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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 (38 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				Fricke sign	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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
2009.1.i.a	$2009$	$1$	2009.i	287.i	$6$	$6$	$3$	$1.003$	6.0.64827.1	$D_{7}$	$\Q(\sqrt{-287}) $	None		$4$	$0$	$1$	$-1$	$0$	$0$		$1$		$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3}-\beta _{4}-\beta _{5})q^{3}+\cdots$
2009.1.i.b	$2009$	$1$	2009.i	287.i	$6$	$6$	$3$	$1.003$	6.0.64827.1	$D_{7}$	$\Q(\sqrt{-287}) $	None		$4$	$0$	$1$	$1$	$0$	$0$		$1$		$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{3}+\cdots$
2009.2.a.a	$2009$	$2$	2009.a	1.a	$1$	$2$	$2$	$16.042$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(1-\beta )q^{3}+(-1+\beta )q^{4}+(-1+\cdots)q^{5}+\cdots$
2009.2.a.b	$2009$	$2$	2009.a	1.a	$1$	$2$	$2$	$16.042$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$-1$	$3$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(1+\beta )q^{3}+(-1+\beta )q^{4}+(1+\cdots)q^{5}+\cdots$
2009.2.a.c	$2009$	$2$	2009.a	1.a	$1$	$2$	$2$	$16.042$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}-2q^{4}+(1-\beta )q^{5}+\beta q^{9}+(-2+\cdots)q^{11}+\cdots$
2009.2.a.d	$2009$	$2$	2009.a	1.a	$1$	$2$	$2$	$16.042$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-2q^{4}+(-1+\beta )q^{5}+\beta q^{9}+\cdots$
2009.2.a.e	$2009$	$2$	2009.a	1.a	$1$	$2$	$2$	$16.042$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$1$	$-2$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+q^{5}-\beta q^{6}+\cdots$
2009.2.a.f	$2009$	$2$	2009.a	1.a	$1$	$2$	$2$	$16.042$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$1$	$2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}-q^{5}+\beta q^{6}+\cdots$
2009.2.a.g	$2009$	$2$	2009.a	1.a	$1$	$3$	$3$	$16.042$	3.3.148.1	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{2})q^{2}-\beta _{2}q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots$
2009.2.a.h	$2009$	$2$	2009.a	1.a	$1$	$3$	$3$	$16.042$	3.3.257.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(-1-\beta _{2})q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots$
2009.2.a.i	$2009$	$2$	2009.a	1.a	$1$	$3$	$3$	$16.042$	3.3.257.1	$_{}$	None	None	✓	$1$	$1$	$0$	$3$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots$
2009.2.a.j	$2009$	$2$	2009.a	1.a	$1$	$3$	$3$	$16.042$	3.3.257.1	$_{}$	None	None	✓	$1$	$1$	$1$	$1$	$-6$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots$
2009.2.a.k	$2009$	$2$	2009.a	1.a	$1$	$3$	$3$	$16.042$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$0$	$4$	$-5$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{2}+(-2+\beta _{1})q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots$
2009.2.a.l	$2009$	$2$	2009.a	1.a	$1$	$5$	$5$	$16.042$	5.5.233489.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$-2$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}-\beta _{3}q^{3}+(1+\beta _{1})q^{4}+\beta _{3}q^{5}+\cdots$
2009.2.a.m	$2009$	$2$	2009.a	1.a	$1$	$5$	$5$	$16.042$	5.5.233489.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+\beta _{3}q^{3}+(1+\beta _{1})q^{4}-\beta _{3}q^{5}+\cdots$
2009.2.a.n	$2009$	$2$	2009.a	1.a	$1$	$5$	$5$	$16.042$	5.5.633117.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$-4$	$5$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1+\beta _{1})q^{3}+(1+\beta _{2})q^{4}+\cdots$
2009.2.a.o	$2009$	$2$	2009.a	1.a	$1$	$6$	$6$	$16.042$	6.6.185257757.1	$_{}$	None	None	✓	$1$	$0$	$-1$	$4$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1-\beta _{2})q^{3}+(1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
2009.2.a.p	$2009$	$2$	2009.a	1.a	$1$	$7$	$7$	$16.042$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-1$	$-7$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(-1+\beta _{1})q^{3}+(1-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$
2009.2.a.q	$2009$	$2$	2009.a	1.a	$1$	$7$	$7$	$16.042$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-1$	$7$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(1-\beta _{1})q^{3}+(1-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$
2009.2.a.r	$2009$	$2$	2009.a	1.a	$1$	$17$	$17$	$16.042$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$-1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{12}q^{3}+(1+\beta _{2})q^{4}+\beta _{13}q^{5}+\cdots$
2009.2.a.s	$2009$	$2$	2009.a	1.a	$1$	$17$	$17$	$16.042$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{12}q^{3}+(1+\beta _{2})q^{4}-\beta _{13}q^{5}+\cdots$
2009.2.a.t	$2009$	$2$	2009.a	1.a	$1$	$20$	$20$	$16.042$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-2$	$-8$	$-8$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{9}q^{3}+(1+\beta _{2})q^{4}-\beta _{18}q^{5}+\cdots$
2009.2.a.u	$2009$	$2$	2009.a	1.a	$1$	$20$	$20$	$16.042$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-2$	$8$	$8$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{9}q^{3}+(1+\beta _{2})q^{4}+\beta _{18}q^{5}+\cdots$
2009.4.a.a	$2009$	$4$	2009.a	1.a	$1$	$1$	$1$	$118.535$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$2$	$12$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}-7q^{4}+12q^{5}-2q^{6}+\cdots$
2009.4.a.b	$2009$	$4$	2009.a	1.a	$1$	$3$	$3$	$118.535$	3.3.404.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$8$	$10$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}-\beta _{2})q^{2}+(3+\beta _{1}-2\beta _{2})q^{3}+\cdots$
2009.4.a.c	$2009$	$4$	2009.a	1.a	$1$	$7$	$7$	$118.535$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$1$	$-4$	$-10$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1-\beta _{4}+\beta _{6})q^{3}+(6+\beta _{1}+\cdots)q^{4}+\cdots$
2009.4.a.d	$2009$	$4$	2009.a	1.a	$1$	$11$	$11$	$118.535$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-3$	$-3$	$14$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{3}q^{3}+(3+\beta _{1}+\beta _{2})q^{4}+\cdots$
2009.4.a.e	$2009$	$4$	2009.a	1.a	$1$	$12$	$12$	$118.535$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-4$	$17$	$14$	$0$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1-\beta _{5})q^{3}+(2+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
2009.4.a.f	$2009$	$4$	2009.a	1.a	$1$	$17$	$17$	$118.535$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$6$	$-11$	$2$	$0$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1+\beta _{7})q^{3}+(6+\beta _{2})q^{4}+\cdots$
2009.4.a.g	$2009$	$4$	2009.a	1.a	$1$	$19$	$19$	$118.535$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$4$	$-13$	$-26$	$0$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1-\beta _{5})q^{3}+(5+\beta _{2})q^{4}+\cdots$
2009.4.a.h	$2009$	$4$	2009.a	1.a	$1$	$30$	$30$	$118.535$		$_{}$	None	None	✓	$1$	$1$	$1$	$-12$	$-20$	$0$	$-$		$\mathrm{SU}(2)$
2009.4.a.i	$2009$	$4$	2009.a	1.a	$1$	$30$	$30$	$118.535$		$_{}$	None	None	✓	$1$	$0$	$1$	$12$	$20$	$0$	$+$		$\mathrm{SU}(2)$
2009.4.a.j	$2009$	$4$	2009.a	1.a	$1$	$36$	$36$	$118.535$		$_{}$	None	None	✓	$1$	$1$	$-5$	$-6$	$4$	$0$	$-$		$\mathrm{SU}(2)$
2009.4.a.k	$2009$	$4$	2009.a	1.a	$1$	$36$	$36$	$118.535$		$_{}$	None	None	✓	$1$	$1$	$-5$	$6$	$-4$	$0$	$-$		$\mathrm{SU}(2)$
2009.4.a.l	$2009$	$4$	2009.a	1.a	$1$	$44$	$44$	$118.535$		$_{}$	None	None	✓	$1$	$0$	$3$	$-6$	$4$	$0$	$+$		$\mathrm{SU}(2)$
2009.4.a.m	$2009$	$4$	2009.a	1.a	$1$	$44$	$44$	$118.535$		$_{}$	None	None	✓	$1$	$0$	$3$	$6$	$-4$	$0$	$+$		$\mathrm{SU}(2)$
2009.4.a.n	$2009$	$4$	2009.a	1.a	$1$	$60$	$60$	$118.535$		$_{}$	None	None	✓	$1$	$1$	$2$	$-24$	$-40$	$0$	$-$		$\mathrm{SU}(2)$
2009.4.a.o	$2009$	$4$	2009.a	1.a	$1$	$60$	$60$	$118.535$		$_{}$	None	None	✓	$1$	$0$	$2$	$24$	$40$	$0$	$+$		$\mathrm{SU}(2)$

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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.