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 (30 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	11	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
6006.2.a.a	$6006$	$2$	6006.a	1.a	$1$	$1$	$1$	$47.958$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$-4$	$-1$	$+$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}-q^{7}+\cdots$
6006.2.a.b	$6006$	$2$	6006.a	1.a	$1$	$1$	$1$	$47.958$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$-4$	$-1$	$+$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}-q^{7}+\cdots$
6006.2.a.c	$6006$	$2$	6006.a	1.a	$1$	$1$	$1$	$47.958$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$-2$	$1$	$+$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots$
6006.2.a.d	$6006$	$2$	6006.a	1.a	$1$	$1$	$1$	$47.958$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$-2$	$1$	$+$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots$
6006.2.a.e	$6006$	$2$	6006.a	1.a	$1$	$1$	$1$	$47.958$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$0$	$-1$	$+$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots$
6006.2.a.f	$6006$	$2$	6006.a	1.a	$1$	$1$	$1$	$47.958$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$0$	$-1$	$+$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots$
6006.2.a.h	$6006$	$2$	6006.a	1.a	$1$	$1$	$1$	$47.958$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$2$	$1$	$+$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots$
6006.2.a.k	$6006$	$2$	6006.a	1.a	$1$	$1$	$1$	$47.958$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$-2$	$-1$	$+$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots$
6006.2.a.m	$6006$	$2$	6006.a	1.a	$1$	$1$	$1$	$47.958$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$0$	$-1$	$+$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots$
6006.2.a.p	$6006$	$2$	6006.a	1.a	$1$	$1$	$1$	$47.958$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$0$	$1$	$+$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots$
6006.2.a.q	$6006$	$2$	6006.a	1.a	$1$	$1$	$1$	$47.958$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$0$	$1$	$+$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots$
6006.2.a.r	$6006$	$2$	6006.a	1.a	$1$	$1$	$1$	$47.958$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$2$	$1$	$+$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots$
6006.2.a.u	$6006$	$2$	6006.a	1.a	$1$	$1$	$1$	$47.958$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$0$	$1$	$-$	$+$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots$
6006.2.a.v	$6006$	$2$	6006.a	1.a	$1$	$1$	$1$	$47.958$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$0$	$1$	$-$	$+$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots$
6006.2.a.x	$6006$	$2$	6006.a	1.a	$1$	$1$	$1$	$47.958$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$0$	$1$	$-$	$+$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots$
6006.2.a.y	$6006$	$2$	6006.a	1.a	$1$	$1$	$1$	$47.958$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$0$	$1$	$-$	$+$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots$
6006.2.a.ba	$6006$	$2$	6006.a	1.a	$1$	$1$	$1$	$47.958$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$-4$	$-1$	$-$	$-$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-4q^{5}+q^{6}-q^{7}+\cdots$
6006.2.a.bb	$6006$	$2$	6006.a	1.a	$1$	$1$	$1$	$47.958$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$-2$	$-1$	$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}-q^{7}+\cdots$
6006.2.a.bc	$6006$	$2$	6006.a	1.a	$1$	$1$	$1$	$47.958$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$-2$	$-1$	$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}-q^{7}+\cdots$
6006.2.a.bd	$6006$	$2$	6006.a	1.a	$1$	$1$	$1$	$47.958$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$-2$	$1$	$-$	$-$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots$
6006.2.a.be	$6006$	$2$	6006.a	1.a	$1$	$1$	$1$	$47.958$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$-2$	$1$	$-$	$-$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots$
6006.2.a.bg	$6006$	$2$	6006.a	1.a	$1$	$2$	$2$	$47.958$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$-2$	$2$	$-4$	$2$	$+$	$-$	$-$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}+q^{7}+\cdots$
6006.2.a.bi	$6006$	$2$	6006.a	1.a	$1$	$2$	$2$	$47.958$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$-2$	$-2$	$-2$	$-$	$+$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots$
6006.2.a.bj	$6006$	$2$	6006.a	1.a	$1$	$2$	$2$	$47.958$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$-2$	$-2$	$-2$	$-$	$+$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots$
6006.2.a.bk	$6006$	$2$	6006.a	1.a	$1$	$2$	$2$	$47.958$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$2$	$-2$	$0$	$-2$	$-$	$+$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+\beta q^{5}-q^{6}-q^{7}+\cdots$
6006.2.a.bl	$6006$	$2$	6006.a	1.a	$1$	$2$	$2$	$47.958$	$\Q(\sqrt{13}) $	None	✓	$1$	$1$	$2$	$-2$	$0$	$-2$	$-$	$+$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots$
6006.2.a.bs	$6006$	$2$	6006.a	1.a	$1$	$3$	$3$	$47.958$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$-3$	$-3$	$2$	$-3$	$+$	$+$	$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(1+\beta _{1})q^{5}+q^{6}+\cdots$
6006.2.a.bt	$6006$	$2$	6006.a	1.a	$1$	$3$	$3$	$47.958$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$-3$	$3$	$0$	$-3$	$+$	$-$	$+$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}-q^{7}+\cdots$
6006.2.a.bv	$6006$	$2$	6006.a	1.a	$1$	$3$	$3$	$47.958$	3.3.316.1	None	✓	$1$	$1$	$3$	$3$	$0$	$-3$	$-$	$-$	$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots$
6006.2.a.bw	$6006$	$2$	6006.a	1.a	$1$	$4$	$4$	$47.958$	4.4.2225.1	None	✓	$1$	$1$	$-4$	$-4$	$-4$	$4$	$+$	$+$	$-$	$+$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(-1+\beta _{2})q^{5}+q^{6}+\cdots$

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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.