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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 (24 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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	5	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
5600.2.a.b	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	$\Q$	None	✓	$1$	$1$	$0$	$-3$	$0$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{7}+6q^{9}+3q^{11}-q^{13}+\cdots$
5600.2.a.d	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}-2q^{9}-3q^{11}+2q^{13}+\cdots$
5600.2.a.f	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}-2q^{9}-q^{11}-3q^{13}+\cdots$
5600.2.a.g	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}-2q^{9}-q^{11}+q^{13}-q^{17}+\cdots$
5600.2.a.i	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}-2q^{9}+5q^{11}-5q^{13}+\cdots$
5600.2.a.j	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-3q^{9}+2q^{13}-2q^{17}+8q^{19}+\cdots$
5600.2.a.p	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}-2q^{9}+q^{11}-3q^{13}+\cdots$
5600.2.a.r	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$-1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}-2q^{9}+3q^{11}+2q^{13}+\cdots$
5600.2.a.t	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$0$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots$
5600.2.a.w	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	$\Q(\sqrt{5}) $	None	✓	$2$	$1$	$0$	$-2$	$0$	$-2$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}-2q^{9}-\beta q^{11}+\beta q^{13}+\cdots$
5600.2.a.x	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$0$	$-2$	$0$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+q^{7}+(1-2\beta )q^{9}+(-2+\cdots)q^{11}+\cdots$
5600.2.a.y	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$0$	$-2$	$0$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+q^{7}+(1-2\beta )q^{9}+(2+\cdots)q^{11}+\cdots$
5600.2.a.ba	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$0$	$-1$	$0$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+q^{7}+(1+\beta )q^{9}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
5600.2.a.bc	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	$\Q(\sqrt{6}) $	None	✓	$1$	$1$	$0$	$0$	$0$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{7}+3q^{9}+(-1-\beta )q^{11}+\cdots$
5600.2.a.bf	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	$\Q(\sqrt{6}) $	None	✓	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+q^{7}+3q^{9}+(1-\beta )q^{11}+(-4+\cdots)q^{13}+\cdots$
5600.2.a.bg	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$0$	$1$	$0$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{7}+(1+\beta )q^{9}+(-4+\beta )q^{11}+\cdots$
5600.2.a.bh	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$0$	$1$	$0$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{7}+(1+\beta )q^{9}-\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
5600.2.a.bl	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	$\Q(\sqrt{5}) $	None	✓	$2$	$1$	$0$	$2$	$0$	$2$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}-2q^{9}+\beta q^{11}+\beta q^{13}+\cdots$
5600.2.a.bn	$5600$	$2$	5600.a	1.a	$1$	$3$	$3$	$44.716$	3.3.1016.1	None	✓	$1$	$1$	$0$	$-1$	$0$	$-3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+(3+\cdots)q^{11}+\cdots$
5600.2.a.bo	$5600$	$2$	5600.a	1.a	$1$	$3$	$3$	$44.716$	3.3.1016.1	None	✓	$1$	$1$	$0$	$1$	$0$	$3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+(-3+\cdots)q^{11}+\cdots$
5600.2.a.bq	$5600$	$2$	5600.a	1.a	$1$	$4$	$4$	$44.716$	4.4.48396.1	None	✓	$1$	$1$	$0$	$-2$	$0$	$-4$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots$
5600.2.a.br	$5600$	$2$	5600.a	1.a	$1$	$4$	$4$	$44.716$	4.4.48396.1	None	✓	$1$	$1$	$0$	$-2$	$0$	$-4$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots$
5600.2.a.bu	$5600$	$2$	5600.a	1.a	$1$	$5$	$5$	$44.716$	5.5.504568.1	None	✓	$1$	$1$	$0$	$-2$	$0$	$5$	$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+q^{7}+(1+\beta _{2}+\beta _{3})q^{9}+(-1+\cdots)q^{11}+\cdots$
5600.2.a.bw	$5600$	$2$	5600.a	1.a	$1$	$5$	$5$	$44.716$	5.5.504568.1	None	✓	$1$	$1$	$0$	$2$	$0$	$-5$	$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}-q^{7}+(1+\beta _{2}+\beta _{3})q^{9}+(-1+\cdots)q^{11}+\cdots$

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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.