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 (19 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	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
3696.2.a.a	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-4$	$1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{5}+q^{7}+q^{9}+q^{11}-2q^{13}+\cdots$
3696.2.a.c	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-3$	$-1$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}-q^{7}+q^{9}-q^{11}-3q^{13}+\cdots$
3696.2.a.e	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-2$	$1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+q^{7}+q^{9}+q^{11}-2q^{13}+\cdots$
3696.2.a.h	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-1$	$1$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{7}+q^{9}-q^{11}+q^{13}+\cdots$
3696.2.a.i	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$-1$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+q^{11}+2q^{13}-2q^{19}+\cdots$
3696.2.a.k	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$1$	$1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{7}+q^{9}+q^{11}-5q^{13}+\cdots$
3696.2.a.l	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$1$	$1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{7}+q^{9}+q^{11}+3q^{13}+\cdots$
3696.2.a.m	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$2$	$1$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+q^{7}+q^{9}-q^{11}-2q^{13}+\cdots$
3696.2.a.o	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$3$	$-1$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}-q^{7}+q^{9}+q^{11}-q^{13}+\cdots$
3696.2.a.r	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-3$	$1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}+q^{7}+q^{9}+q^{11}+q^{13}+\cdots$
3696.2.a.s	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-2$	$-1$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-q^{7}+q^{9}-q^{11}+2q^{13}+\cdots$
3696.2.a.v	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-1$	$-1$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-q^{7}+q^{9}+q^{11}-3q^{13}+\cdots$
3696.2.a.x	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+q^{11}+2q^{13}-8q^{17}+\cdots$
3696.2.a.y	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}+q^{11}-2q^{13}-4q^{17}+\cdots$
3696.2.a.z	$3696$	$2$	3696.a	1.a	$1$	$1$	$1$	$29.513$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$1$	$-1$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-q^{7}+q^{9}-q^{11}-q^{13}+\cdots$
3696.2.a.bf	$3696$	$2$	3696.a	1.a	$1$	$2$	$2$	$29.513$	$\Q(\sqrt{33}) $	None	✓	$1$	$1$	$0$	$2$	$-3$	$-2$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta )q^{5}-q^{7}+q^{9}+q^{11}+\cdots$
3696.2.a.bg	$3696$	$2$	3696.a	1.a	$1$	$2$	$2$	$29.513$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$0$	$2$	$-3$	$2$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta )q^{5}+q^{7}+q^{9}-q^{11}+\cdots$
3696.2.a.bh	$3696$	$2$	3696.a	1.a	$1$	$2$	$2$	$29.513$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$0$	$2$	$-3$	$2$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta )q^{5}+q^{7}+q^{9}-q^{11}+\cdots$
3696.2.a.bm	$3696$	$2$	3696.a	1.a	$1$	$3$	$3$	$29.513$	3.3.568.1	None	✓	$1$	$1$	$0$	$-3$	$1$	$-3$	$+$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{2}q^{5}-q^{7}+q^{9}-q^{11}+\beta _{1}q^{13}+\cdots$

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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.