}^{2}+\zeta_{8}^{3}+\cdots)q^{7}+\cdots$
380.1.g.a	$380$	$1$	380.g	95.d	$2$	$2$	$2$	$0.190$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+\zeta_{6}^{2}q^{5}+(\zeta_{6}+\zeta_{6}^{2})q^{7}-q^{9}+q^{11}+\cdots$
437.1.o.a	$437$	$1$	437.o	437.o	$22$	$10$	$1$	$0.218$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$-2$	$1$		$q+\zeta_{22}^{8}q^{4}+(-\zeta_{22}-\zeta_{22}^{3})q^{5}+(-\zeta_{22}^{3}+\cdots)q^{7}+\cdots$
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}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}+q^{9}-2q^{11}+q^{16}-q^{19}+\cdots$
475.1.m.a	$475$	$1$	475.m	475.m	$10$	$4$	$1$	$0.237$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+\zeta_{10}^{3}q^{4}-\zeta_{10}q^{5}+(\zeta_{10}+\zeta_{10}^{4}+\cdots)q^{7}+\cdots$
475.1.o.a	$475$	$1$	475.o	475.o	$10$	$4$	$1$	$0.237$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-1$	$-2$	$1$		$q+\zeta_{10}^{2}q^{4}+\zeta_{10}^{4}q^{5}+(-\zeta_{10}+\zeta_{10}^{4}+\cdots)q^{7}+\cdots$
532.1.bc.a	$532$	$1$	532.bc	133.r	$6$	$2$	$1$	$0.266$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$-1$	$1$		$q+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{11}+\cdots$
532.1.bc.b	$532$	$1$	532.bc	133.r	$6$	$2$	$1$	$0.266$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$1$	$2$	$1$		$q-\zeta_{6}^{2}q^{5}+q^{7}+\zeta_{6}^{2}q^{9}-\zeta_{6}q^{11}+\cdots$
665.1.n.a	$665$	$1$	665.n	665.n	$4$	$2$	$1$	$0.332$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$-2$	$1$		$q-iq^{4}-q^{5}-q^{7}-iq^{9}-q^{16}+(-1+\cdots)q^{17}+\cdots$
665.1.n.b	$665$	$1$	665.n	665.n	$4$	$2$	$1$	$0.332$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q-iq^{4}+q^{5}+iq^{7}-iq^{9}-q^{16}+\cdots$
665.1.x.a	$665$	$1$	665.x	665.x	$6$	$2$	$1$	$0.332$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-1$	$1$	$1$		$q-\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\zeta_{6}q^{9}+\cdots$
665.1.x.b	$665$	$1$	665.x	665.x	$6$	$2$	$1$	$0.332$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$2$	$-1$	$1$		$q-\zeta_{6}^{2}q^{4}+q^{5}-\zeta_{6}q^{7}+\zeta_{6}q^{9}+\zeta_{6}^{2}q^{11}+\cdots$
665.1.ca.a	$665$	$1$	665.ca	665.ba	$12$	$4$	$1$	$0.332$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-4$	$2$	$1$		$q-\zeta_{12}^{5}q^{4}-q^{5}-\zeta_{12}^{4}q^{7}-\zeta_{12}q^{9}+\cdots$
665.1.ca.b	$665$	$1$	665.ca	665.ba	$12$	$4$	$1$	$0.332$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-\zeta_{12}^{5}q^{4}-\zeta_{12}^{2}q^{5}+\zeta_{12}q^{7}-\zeta_{12}q^{9}+\cdots$
684.1.h.a	$684$	$1$	684.h	19.b	$2$	$1$	$1$	$0.341$	$\Q$	$D_{3}$	$\Q(\sqrt{-19}) $	None	✓	$2$	$0$	$0$	$0$	$1$	$-1$	$1$		$q+q^{5}-q^{7}+q^{11}+q^{17}+q^{19}-2q^{23}+\cdots$
684.1.h.b	$684$	$1$	684.h	19.b	$2$	$2$	$2$	$0.341$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-19}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q-\beta q^{5}+q^{7}+\beta q^{11}+\beta q^{17}-q^{19}+\cdots$
817.1.i.a	$817$	$1$	817.i	817.i	$6$	$2$	$1$	$0.408$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$1$	$1$		$q+q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}-\zeta_{6}q^{9}-q^{11}+\cdots$
817.1.z.a	$817$	$1$	817.z	817.z	$14$	$6$	$1$	$0.408$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$-2$	$1$		$q+\zeta_{14}^{2}q^{4}+(\zeta_{14}^{2}+\zeta_{14}^{4})q^{5}+(-\zeta_{14}+\cdots)q^{7}+\cdots$
817.1.bz.a	$817$	$1$	817.bz	817.az	$42$	$12$	$1$	$0.408$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$2$	$-1$	$1$		$q+\zeta_{42}^{12}q^{4}+(\zeta_{42}^{10}-\zeta_{42}^{19})q^{5}+\cdots$
836.1.v.a	$836$	$1$	836.v	209.m	$10$	$8$	$2$	$0.417$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$2$	$-3$	$1$		$q+(-\zeta_{30}^{7}-\zeta_{30}^{11})q^{5}+(\zeta_{30}^{4}-\zeta_{30}^{5}+\cdots)q^{7}+\cdots$
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}) $	✓	$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q-q^{4}-q^{5}+2q^{11}+q^{16}+q^{19}+\cdots$
855.1.g.b	$855$	$1$	855.g	95.d	$2$	$2$	$2$	$0.427$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-19}) $	$\Q(\sqrt{285}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{4}-iq^{5}+q^{16}-iq^{17}-q^{19}+\cdots$
855.1.m.a	$855$	$1$	855.m	285.j	$4$	$4$	$2$	$0.427$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-19}) $	None		$8$	$0$	$0$	$0$	$0$	$-4$	$1$		$q-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{5}+(-1-\zeta_{8}^{2})q^{7}+\cdots$
855.1.m.b	$855$	$1$	855.m	285.j	$4$	$4$	$2$	$0.427$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-19}) $	None		$8$	$0$	$0$	$0$	$0$	$4$	$1$		$q-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+(1+\zeta_{8}^{2})q^{7}+\cdots$
893.1.o.a	$893$	$1$	893.o	893.o	$46$	$22$	$1$	$0.446$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$-2$	$1$		$q-\zeta_{46}^{19}q^{4}+(\zeta_{46}^{12}-\zeta_{46}^{21})q^{5}+\cdots$
931.1.b.a	$931$	$1$	931.b	19.b	$2$	$1$	$1$	$0.465$	$\Q$	$D_{3}$	$\Q(\sqrt{-19}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+q^{4}-q^{5}+q^{9}-q^{11}+q^{16}+2q^{17}+\cdots$
931.1.b.b	$931$	$1$	931.b	19.b	$2$	$1$	$1$	$0.465$	$\Q$	$D_{3}$	$\Q(\sqrt{-19}) $	None	✓	$2$	$0$	$0$	$0$	$1$	$0$	$1$		$q+q^{4}+q^{5}+q^{9}-q^{11}+q^{16}-2q^{17}+\cdots$
931.1.r.a	$931$	$1$	931.r	133.r	$6$	$2$	$1$	$0.465$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}+\cdots$
931.1.ba.a	$931$	$1$	931.ba	931.aa	$14$	$6$	$1$	$0.465$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$-1$	$1$		$q-\zeta_{14}^{5}q^{4}+(\zeta_{14}^{2}+\zeta_{14}^{6})q^{5}+\zeta_{14}^{4}q^{7}+\cdots$
931.1.bq.a	$931$	$1$	931.bq	931.aq	$42$	$12$	$1$	$0.465$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-1$	$1$	$1$		$q-\zeta_{42}^{17}q^{4}+(-\zeta_{42}^{5}+\zeta_{42}^{18})q^{5}+\cdots$
19.3.b.a	$19$	$3$	19.b	19.b	$2$	$1$	$1$	$0.518$	$\Q$	$_{}$	$\Q(\sqrt{-19}) $	None	✓	$2$	$0$	$0$	$0$	$-9$	$-5$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{4}-9q^{5}-5q^{7}+9q^{9}+3q^{11}+\cdots$
1045.1.k.b	$1045$	$1$	1045.k	1045.k	$4$	$2$	$1$	$0.522$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$2$	$-2$	$1$		$q-iq^{4}+q^{5}+(-1+i)q^{7}-iq^{9}+\cdots$
1045.1.k.c	$1045$	$1$	1045.k	1045.k	$4$	$2$	$1$	$0.522$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$2$	$2$	$1$		$q-iq^{4}+q^{5}+(1-i)q^{7}-iq^{9}+iq^{11}+\cdots$
1045.1.w.b	$1045$	$1$	1045.w	1045.w	$10$	$4$	$1$	$0.522$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-1$	$-5$	$1$		$q+\zeta_{10}q^{4}-\zeta_{10}q^{5}+(-1+\zeta_{10}^{2}+\cdots)q^{7}+\cdots$
1045.1.w.c	$1045$	$1$	1045.w	1045.w	$10$	$4$	$1$	$0.522$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-1$	$5$	$1$		$q+\zeta_{10}q^{4}-\zeta_{10}^{3}q^{5}+(1-\zeta_{10}^{2})q^{7}+\cdots$
1045.1.br.a	$1045$	$1$	1045.br	1045.ar	$20$	$8$	$1$	$0.522$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$-8$	$1$		$q-\zeta_{20}^{3}q^{4}+\zeta_{20}^{4}q^{5}+(-1-\zeta_{20}+\cdots)q^{7}+\cdots$
1045.1.br.b	$1045$	$1$	1045.br	1045.ar	$20$	$8$	$1$	$0.522$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$-2$	$1$		$q-\zeta_{20}^{3}q^{4}+\zeta_{20}^{8}q^{5}+(\zeta_{20}^{5}-\zeta_{20}^{6}+\cdots)q^{7}+\cdots$
1159.1.d.a	$1159$	$1$	1159.d	1159.d	$2$	$1$	$1$	$0.578$	$\Q$	$D_{2}$	$\Q(\sqrt{-19}) $, $\Q(\sqrt{-1159}) $	$\Q(\sqrt{61}) $	✓	$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-q^{4}-2q^{5}+q^{9}+q^{16}+q^{19}+2q^{20}+\cdots$
1159.1.n.a	$1159$	$1$	1159.n	1159.n	$6$	$2$	$1$	$0.578$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-1$	$3$	$1$		$q-\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+(1-\zeta_{6}^{2})q^{7}+q^{9}+\cdots$
1159.1.q.a	$1159$	$1$	1159.q	1159.q	$6$	$2$	$1$	$0.578$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$1$	$1$	$1$		$q-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}^{2}q^{7}+q^{9}+\cdots$
1159.1.ba.a	$1159$	$1$	1159.ba	1159.aa	$10$	$4$	$1$	$0.578$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+\zeta_{10}q^{4}+(\zeta_{10}^{3}-\zeta_{10}^{4})q^{5}-\zeta_{10}q^{9}+\cdots$
1159.1.bc.a	$1159$	$1$	1159.bc	1159.ac	$10$	$4$	$1$	$0.578$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$-2$	$1$		$q+\zeta_{10}^{2}q^{4}+(-\zeta_{10}-\zeta_{10}^{3})q^{5}+\zeta_{10}^{4}q^{7}+\cdots$

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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.