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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 (40 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
219.1.c.a	$219$	$1$	219.c	219.c	$2$	$1$	$1$	$0.109$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-219}) $	$\Q(\sqrt{73}) $	✓	$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-q^{3}+q^{4}+q^{9}-q^{12}+q^{16}-2q^{19}+\cdots$
876.1.g.a	$876$	$1$	876.g	219.c	$2$	$1$	$1$	$0.437$	$\Q$	$D_{3}$	$\Q(\sqrt{-219}) $	None	✓	$2$	$0$	$0$	$1$	$-1$	$0$	$1$		$q+q^{3}-q^{5}+q^{9}+2q^{11}-q^{15}-q^{17}+\cdots$
876.1.g.b	$876$	$1$	876.g	219.c	$2$	$1$	$1$	$0.437$	$\Q$	$D_{3}$	$\Q(\sqrt{-219}) $	None	✓	$2$	$0$	$0$	$1$	$1$	$0$	$1$		$q+q^{3}+q^{5}+q^{9}-2q^{11}+q^{15}+q^{17}+\cdots$
876.1.g.c	$876$	$1$	876.g	219.c	$2$	$2$	$2$	$0.437$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-219}) $	None	✓	$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-q^{3}-\beta q^{5}+q^{9}+\beta q^{15}+\beta q^{17}+\cdots$
1095.1.h.e	$1095$	$1$	1095.h	1095.h	$2$	$4$	$4$	$0.546$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-219}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{2}q^{3}-q^{4}-\zeta_{8}q^{5}-q^{9}+(-\zeta_{8}+\cdots)q^{11}+\cdots$
1971.1.c.a	$1971$	$1$	1971.c	219.c	$2$	$1$	$1$	$0.984$	$\Q$	$D_{3}$	$\Q(\sqrt{-219}) $	None	✓	$2$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+q^{4}-2q^{5}+q^{11}+q^{16}+q^{17}+\cdots$
1971.1.c.b	$1971$	$1$	1971.c	219.c	$2$	$1$	$1$	$0.984$	$\Q$	$D_{3}$	$\Q(\sqrt{-219}) $	None	✓	$2$	$0$	$0$	$0$	$2$	$0$	$1$		$q+q^{4}+2q^{5}-q^{11}+q^{16}-q^{17}+\cdots$
1971.1.c.c	$1971$	$1$	1971.c	219.c	$2$	$2$	$2$	$0.984$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-219}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}-\beta q^{11}+q^{16}+\beta q^{17}+q^{19}+\cdots$
2409.1.bd.a	$2409$	$1$	2409.bd	2409.ad	$10$	$4$	$1$	$1.202$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-219}) $	None		$4$	$0$	$0$	$-1$	$-3$	$0$	$1$		$q+\zeta_{10}^{4}q^{3}-\zeta_{10}q^{4}+(-1-\zeta_{10}^{4}+\cdots)q^{5}+\cdots$
2409.1.bd.b	$2409$	$1$	2409.bd	2409.ad	$10$	$4$	$1$	$1.202$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-219}) $	None		$4$	$0$	$0$	$-1$	$3$	$0$	$1$		$q+\zeta_{10}^{4}q^{3}-\zeta_{10}q^{4}+(1+\zeta_{10}^{4})q^{5}+\cdots$
2409.1.bd.c	$2409$	$1$	2409.bd	2409.ad	$10$	$8$	$2$	$1.202$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-219}) $	None		$8$	$0$	$0$	$2$	$0$	$0$	$1$		$q-\zeta_{20}^{8}q^{3}-\zeta_{20}^{2}q^{4}+(\zeta_{20}^{3}+\zeta_{20}^{5}+\cdots)q^{5}+\cdots$
3285.1.q.a	$3285$	$1$	3285.q	365.i	$4$	$8$	$4$	$1.639$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-219}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{16}^{4}q^{4}+\zeta_{16}^{3}q^{5}+(\zeta_{16}^{3}+\zeta_{16}^{5}+\cdots)q^{11}+\cdots$
3504.1.l.a	$3504$	$1$	3504.l	219.c	$2$	$1$	$1$	$1.749$	$\Q$	$D_{3}$	$\Q(\sqrt{-219}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$0$	$1$		$q-q^{3}-q^{5}+q^{9}-2q^{11}+q^{15}-q^{17}+\cdots$
3504.1.l.b	$3504$	$1$	3504.l	219.c	$2$	$1$	$1$	$1.749$	$\Q$	$D_{3}$	$\Q(\sqrt{-219}) $	None	✓	$2$	$0$	$0$	$-1$	$1$	$0$	$1$		$q-q^{3}+q^{5}+q^{9}+2q^{11}-q^{15}+q^{17}+\cdots$
3504.1.l.c	$3504$	$1$	3504.l	219.c	$2$	$1$	$1$	$1.749$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-219}) $	$\Q(\sqrt{73}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{9}+2q^{19}-q^{25}+q^{27}+\cdots$
3504.1.l.d	$3504$	$1$	3504.l	219.c	$2$	$2$	$2$	$1.749$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-219}) $	None	✓	$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+q^{3}-\beta q^{5}+q^{9}-\beta q^{15}+\beta q^{17}+\cdots$
3723.1.b.e	$3723$	$1$	3723.b	3723.b	$2$	$4$	$4$	$1.858$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-219}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}^{2}q^{3}+q^{4}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$
3723.1.q.a	$3723$	$1$	3723.q	3723.q	$4$	$8$	$4$	$1.858$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-219}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{16}^{6}q^{3}-q^{4}+(\zeta_{16}-\zeta_{16}^{3})q^{5}+\cdots$
3723.1.bq.a	$3723$	$1$	3723.bq	3723.aq	$8$	$16$	$4$	$1.858$	$\Q(\zeta_{32})$	$D_{16}$	$\Q(\sqrt{-219}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{32}^{10}q^{3}-\zeta_{32}^{8}q^{4}+(-\zeta_{32}^{9}+\cdots)q^{5}+\cdots$
657.2.d.d	$657$	$2$	657.d	73.b	$2$	$4$	$4$	$5.246$	4.0.63948.1	$_{}$	$\Q(\sqrt{-219}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{4}-\beta _{2}q^{5}-\beta _{1}q^{11}+4q^{16}+\cdots$
219.3.c.a	$219$	$3$	219.c	219.c	$2$	$2$	$2$	$5.967$	$\Q(\sqrt{73}) $	$_{}$	$\Q(\sqrt{-219}) $	None	✓	$4$	$0$	$0$	$-6$	$0$	$0$	$2$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{3}+4q^{4}+\beta q^{5}+9q^{9}-2\beta q^{11}+\cdots$
219.3.c.b	$219$	$3$	219.c	219.c	$2$	$2$	$2$	$5.967$	$\Q(\sqrt{3}) $	$_{}$	$\Q(\sqrt{-219}) $	None	✓	$4$	$0$	$0$	$6$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+3q^{3}+4q^{4}+3\beta q^{5}+9q^{9}-8\beta q^{11}+\cdots$
1971.2.d.e	$1971$	$2$	1971.d	73.b	$2$	$4$	$4$	$15.739$	4.0.63948.1	$_{}$	$\Q(\sqrt{-219}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{4}+\beta _{2}q^{5}+\beta _{2}q^{11}+4q^{16}+\cdots$
1971.2.d.f	$1971$	$2$	1971.d	73.b	$2$	$4$	$4$	$15.739$	4.0.63948.1	$_{}$	$\Q(\sqrt{-219}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$2$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{4}+\beta _{2}q^{5}+(-2\beta _{1}-\beta _{2})q^{11}+\cdots$
2628.2.b.b	$2628$	$2$	2628.b	73.b	$2$	$4$	$4$	$20.985$	4.0.63948.1	$_{}$	$\Q(\sqrt{-219}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{5}-2\beta _{1}q^{11}+\beta _{1}q^{17}+(-2+\cdots)q^{19}+\cdots$
2628.2.b.d	$2628$	$2$	2628.b	73.b	$2$	$4$	$4$	$20.985$	4.0.63948.1	$_{}$	$\Q(\sqrt{-219}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{11}+(\beta _{1}-2\beta _{2}+\cdots)q^{17}+\cdots$
219.5.c.a	$219$	$5$	219.c	219.c	$2$	$1$	$1$	$22.638$	$\Q$	$_{}$	$\Q(\sqrt{-219}) $	None	✓	$2$	$0$	$0$	$9$	$-23$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+9q^{3}+2^{4}q^{4}-23q^{5}+3^{4}q^{9}-50q^{11}+\cdots$
219.5.c.b	$219$	$5$	219.c	219.c	$2$	$1$	$1$	$22.638$	$\Q$	$_{}$	$\Q(\sqrt{-219}) $	None	✓	$2$	$0$	$0$	$9$	$23$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+9q^{3}+2^{4}q^{4}+23q^{5}+3^{4}q^{9}+50q^{11}+\cdots$
219.5.c.c	$219$	$5$	219.c	219.c	$2$	$2$	$2$	$22.638$	$\Q(\sqrt{219}) $	$_{}$	$\Q(\sqrt{-219}) $	None	✓	$4$	$0$	$0$	$-18$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-9q^{3}+2^{4}q^{4}+3\beta q^{5}+3^{4}q^{9}+2^{4}\beta q^{11}+\cdots$
876.3.g.a	$876$	$3$	876.g	219.c	$2$	$2$	$2$	$23.869$	$\Q(\sqrt{73}) $	$_{}$	$\Q(\sqrt{-219}) $	None	✓	$2$	$0$	$0$	$-6$	$-9$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{3}+(-4-\beta )q^{5}+9q^{9}+(2-4\beta )q^{11}+\cdots$
876.3.g.b	$876$	$3$	876.g	219.c	$2$	$2$	$2$	$23.869$	$\Q(\sqrt{73}) $	$_{}$	$\Q(\sqrt{-219}) $	None	✓	$2$	$0$	$0$	$-6$	$9$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{3}+(5-\beta )q^{5}+9q^{9}+(2-4\beta )q^{11}+\cdots$
876.3.g.d	$876$	$3$	876.g	219.c	$2$	$4$	$4$	$23.869$	$\Q(\sqrt{3}, \sqrt{73})$	$_{}$	$\Q(\sqrt{-219}) $	None	✓	$4$	$0$	$0$	$12$	$0$	$0$	$2^{3}\cdot 3$	$\mathrm{U}(1)[D_{2}]$	$q+3q^{3}+\beta _{2}q^{5}+9q^{9}+(\beta _{2}+\beta _{3})q^{11}+\cdots$
657.4.d.b	$657$	$4$	657.d	73.b	$2$	$4$	$4$	$38.764$	4.0.63948.1	$_{}$	$\Q(\sqrt{-219}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{4}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-8q^{4}-\beta _{1}q^{5}+(2\beta _{1}-3\beta _{2})q^{11}+\cdots$
7884.2.b.d	$7884$	$2$	7884.b	73.b	$2$	$4$	$4$	$62.954$	4.0.63948.1	$_{}$	$\Q(\sqrt{-219}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$2$	$\mathrm{U}(1)[D_{2}]$	$q+(-\beta _{1}+\beta _{2})q^{5}+(2\beta _{1}+\beta _{2})q^{11}+\cdots$
7884.2.b.e	$7884$	$2$	7884.b	73.b	$2$	$4$	$4$	$62.954$	4.0.63948.1	$_{}$	$\Q(\sqrt{-219}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$2$	$\mathrm{U}(1)[D_{2}]$	$q+(-\beta _{1}+\beta _{2})q^{5}-\beta _{2}q^{11}+\beta _{1}q^{17}+\cdots$
7884.2.b.f	$7884$	$2$	7884.b	73.b	$2$	$4$	$4$	$62.954$	4.0.63948.1	$_{}$	$\Q(\sqrt{-219}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$2$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{5}+(2\beta _{1}+\beta _{2})q^{11}+(-3\beta _{1}+\cdots)q^{17}+\cdots$
7884.2.b.g	$7884$	$2$	7884.b	73.b	$2$	$4$	$4$	$62.954$	4.0.63948.1	$_{}$	$\Q(\sqrt{-219}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$2$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{5}-\beta _{2}q^{11}+(2\beta _{1}+\beta _{2})q^{17}+\cdots$
876.5.g.b	$876$	$5$	876.g	219.c	$2$	$2$	$2$	$90.552$	$\Q(\sqrt{73}) $	$_{}$	$\Q(\sqrt{-219}) $	None	✓	$2$	$0$	$0$	$18$	$-23$	$0$	$3$	$\mathrm{U}(1)[D_{2}]$	$q+9q^{3}+(-10-3\beta )q^{5}+3^{4}q^{9}+50q^{11}+\cdots$
876.5.g.c	$876$	$5$	876.g	219.c	$2$	$2$	$2$	$90.552$	$\Q(\sqrt{73}) $	$_{}$	$\Q(\sqrt{-219}) $	None	✓	$2$	$0$	$0$	$18$	$23$	$0$	$3$	$\mathrm{U}(1)[D_{2}]$	$q+9q^{3}+(10+3\beta )q^{5}+3^{4}q^{9}-50q^{11}+\cdots$
876.5.g.d	$876$	$5$	876.g	219.c	$2$	$4$	$4$	$90.552$	$\Q(\sqrt{3}, \sqrt{73})$	$_{}$	$\Q(\sqrt{-219}) $	None	✓	$4$	$0$	$0$	$-36$	$0$	$0$	$2^{4}\cdot 3$	$\mathrm{U}(1)[D_{2}]$	$q-9q^{3}+(2\beta _{2}-\beta _{3})q^{5}+3^{4}q^{9}+(-29\beta _{2}+\cdots)q^{11}+\cdots$

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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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.