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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 (37 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
1519.1.c.a	$1519$	$1$	1519.c	31.b	$2$	$1$	$1$	$0.758$	$\Q$	$D_{3}$	$\Q(\sqrt{-31}) $	None	✓	$2$	$0$	$-1$	$0$	$1$	$0$		$1$		$q-q^{2}+q^{5}+q^{8}+q^{9}-q^{10}-q^{16}+\cdots$
1519.1.c.b	$1519$	$1$	1519.c	31.b	$2$	$3$	$3$	$0.758$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-31}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\beta _{1}-\beta _{2})q^{2}+(1-\beta _{1})q^{4}-\beta _{1}q^{5}+\cdots$
1519.1.c.c	$1519$	$1$	1519.c	31.b	$2$	$3$	$3$	$0.758$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-31}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\beta _{1}-\beta _{2})q^{2}+(1-\beta _{1})q^{4}+\beta _{1}q^{5}+\cdots$
1519.1.n.a	$1519$	$1$	1519.n	217.n	$6$	$2$	$1$	$0.758$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$1$	$0$	$-1$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
1519.1.n.b	$1519$	$1$	1519.n	217.n	$6$	$2$	$1$	$0.758$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$1$	$0$	$1$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
1519.1.n.c	$1519$	$1$	1519.n	217.n	$6$	$6$	$3$	$0.758$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$3$		$q+(-\zeta_{18}^{7}+\zeta_{18}^{8})q^{2}+(-\zeta_{18}^{5}+\zeta_{18}^{6}+\cdots)q^{4}+\cdots$
1519.1.ba.a	$1519$	$1$	1519.ba	1519.aa	$14$	$6$	$1$	$0.758$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$-2$	$0$	$-2$	$-1$		$1$		$q+(\zeta_{14}^{4}-\zeta_{14}^{5})q^{2}+(-\zeta_{14}+\zeta_{14}^{2}+\cdots)q^{4}+\cdots$
1519.1.ba.b	$1519$	$1$	1519.ba	1519.aa	$14$	$12$	$2$	$0.758$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$2$	$0$	$2$	$1$		$1$		$q+(\zeta_{42}^{8}+\zeta_{42}^{10})q^{2}+(\zeta_{42}^{16}+\zeta_{42}^{18}+\cdots)q^{4}+\cdots$
1519.1.ce.a	$1519$	$1$	1519.ce	1519.be	$42$	$36$	$3$	$0.758$	$\Q(\zeta_{63})$	$D_{63}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{126}^{43}-\zeta_{126}^{59})q^{2}+(-\zeta_{126}^{23}+\cdots)q^{4}+\cdots$
1519.2.a.a	$1519$	$2$	1519.a	1.a	$1$	$2$	$2$	$12.129$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$1$	$2$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+2\beta q^{3}+(-1+\beta )q^{4}-q^{5}+\cdots$
1519.2.a.b	$1519$	$2$	1519.a	1.a	$1$	$3$	$3$	$12.129$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	$1$	$1$	$-3$	$3$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1+\beta _{1}-\beta _{2})q^{3}+\cdots$
1519.2.a.c	$1519$	$2$	1519.a	1.a	$1$	$3$	$3$	$12.129$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	$1$	$0$	$-3$	$3$	$6$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+\cdots$
1519.2.a.d	$1519$	$2$	1519.a	1.a	$1$	$4$	$4$	$12.129$	4.4.6809.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots$
1519.2.a.e	$1519$	$2$	1519.a	1.a	$1$	$5$	$5$	$12.129$	5.5.138136.1	$_{}$	None	None	✓	$1$	$0$	$3$	$-3$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{4})q^{2}+(-1+\beta _{2})q^{3}+(2+\beta _{3}+\cdots)q^{4}+\cdots$
1519.2.a.f	$1519$	$2$	1519.a	1.a	$1$	$7$	$7$	$12.129$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-3$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{2}-\beta _{1}q^{3}+(1+\beta _{2}-\beta _{4}+\beta _{6})q^{4}+\cdots$
1519.2.a.g	$1519$	$2$	1519.a	1.a	$1$	$7$	$7$	$12.129$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-3$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{4}q^{2}+\beta _{1}q^{3}+(1+\beta _{2}-\beta _{4}+\beta _{6})q^{4}+\cdots$
1519.2.a.h	$1519$	$2$	1519.a	1.a	$1$	$7$	$7$	$12.129$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-1$	$-2$	$-8$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2}-\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots$
1519.2.a.i	$1519$	$2$	1519.a	1.a	$1$	$7$	$7$	$12.129$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-1$	$2$	$8$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2}-\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots$
1519.2.a.j	$1519$	$2$	1519.a	1.a	$1$	$13$	$13$	$12.129$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$5$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}-\beta _{9}q^{5}+\cdots$
1519.2.a.k	$1519$	$2$	1519.a	1.a	$1$	$13$	$13$	$12.129$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$5$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{2})q^{4}+\beta _{9}q^{5}+\cdots$
1519.2.a.l	$1519$	$2$	1519.a	1.a	$1$	$16$	$16$	$12.129$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$0$	$-4$	$-16$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{12}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
1519.2.a.m	$1519$	$2$	1519.a	1.a	$1$	$16$	$16$	$12.129$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$4$	$16$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{12}q^{3}+(1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
1519.4.a.a	$1519$	$4$	1519.a	1.a	$1$	$1$	$1$	$89.624$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$8$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+8q^{3}-7q^{4}-4q^{5}-8q^{6}+\cdots$
1519.4.a.b	$1519$	$4$	1519.a	1.a	$1$	$2$	$2$	$89.624$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$-5$	$2$	$25$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-2-\beta )q^{2}+(2-2\beta )q^{3}+5\beta q^{4}+\cdots$
1519.4.a.c	$1519$	$4$	1519.a	1.a	$1$	$5$	$5$	$89.624$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$-4$	$-15$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(\beta _{2}-\beta _{3}+\beta _{4})q^{3}+(7+\cdots)q^{4}+\cdots$
1519.4.a.d	$1519$	$4$	1519.a	1.a	$1$	$10$	$10$	$89.624$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-5$	$6$	$14$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1+\beta _{6})q^{3}+(5-\beta _{1}+\cdots)q^{4}+\cdots$
1519.4.a.e	$1519$	$4$	1519.a	1.a	$1$	$10$	$10$	$89.624$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-5$	$12$	$38$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1-\beta _{7})q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots$
1519.4.a.f	$1519$	$4$	1519.a	1.a	$1$	$12$	$12$	$89.624$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$7$	$-12$	$14$	$0$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(-1+\beta _{5})q^{3}+(6-\beta _{1}+\cdots)q^{4}+\cdots$
1519.4.a.g	$1519$	$4$	1519.a	1.a	$1$	$13$	$13$	$89.624$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$6$	$-10$	$-46$	$0$	$-$	$2^{3}\cdot 3^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1-\beta _{7})q^{3}+(4+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
1519.4.a.h	$1519$	$4$	1519.a	1.a	$1$	$23$	$23$	$89.624$		$_{}$	None	None	✓	$1$	$1$	$5$	$-6$	$-40$	$0$	$-$		$\mathrm{SU}(2)$
1519.4.a.i	$1519$	$4$	1519.a	1.a	$1$	$23$	$23$	$89.624$		$_{}$	None	None	✓	$1$	$0$	$5$	$6$	$40$	$0$	$+$		$\mathrm{SU}(2)$
1519.4.a.j	$1519$	$4$	1519.a	1.a	$1$	$27$	$27$	$89.624$		$_{}$	None	None	✓	$1$	$1$	$-9$	$0$	$-6$	$0$	$-$		$\mathrm{SU}(2)$
1519.4.a.k	$1519$	$4$	1519.a	1.a	$1$	$27$	$27$	$89.624$		$_{}$	None	None	✓	$1$	$1$	$-9$	$0$	$6$	$0$	$-$		$\mathrm{SU}(2)$
1519.4.a.l	$1519$	$4$	1519.a	1.a	$1$	$33$	$33$	$89.624$		$_{}$	None	None	✓	$1$	$0$	$7$	$0$	$-6$	$0$	$+$		$\mathrm{SU}(2)$
1519.4.a.m	$1519$	$4$	1519.a	1.a	$1$	$33$	$33$	$89.624$		$_{}$	None	None	✓	$1$	$0$	$7$	$0$	$6$	$0$	$+$		$\mathrm{SU}(2)$
1519.4.a.n	$1519$	$4$	1519.a	1.a	$1$	$44$	$44$	$89.624$		$_{}$	None	None	✓	$1$	$1$	$-2$	$-12$	$-80$	$0$	$-$		$\mathrm{SU}(2)$
1519.4.a.o	$1519$	$4$	1519.a	1.a	$1$	$44$	$44$	$89.624$		$_{}$	None	None	✓	$1$	$0$	$-2$	$12$	$80$	$0$	$+$		$\mathrm{SU}(2)$

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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.