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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 (36 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
260.1.g.a	$260$	$1$	260.g	260.g	$2$	$1$	$1$	$0.130$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-65}) $	$\Q(\sqrt{65}) $	✓	$4$	$0$	$-1$	$0$	$1$	$0$	$1$		$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{9}-q^{10}+\cdots$
260.1.g.b	$260$	$1$	260.g	260.g	$2$	$1$	$1$	$0.130$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-65}) $	$\Q(\sqrt{65}) $	✓	$4$	$0$	$1$	$0$	$-1$	$0$	$1$		$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{9}-q^{10}+\cdots$
1040.1.l.a	$1040$	$1$	1040.l	260.g	$2$	$2$	$2$	$0.519$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-65}) $	None	✓	$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-\beta q^{3}-q^{5}+q^{9}-\beta q^{11}+q^{13}+\cdots$
1040.1.l.b	$1040$	$1$	1040.l	260.g	$2$	$2$	$2$	$0.519$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-65}) $	None	✓	$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q-\beta q^{3}+q^{5}+q^{9}+\beta q^{11}-q^{13}+\cdots$
1300.1.e.e	$1300$	$1$	1300.e	52.b	$2$	$2$	$2$	$0.649$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-65}) $	$\Q(\sqrt{65}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-q^{4}+iq^{8}+q^{9}-iq^{13}+\cdots$
2340.1.i.a	$2340$	$1$	2340.i	260.g	$2$	$1$	$1$	$1.168$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-65}) $	$\Q(\sqrt{65}) $	✓	$4$	$0$	$-1$	$0$	$1$	$0$	$1$		$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-q^{13}+\cdots$
2340.1.i.b	$2340$	$1$	2340.i	260.g	$2$	$1$	$1$	$1.168$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-65}) $	$\Q(\sqrt{65}) $	✓	$4$	$0$	$1$	$0$	$-1$	$0$	$1$		$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+q^{13}+\cdots$
2340.1.db.a	$2340$	$1$	2340.db	2340.cb	$6$	$2$	$1$	$1.168$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-65}) $	None		$4$	$0$	$-1$	$-2$	$-1$	$0$	$1$		$q-\zeta_{6}q^{2}-q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+\cdots$
2340.1.db.b	$2340$	$1$	2340.db	2340.cb	$6$	$2$	$1$	$1.168$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-65}) $	None		$4$	$0$	$-1$	$2$	$-1$	$0$	$1$		$q-\zeta_{6}q^{2}+q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+\cdots$
2340.1.db.c	$2340$	$1$	2340.db	2340.cb	$6$	$2$	$1$	$1.168$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-65}) $	None		$4$	$0$	$1$	$-2$	$1$	$0$	$1$		$q+\zeta_{6}q^{2}-q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+\cdots$
2340.1.db.d	$2340$	$1$	2340.db	2340.cb	$6$	$2$	$1$	$1.168$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-65}) $	None		$4$	$0$	$1$	$2$	$1$	$0$	$1$		$q+\zeta_{6}q^{2}+q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+\cdots$
2340.1.db.e	$2340$	$1$	2340.db	2340.cb	$6$	$4$	$2$	$1.168$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-65}) $	None		$8$	$0$	$-2$	$0$	$2$	$0$	$1$		$q+\zeta_{12}^{4}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{2}q^{4}+\cdots$
2340.1.db.f	$2340$	$1$	2340.db	2340.cb	$6$	$4$	$2$	$1.168$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-65}) $	None		$8$	$0$	$2$	$0$	$-2$	$0$	$1$		$q-\zeta_{12}^{4}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{2}q^{4}+\cdots$
2860.1.ck.a	$2860$	$1$	2860.ck	2860.bk	$10$	$4$	$1$	$1.427$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-65}) $	None		$4$	$0$	$-1$	$-2$	$-1$	$0$	$1$		$q-\zeta_{10}^{3}q^{2}+(-\zeta_{10}+\zeta_{10}^{2})q^{3}-\zeta_{10}q^{4}+\cdots$
2860.1.ck.b	$2860$	$1$	2860.ck	2860.bk	$10$	$4$	$1$	$1.427$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-65}) $	None		$4$	$0$	$-1$	$2$	$-1$	$0$	$1$		$q-\zeta_{10}^{3}q^{2}+(\zeta_{10}-\zeta_{10}^{2})q^{3}-\zeta_{10}q^{4}+\cdots$
2860.1.ck.c	$2860$	$1$	2860.ck	2860.bk	$10$	$4$	$1$	$1.427$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-65}) $	None		$4$	$0$	$1$	$-2$	$1$	$0$	$1$		$q+\zeta_{10}^{3}q^{2}+(-\zeta_{10}+\zeta_{10}^{2})q^{3}-\zeta_{10}q^{4}+\cdots$
2860.1.ck.d	$2860$	$1$	2860.ck	2860.bk	$10$	$4$	$1$	$1.427$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-65}) $	None		$4$	$0$	$1$	$2$	$1$	$0$	$1$		$q+\zeta_{10}^{3}q^{2}+(\zeta_{10}-\zeta_{10}^{2})q^{3}-\zeta_{10}q^{4}+\cdots$
2860.1.ck.e	$2860$	$1$	2860.ck	2860.bk	$10$	$8$	$2$	$1.427$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-65}) $	None		$8$	$0$	$-2$	$0$	$2$	$0$	$1$		$q-\zeta_{20}^{6}q^{2}+(\zeta_{20}^{7}+\zeta_{20}^{9})q^{3}-\zeta_{20}^{2}q^{4}+\cdots$
2860.1.ck.f	$2860$	$1$	2860.ck	2860.bk	$10$	$8$	$2$	$1.427$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-65}) $	None		$8$	$0$	$2$	$0$	$-2$	$0$	$1$		$q+\zeta_{20}^{6}q^{2}+(\zeta_{20}^{7}+\zeta_{20}^{9})q^{3}-\zeta_{20}^{2}q^{4}+\cdots$
3380.1.h.a	$3380$	$1$	3380.h	20.d	$2$	$2$	$2$	$1.687$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-65}) $	$\Q(\sqrt{65}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{2}-q^{4}-iq^{5}-iq^{8}-q^{9}+q^{10}+\cdots$
3380.1.v.a	$3380$	$1$	3380.v	260.v	$6$	$4$	$2$	$1.687$	$\Q(\zeta_{12})$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-65}) $	$\Q(\sqrt{65}) $		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}-\zeta_{12}^{3}q^{8}+\cdots$
3380.1.w.a	$3380$	$1$	3380.w	260.w	$6$	$2$	$1$	$1.687$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-65}) $	$\Q(\sqrt{65}) $		$8$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{5}+q^{8}+\zeta_{6}q^{9}+\cdots$
3380.1.w.d	$3380$	$1$	3380.w	260.w	$6$	$2$	$1$	$1.687$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-65}) $	$\Q(\sqrt{65}) $		$8$	$0$	$1$	$0$	$2$	$0$	$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{5}-q^{8}+\zeta_{6}q^{9}+\cdots$
3900.1.w.a	$3900$	$1$	3900.w	780.w	$4$	$4$	$2$	$1.946$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-65}) $	None		$8$	$0$	$0$	$-4$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}-q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}q^{6}-\zeta_{8}^{3}q^{8}+\cdots$
3900.1.w.b	$3900$	$1$	3900.w	780.w	$4$	$4$	$2$	$1.946$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-65}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{3}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{6}+\cdots$
3900.1.w.c	$3900$	$1$	3900.w	780.w	$4$	$4$	$2$	$1.946$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-65}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}-\zeta_{8}^{2}q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{6}+\cdots$
3900.1.w.d	$3900$	$1$	3900.w	780.w	$4$	$4$	$2$	$1.946$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-65}) $	None		$8$	$0$	$0$	$4$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+q^{3}+\zeta_{8}^{2}q^{4}-\zeta_{8}q^{6}-\zeta_{8}^{3}q^{8}+\cdots$
780.2.d.c	$780$	$2$	780.d	780.d	$2$	$16$	$16$	$6.228$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	$\Q(\sqrt{-65}) $	None		$16$	$0$	$0$	$0$	$0$	$0$	$2^{8}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{4}q^{2}+\beta _{5}q^{3}-2q^{4}-\beta _{6}q^{5}-\beta _{13}q^{6}+\cdots$
260.3.g.a	$260$	$3$	260.g	260.g	$2$	$2$	$2$	$7.084$	$\Q(\sqrt{10}) $	$_{}$	$\Q(\sqrt{-65}) $	None	✓	$4$	$0$	$-4$	$0$	$-10$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}+\beta q^{3}+4q^{4}-5q^{5}-2\beta q^{6}+\cdots$
260.3.g.b	$260$	$3$	260.g	260.g	$2$	$2$	$2$	$7.084$	$\Q(\sqrt{26}) $	$_{}$	$\Q(\sqrt{-65}) $	None	✓	$4$	$0$	$-4$	$0$	$10$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}+\beta q^{3}+4q^{4}+5q^{5}-2\beta q^{6}+\cdots$
260.3.g.c	$260$	$3$	260.g	260.g	$2$	$2$	$2$	$7.084$	$\Q(\sqrt{26}) $	$_{}$	$\Q(\sqrt{-65}) $	None	✓	$4$	$0$	$4$	$0$	$-10$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+\beta q^{3}+4q^{4}-5q^{5}+2\beta q^{6}+\cdots$
260.3.g.d	$260$	$3$	260.g	260.g	$2$	$2$	$2$	$7.084$	$\Q(\sqrt{10}) $	$_{}$	$\Q(\sqrt{-65}) $	None	✓	$4$	$0$	$4$	$0$	$10$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+\beta q^{3}+4q^{4}+5q^{5}+2\beta q^{6}+\cdots$
2080.2.f.f	$2080$	$2$	2080.f	65.d	$2$	$8$	$8$	$16.609$	8.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-65}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{9}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{3}+\beta _{5}q^{5}+(-3+\beta _{4}-\beta _{5}+\cdots)q^{9}+\cdots$
2080.2.f.g	$2080$	$2$	2080.f	65.d	$2$	$8$	$8$	$16.609$	8.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-65}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{9}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{3}-\beta _{5}q^{5}+(-3+\beta _{4}-\beta _{5}+\cdots)q^{9}+\cdots$
1040.3.l.c	$1040$	$3$	1040.l	260.g	$2$	$4$	$4$	$28.338$	$\Q(\sqrt{5}, \sqrt{13})$	$_{}$	$\Q(\sqrt{-65}) $	None	✓	$4$	$0$	$0$	$0$	$-20$	$0$	$2^{8}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}-5q^{5}+(9+\beta _{3})q^{9}+(\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots$
1040.3.l.d	$1040$	$3$	1040.l	260.g	$2$	$4$	$4$	$28.338$	$\Q(\sqrt{5}, \sqrt{13})$	$_{}$	$\Q(\sqrt{-65}) $	None	✓	$4$	$0$	$0$	$0$	$20$	$0$	$2^{8}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}+5q^{5}+(9+\beta _{3})q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots$

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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.