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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 (39 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	3	7	17	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
6069.2.a.a	$6069$	$2$	6069.a	1.a	$1$	$1$	$1$	$48.461$	$\Q$	None	✓	$1$	$1$	$-2$	$-1$	$3$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}+3q^{5}+2q^{6}+\cdots$
6069.2.a.b	$6069$	$2$	6069.a	1.a	$1$	$1$	$1$	$48.461$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$2$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+2q^{5}+q^{6}+q^{7}+\cdots$
6069.2.a.c	$6069$	$2$	6069.a	1.a	$1$	$1$	$1$	$48.461$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-1$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-q^{5}-q^{7}+q^{9}+5q^{11}+\cdots$
6069.2.a.d	$6069$	$2$	6069.a	1.a	$1$	$1$	$1$	$48.461$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-1$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-q^{5}+q^{7}+q^{9}-3q^{11}+\cdots$
6069.2.a.e	$6069$	$2$	6069.a	1.a	$1$	$1$	$1$	$48.461$	$\Q$	None	✓	$1$	$0$	$2$	$-1$	$-1$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}+q^{7}+\cdots$
6069.2.a.f	$6069$	$2$	6069.a	1.a	$1$	$2$	$2$	$48.461$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$-2$	$-2$	$4$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}-q^{3}+(2-2\beta )q^{4}+(2+\cdots)q^{5}+\cdots$
6069.2.a.g	$6069$	$2$	6069.a	1.a	$1$	$2$	$2$	$48.461$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$2$	$2$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(1+\beta )q^{5}+\beta q^{6}+q^{7}+\cdots$
6069.2.a.h	$6069$	$2$	6069.a	1.a	$1$	$2$	$2$	$48.461$	$\Q(\sqrt{13}) $	None	✓	$1$	$1$	$1$	$-2$	$0$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(1+\beta )q^{4}-\beta q^{6}-q^{7}+\cdots$
6069.2.a.i	$6069$	$2$	6069.a	1.a	$1$	$2$	$2$	$48.461$	$\Q(\sqrt{13}) $	None	✓	$1$	$0$	$1$	$2$	$0$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(1+\beta )q^{4}+\beta q^{6}+q^{7}+\cdots$
6069.2.a.j	$6069$	$2$	6069.a	1.a	$1$	$3$	$3$	$48.461$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$-2$	$-3$	$-2$	$-3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots$
6069.2.a.k	$6069$	$2$	6069.a	1.a	$1$	$3$	$3$	$48.461$	3.3.148.1	None	✓	$1$	$1$	$-2$	$-3$	$3$	$-3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
6069.2.a.l	$6069$	$2$	6069.a	1.a	$1$	$3$	$3$	$48.461$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$-2$	$3$	$2$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots$
6069.2.a.m	$6069$	$2$	6069.a	1.a	$1$	$3$	$3$	$48.461$	3.3.148.1	None	✓	$1$	$1$	$-2$	$3$	$-3$	$3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
6069.2.a.n	$6069$	$2$	6069.a	1.a	$1$	$3$	$3$	$48.461$	$\Q(\zeta_{18})^+$	None	✓	$1$	$0$	$0$	$-3$	$0$	$3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots$
6069.2.a.o	$6069$	$2$	6069.a	1.a	$1$	$3$	$3$	$48.461$	3.3.257.1	None	✓	$1$	$0$	$0$	$-3$	$2$	$-3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}-q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
6069.2.a.p	$6069$	$2$	6069.a	1.a	$1$	$3$	$3$	$48.461$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$0$	$3$	$0$	$-3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots$
6069.2.a.q	$6069$	$2$	6069.a	1.a	$1$	$3$	$3$	$48.461$	3.3.257.1	None	✓	$1$	$1$	$0$	$3$	$-2$	$3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
6069.2.a.r	$6069$	$2$	6069.a	1.a	$1$	$3$	$3$	$48.461$	3.3.316.1	None	✓	$1$	$1$	$1$	$-3$	$-2$	$-3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
6069.2.a.s	$6069$	$2$	6069.a	1.a	$1$	$4$	$4$	$48.461$	4.4.7232.1	None	✓	$1$	$0$	$2$	$4$	$2$	$-4$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+q^{3}+(1-\beta _{2}-\beta _{3})q^{4}-\beta _{1}q^{5}+\cdots$
6069.2.a.t	$6069$	$2$	6069.a	1.a	$1$	$5$	$5$	$48.461$	5.5.1669781.1	None	✓	$1$	$1$	$-1$	$-5$	$-4$	$5$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
6069.2.a.u	$6069$	$2$	6069.a	1.a	$1$	$5$	$5$	$48.461$	5.5.1669781.1	None	✓	$1$	$0$	$-1$	$5$	$4$	$-5$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
6069.2.a.v	$6069$	$2$	6069.a	1.a	$1$	$5$	$5$	$48.461$	5.5.1502576.1	None	✓	$1$	$0$	$0$	$-5$	$3$	$5$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots$
6069.2.a.w	$6069$	$2$	6069.a	1.a	$1$	$5$	$5$	$48.461$	5.5.1502576.1	None	✓	$1$	$0$	$0$	$5$	$-3$	$-5$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots$
6069.2.a.x	$6069$	$2$	6069.a	1.a	$1$	$6$	$6$	$48.461$	6.6.2803712.1	None	✓	$1$	$1$	$0$	$-6$	$6$	$-6$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(1+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
6069.2.a.y	$6069$	$2$	6069.a	1.a	$1$	$6$	$6$	$48.461$	6.6.2803712.1	None	✓	$1$	$1$	$0$	$6$	$-6$	$6$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots$
6069.2.a.z	$6069$	$2$	6069.a	1.a	$1$	$9$	$9$	$48.461$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$0$	$-9$	$3$	$-9$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1-\beta _{3}+\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots$
6069.2.a.ba	$6069$	$2$	6069.a	1.a	$1$	$9$	$9$	$48.461$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$0$	$-9$	$3$	$9$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1-\beta _{4}+\beta _{5})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
6069.2.a.bb	$6069$	$2$	6069.a	1.a	$1$	$9$	$9$	$48.461$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$0$	$9$	$-3$	$-9$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1-\beta _{4}+\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
6069.2.a.bc	$6069$	$2$	6069.a	1.a	$1$	$9$	$9$	$48.461$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$0$	$9$	$-3$	$9$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1-\beta _{3}+\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots$
6069.2.a.bd	$6069$	$2$	6069.a	1.a	$1$	$10$	$10$	$48.461$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$4$	$-10$	$6$	$10$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
6069.2.a.be	$6069$	$2$	6069.a	1.a	$1$	$10$	$10$	$48.461$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$4$	$10$	$-6$	$-10$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
6069.2.a.bf	$6069$	$2$	6069.a	1.a	$1$	$15$	$15$	$48.461$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$1$	$0$	$-15$	$-9$	$-15$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{12}+\cdots)q^{5}+\cdots$
6069.2.a.bg	$6069$	$2$	6069.a	1.a	$1$	$15$	$15$	$48.461$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$1$	$0$	$-15$	$-9$	$15$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{13}+\cdots)q^{5}+\cdots$
6069.2.a.bh	$6069$	$2$	6069.a	1.a	$1$	$15$	$15$	$48.461$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$0$	$0$	$15$	$9$	$-15$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{13}+\cdots)q^{5}+\cdots$
6069.2.a.bi	$6069$	$2$	6069.a	1.a	$1$	$15$	$15$	$48.461$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$0$	$0$	$15$	$9$	$15$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{12}+\cdots)q^{5}+\cdots$
6069.2.a.bj	$6069$	$2$	6069.a	1.a	$1$	$16$	$16$	$48.461$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$1$	$1$	$-4$	$-16$	$-4$	$16$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{14}q^{5}+\cdots$
6069.2.a.bk	$6069$	$2$	6069.a	1.a	$1$	$16$	$16$	$48.461$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$1$	$1$	$-4$	$16$	$4$	$-16$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{14}q^{5}+\cdots$
6069.2.a.bl	$6069$	$2$	6069.a	1.a	$1$	$24$	$24$	$48.461$		None	✓	$1$	$0$	$4$	$-24$	$-4$	$-24$	$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
6069.2.a.bm	$6069$	$2$	6069.a	1.a	$1$	$24$	$24$	$48.461$		None	✓	$1$	$0$	$4$	$24$	$4$	$24$	$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

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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.