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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
212.1.d.a	$212$	$1$	212.d	212.d	$2$	$1$	$1$	$0.106$	$\Q$	$D_{3}$	$\Q(\sqrt{-53}) $	None	✓	$2$	$0$	$-1$	$1$	$0$	$0$	$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{12}+\cdots$
212.1.d.b	$212$	$1$	212.d	212.d	$2$	$1$	$1$	$0.106$	$\Q$	$D_{3}$	$\Q(\sqrt{-53}) $	None	✓	$2$	$0$	$1$	$-1$	$0$	$0$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-q^{12}+\cdots$
848.1.f.a	$848$	$1$	848.f	212.d	$2$	$1$	$1$	$0.423$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-53}) $	$\Q(\sqrt{53}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{9}+2q^{13}+2q^{17}+q^{25}-2q^{29}+\cdots$
848.1.f.b	$848$	$1$	848.f	212.d	$2$	$2$	$2$	$0.423$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-53}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta q^{3}+2q^{9}-q^{13}-q^{17}+\beta q^{19}+\cdots$
1908.1.b.a	$1908$	$1$	1908.b	212.d	$2$	$1$	$1$	$0.952$	$\Q$	$D_{3}$	$\Q(\sqrt{-53}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-q^{8}-q^{13}+q^{16}+q^{17}+\cdots$
1908.1.b.b	$1908$	$1$	1908.b	212.d	$2$	$1$	$1$	$0.952$	$\Q$	$D_{3}$	$\Q(\sqrt{-53}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}+q^{8}-q^{13}+q^{16}+q^{17}+\cdots$
1908.1.t.a	$1908$	$1$	1908.t	1908.t	$6$	$6$	$3$	$0.952$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-53}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{3}q^{2}+\zeta_{18}^{4}q^{3}+\zeta_{18}^{6}q^{4}+\cdots$
1908.1.t.b	$1908$	$1$	1908.t	1908.t	$6$	$6$	$3$	$0.952$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-53}) $	None		$4$	$0$	$3$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{3}q^{2}+\zeta_{18}^{7}q^{3}+\zeta_{18}^{6}q^{4}+\cdots$
2756.1.h.e	$2756$	$1$	2756.h	2756.h	$2$	$2$	$2$	$1.375$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-13}) $, $\Q(\sqrt{-53}) $	$\Q(\sqrt{689}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-q^{4}+iq^{8}-q^{9}-q^{13}+q^{16}+\cdots$
2756.1.h.i	$2756$	$1$	2756.h	2756.h	$2$	$4$	$4$	$1.375$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-53}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}^{3}q^{2}+(-\zeta_{12}+\zeta_{12}^{5})q^{3}-q^{4}+\cdots$
2756.1.v.a	$2756$	$1$	2756.v	2756.v	$6$	$2$	$1$	$1.375$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-53}) $	None		$4$	$0$	$-1$	$-2$	$0$	$0$	$1$		$q-\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+2\zeta_{6}^{2}q^{6}+\cdots$
2756.1.v.b	$2756$	$1$	2756.v	2756.v	$6$	$2$	$1$	$1.375$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-53}) $	None		$4$	$0$	$-1$	$1$	$0$	$0$	$1$		$q-\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{6}+\cdots$
2756.1.v.c	$2756$	$1$	2756.v	2756.v	$6$	$2$	$1$	$1.375$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-53}) $	None		$4$	$0$	$-1$	$1$	$0$	$0$	$1$		$q-\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{6}+\cdots$
2756.1.v.d	$2756$	$1$	2756.v	2756.v	$6$	$2$	$1$	$1.375$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-53}) $	None		$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q+\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{6}+\cdots$
2756.1.v.e	$2756$	$1$	2756.v	2756.v	$6$	$2$	$1$	$1.375$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-53}) $	None		$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q+\zeta_{6}q^{2}-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{6}+\cdots$
2756.1.v.f	$2756$	$1$	2756.v	2756.v	$6$	$2$	$1$	$1.375$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-53}) $	None		$4$	$0$	$1$	$2$	$0$	$0$	$1$		$q+\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+2\zeta_{6}^{2}q^{6}+\cdots$
2756.1.x.c	$2756$	$1$	2756.x	2756.x	$6$	$4$	$2$	$1.375$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-53}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
2756.1.x.d	$2756$	$1$	2756.x	2756.x	$6$	$4$	$2$	$1.375$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-53}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{8}+\zeta_{12}^{2}q^{9}+\cdots$
2756.1.x.e	$2756$	$1$	2756.x	2756.x	$6$	$4$	$2$	$1.375$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-53}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}+(\zeta_{12}^{3}+\zeta_{12}^{5})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$
3392.1.f.a	$3392$	$1$	3392.f	212.d	$2$	$1$	$1$	$1.693$	$\Q$	$D_{3}$	$\Q(\sqrt{-53}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-q^{3}+q^{13}-q^{17}-q^{19}+q^{23}+\cdots$
3392.1.f.b	$3392$	$1$	3392.f	212.d	$2$	$1$	$1$	$1.693$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-53}) $	$\Q(\sqrt{53}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{9}-2q^{13}+2q^{17}+q^{25}+2q^{29}+\cdots$
3392.1.f.c	$3392$	$1$	3392.f	212.d	$2$	$1$	$1$	$1.693$	$\Q$	$D_{3}$	$\Q(\sqrt{-53}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{13}-q^{17}+q^{19}-q^{23}+\cdots$
3392.1.f.d	$3392$	$1$	3392.f	212.d	$2$	$2$	$2$	$1.693$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-53}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\beta q^{3}+2q^{9}+q^{13}-q^{17}-\beta q^{19}+\cdots$
3604.1.e.b	$3604$	$1$	3604.e	3604.e	$2$	$1$	$1$	$1.799$	$\Q$	$D_{2}$	$\Q(\sqrt{-53}) $, $\Q(\sqrt{-901}) $	$\Q(\sqrt{17}) $	✓	$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-q^{8}+q^{9}+2q^{13}+q^{16}+\cdots$
3604.1.e.e	$3604$	$1$	3604.e	3604.e	$2$	$1$	$1$	$1.799$	$\Q$	$D_{2}$	$\Q(\sqrt{-53}) $, $\Q(\sqrt{-901}) $	$\Q(\sqrt{17}) $	✓	$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}+q^{8}+q^{9}+2q^{13}+q^{16}+\cdots$
3604.1.e.g	$3604$	$1$	3604.e	3604.e	$2$	$2$	$2$	$1.799$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-53}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-q^{2}+(\zeta_{6}+\zeta_{6}^{2})q^{3}+q^{4}+(-\zeta_{6}+\cdots)q^{6}+\cdots$
3604.1.e.i	$3604$	$1$	3604.e	3604.e	$2$	$2$	$2$	$1.799$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-53}) $	None		$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+q^{2}+(\zeta_{6}+\zeta_{6}^{2})q^{3}+q^{4}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{6}+\cdots$
3604.1.o.a	$3604$	$1$	3604.o	3604.o	$4$	$2$	$1$	$1.799$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-53}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-iq^{2}+(-1+i)q^{3}-q^{4}+(1+i+\cdots)q^{6}+\cdots$
3604.1.o.b	$3604$	$1$	3604.o	3604.o	$4$	$2$	$1$	$1.799$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-53}) $	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+iq^{2}+(1-i)q^{3}-q^{4}+(1+i)q^{6}+\cdots$
3604.1.o.c	$3604$	$1$	3604.o	3604.o	$4$	$4$	$2$	$1.799$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-53}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q+\zeta_{12}^{3}q^{2}+(\zeta_{12}^{4}+\zeta_{12}^{5})q^{3}-q^{4}+\cdots$
3604.1.o.d	$3604$	$1$	3604.o	3604.o	$4$	$4$	$2$	$1.799$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-53}) $	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q-\zeta_{12}^{3}q^{2}+(-\zeta_{12}+\zeta_{12}^{2})q^{3}-q^{4}+\cdots$
3604.1.z.a	$3604$	$1$	3604.z	3604.z	$8$	$4$	$1$	$1.799$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-53}) $	None		$4$	$0$	$0$	$-4$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+(-1+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$
3604.1.z.d	$3604$	$1$	3604.z	3604.z	$8$	$4$	$1$	$1.799$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-53}) $	None		$4$	$0$	$0$	$4$	$0$	$0$	$1$		$q+\zeta_{8}q^{2}+(1-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+(1+\cdots)q^{6}+\cdots$
3604.1.z.e	$3604$	$1$	3604.z	3604.z	$8$	$8$	$2$	$1.799$	$\Q(\zeta_{24})$	$D_{24}$	$\Q(\sqrt{-53}) $	None		$4$	$0$	$0$	$-4$	$0$	$0$	$1$		$q+\zeta_{24}^{9}q^{2}+(-\zeta_{24}^{4}-\zeta_{24}^{11})q^{3}+\cdots$
3604.1.z.f	$3604$	$1$	3604.z	3604.z	$8$	$8$	$2$	$1.799$	$\Q(\zeta_{24})$	$D_{24}$	$\Q(\sqrt{-53}) $	None		$4$	$0$	$0$	$4$	$0$	$0$	$1$		$q-\zeta_{24}^{9}q^{2}+(\zeta_{24}^{4}+\zeta_{24}^{11})q^{3}-\zeta_{24}^{6}q^{4}+\cdots$
636.2.g.b	$636$	$2$	636.g	636.g	$2$	$12$	$12$	$5.078$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	$\Q(\sqrt{-53}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{4}q^{2}+\beta _{6}q^{3}-2q^{4}-\beta _{3}q^{6}+2\beta _{4}q^{8}+\cdots$
212.3.d.b	$212$	$3$	212.d	212.d	$2$	$3$	$3$	$5.777$	3.3.5724.1	$_{}$	$\Q(\sqrt{-53}) $	None	✓	$2$	$0$	$-6$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}-\beta _{2}q^{3}+4q^{4}+2\beta _{2}q^{6}-8q^{8}+\cdots$
212.3.d.c	$212$	$3$	212.d	212.d	$2$	$3$	$3$	$5.777$	3.3.5724.1	$_{}$	$\Q(\sqrt{-53}) $	None	✓	$2$	$0$	$6$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+\beta _{2}q^{3}+4q^{4}+2\beta _{2}q^{6}+8q^{8}+\cdots$
1696.2.c.c	$1696$	$2$	1696.c	53.b	$2$	$12$	$12$	$13.543$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	$\Q(\sqrt{-53}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{16}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{3}+(-3-\beta _{3})q^{9}-\beta _{9}q^{13}+\cdots$
848.3.f.a	$848$	$3$	848.f	212.d	$2$	$6$	$6$	$23.106$	6.6.1736501328.1	$_{}$	$\Q(\sqrt{-53}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$2^{8}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{3}+(9-\beta _{4}+\beta _{5})q^{9}+(3\beta _{4}+\beta _{5})q^{13}+\cdots$

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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.