LMFDB - Newform search results

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 (32 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	3	7	17	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4998.2.a.a	$4998$	$2$	4998.a	1.a	$1$	$1$	$1$	$39.909$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$-3$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{8}+\cdots$
4998.2.a.b	$4998$	$2$	4998.a	1.a	$1$	$1$	$1$	$39.909$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$-2$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots$
4998.2.a.d	$4998$	$2$	4998.a	1.a	$1$	$1$	$1$	$39.909$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$0$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
4998.2.a.g	$4998$	$2$	4998.a	1.a	$1$	$1$	$1$	$39.909$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$1$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots$
4998.2.a.i	$4998$	$2$	4998.a	1.a	$1$	$1$	$1$	$39.909$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$1$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots$
4998.2.a.k	$4998$	$2$	4998.a	1.a	$1$	$1$	$1$	$39.909$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$-3$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{8}+\cdots$
4998.2.a.m	$4998$	$2$	4998.a	1.a	$1$	$1$	$1$	$39.909$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$-1$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots$
4998.2.a.p	$4998$	$2$	4998.a	1.a	$1$	$1$	$1$	$39.909$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$-1$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots$
4998.2.a.q	$4998$	$2$	4998.a	1.a	$1$	$1$	$1$	$39.909$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$-1$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots$
4998.2.a.r	$4998$	$2$	4998.a	1.a	$1$	$1$	$1$	$39.909$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$-1$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots$
4998.2.a.t	$4998$	$2$	4998.a	1.a	$1$	$1$	$1$	$39.909$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$2$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots$
4998.2.a.u	$4998$	$2$	4998.a	1.a	$1$	$1$	$1$	$39.909$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$2$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots$
4998.2.a.y	$4998$	$2$	4998.a	1.a	$1$	$1$	$1$	$39.909$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$-3$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+q^{8}+\cdots$
4998.2.a.z	$4998$	$2$	4998.a	1.a	$1$	$1$	$1$	$39.909$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$-1$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots$
4998.2.a.ba	$4998$	$2$	4998.a	1.a	$1$	$1$	$1$	$39.909$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$1$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
4998.2.a.bd	$4998$	$2$	4998.a	1.a	$1$	$1$	$1$	$39.909$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$1$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
4998.2.a.be	$4998$	$2$	4998.a	1.a	$1$	$1$	$1$	$39.909$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$2$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots$
4998.2.a.bh	$4998$	$2$	4998.a	1.a	$1$	$1$	$1$	$39.909$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$-3$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{8}+\cdots$
4998.2.a.bj	$4998$	$2$	4998.a	1.a	$1$	$1$	$1$	$39.909$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$-3$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{8}+\cdots$
4998.2.a.bl	$4998$	$2$	4998.a	1.a	$1$	$1$	$1$	$39.909$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$-1$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
4998.2.a.bm	$4998$	$2$	4998.a	1.a	$1$	$1$	$1$	$39.909$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$-1$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
4998.2.a.bo	$4998$	$2$	4998.a	1.a	$1$	$1$	$1$	$39.909$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$1$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{8}+\cdots$
4998.2.a.bs	$4998$	$2$	4998.a	1.a	$1$	$2$	$2$	$39.909$	$\Q(\sqrt{41}) $	None	✓	$1$	$1$	$-2$	$-2$	$-1$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-\beta q^{5}+q^{6}-q^{8}+\cdots$
4998.2.a.bt	$4998$	$2$	4998.a	1.a	$1$	$2$	$2$	$39.909$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$-2$	$-2$	$2$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots$
4998.2.a.bx	$4998$	$2$	4998.a	1.a	$1$	$2$	$2$	$39.909$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$2$	$-2$	$-3$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots$
4998.2.a.by	$4998$	$2$	4998.a	1.a	$1$	$2$	$2$	$39.909$	$\Q(\sqrt{57}) $	None	✓	$1$	$1$	$2$	$-2$	$-2$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots$
4998.2.a.bz	$4998$	$2$	4998.a	1.a	$1$	$2$	$2$	$39.909$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$2$	$-2$	$0$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(1-2\beta )q^{5}-q^{6}+\cdots$
4998.2.a.cb	$4998$	$2$	4998.a	1.a	$1$	$2$	$2$	$39.909$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$2$	$-2$	$2$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
4998.2.a.cc	$4998$	$2$	4998.a	1.a	$1$	$2$	$2$	$39.909$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$2$	$2$	$-2$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
4998.2.a.cg	$4998$	$2$	4998.a	1.a	$1$	$3$	$3$	$39.909$	3.3.1944.1	None	✓	$1$	$1$	$-3$	$-3$	$-3$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(-1-\beta _{2})q^{5}+q^{6}+\cdots$
4998.2.a.ck	$4998$	$2$	4998.a	1.a	$1$	$4$	$4$	$39.909$	4.4.10304.1	None	✓	$1$	$1$	$-4$	$-4$	$-2$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(-1+\beta _{1})q^{5}+q^{6}+\cdots$
4998.2.a.cn	$4998$	$2$	4998.a	1.a	$1$	$4$	$4$	$39.909$	4.4.10304.1	None	✓	$1$	$1$	$-4$	$4$	$2$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(1-\beta _{1})q^{5}-q^{6}+\cdots$

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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.