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Note: Search results may be incomplete due to uncomputed quantities: fricke_eigenval (110727 objects)

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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 (21 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	11	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4719.2.a.b	$4719$	$2$	4719.a	1.a	$1$	$1$	$1$	$37.681$	$\Q$	None	✓	$1$	$1$	$-2$	$1$	$-2$	$-3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+2q^{4}-2q^{5}-2q^{6}+\cdots$
4719.2.a.e	$4719$	$2$	4719.a	1.a	$1$	$1$	$1$	$37.681$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$2$	$-3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+2q^{5}-3q^{7}+q^{9}+2q^{12}+\cdots$
4719.2.a.g	$4719$	$2$	4719.a	1.a	$1$	$1$	$1$	$37.681$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$2$	$5$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+2q^{5}+5q^{7}+q^{9}+2q^{12}+\cdots$
4719.2.a.i	$4719$	$2$	4719.a	1.a	$1$	$1$	$1$	$37.681$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+q^{7}+q^{9}-2q^{12}-q^{13}+\cdots$
4719.2.a.k	$4719$	$2$	4719.a	1.a	$1$	$1$	$1$	$37.681$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$-2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}-2q^{5}+q^{6}-3q^{8}+\cdots$
4719.2.a.l	$4719$	$2$	4719.a	1.a	$1$	$1$	$1$	$37.681$	$\Q$	None	✓	$1$	$1$	$2$	$-1$	$0$	$-3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+2q^{4}-2q^{6}-3q^{7}+\cdots$
4719.2.a.n	$4719$	$2$	4719.a	1.a	$1$	$2$	$2$	$37.681$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$0$	$-2$	$-2$	$4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+q^{4}+(-1+\beta )q^{5}-\beta q^{6}+\cdots$
4719.2.a.r	$4719$	$2$	4719.a	1.a	$1$	$3$	$3$	$37.681$	3.3.321.1	None	✓	$1$	$1$	$-2$	$-3$	$-5$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}-q^{3}+(3-\beta _{1})q^{4}+\cdots$
4719.2.a.t	$4719$	$2$	4719.a	1.a	$1$	$3$	$3$	$37.681$	3.3.148.1	None	✓	$1$	$1$	$-1$	$3$	$0$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{2}q^{5}+\cdots$
4719.2.a.u	$4719$	$2$	4719.a	1.a	$1$	$3$	$3$	$37.681$	3.3.564.1	None	✓	$1$	$1$	$1$	$-3$	$-2$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
4719.2.a.w	$4719$	$2$	4719.a	1.a	$1$	$3$	$3$	$37.681$	3.3.169.1	None	✓	$1$	$1$	$2$	$3$	$3$	$-4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
4719.2.a.x	$4719$	$2$	4719.a	1.a	$1$	$4$	$4$	$37.681$	4.4.2777.1	None	✓	$1$	$1$	$-2$	$-4$	$-3$	$5$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{3})q^{2}-q^{3}+(1-\beta _{2}-\beta _{3})q^{4}+\cdots$
4719.2.a.ba	$4719$	$2$	4719.a	1.a	$1$	$5$	$5$	$37.681$	5.5.210557.1	None	✓	$1$	$1$	$-2$	$5$	$3$	$-6$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+q^{3}+(1-\beta _{4})q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots$
4719.2.a.bb	$4719$	$2$	4719.a	1.a	$1$	$5$	$5$	$37.681$	5.5.394064.1	None	✓	$1$	$1$	$-1$	$-5$	$2$	$2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots$
4719.2.a.bc	$4719$	$2$	4719.a	1.a	$1$	$5$	$5$	$37.681$	5.5.303952.1	None	✓	$1$	$1$	$-1$	$5$	$-2$	$-6$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2}-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots$
4719.2.a.bg	$4719$	$2$	4719.a	1.a	$1$	$6$	$6$	$37.681$	6.6.966125.1	None	✓	$1$	$1$	$-1$	$6$	$-6$	$-5$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(-1+\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots$
4719.2.a.bh	$4719$	$2$	4719.a	1.a	$1$	$6$	$6$	$37.681$	6.6.966125.1	None	✓	$1$	$1$	$1$	$6$	$-6$	$5$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(-1+\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots$
4719.2.a.bi	$4719$	$2$	4719.a	1.a	$1$	$10$	$10$	$37.681$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-3$	$-10$	$-8$	$-1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{5}+\beta _{6})q^{4}+(-1+\cdots)q^{5}+\cdots$
4719.2.a.bj	$4719$	$2$	4719.a	1.a	$1$	$10$	$10$	$37.681$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-2$	$-10$	$4$	$4$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots$
4719.2.a.bk	$4719$	$2$	4719.a	1.a	$1$	$10$	$10$	$37.681$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-2$	$10$	$-4$	$-12$	$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots$
4719.2.a.bn	$4719$	$2$	4719.a	1.a	$1$	$10$	$10$	$37.681$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$3$	$-10$	$-8$	$1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{5}+\beta _{6})q^{4}+(-1+\cdots)q^{5}+\cdots$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
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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.