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	5	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
3920.2.a.b	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	None	✓	$1$	$0$	$0$	$-3$	$-1$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{5}+6q^{9}+2q^{11}+3q^{15}+\cdots$
3920.2.a.c	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	None	✓	$1$	$0$	$0$	$-3$	$-1$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{5}+6q^{9}+5q^{11}+5q^{13}+\cdots$
3920.2.a.d	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	None	✓	$1$	$0$	$0$	$-3$	$1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+q^{5}+6q^{9}+2q^{11}+6q^{13}+\cdots$
3920.2.a.g	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	None	✓	$1$	$0$	$0$	$-2$	$1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+q^{9}-3q^{11}-5q^{13}+\cdots$
3920.2.a.h	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	None	✓	$1$	$0$	$0$	$-2$	$1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+q^{9}-2q^{13}-2q^{15}+\cdots$
3920.2.a.j	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	None	✓	$1$	$0$	$0$	$-2$	$1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots$
3920.2.a.k	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$-1$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{9}-6q^{11}+2q^{13}+\cdots$
3920.2.a.l	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$-1$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{9}-3q^{11}-q^{13}+\cdots$
3920.2.a.o	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$-1$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{9}+5q^{11}+7q^{13}+\cdots$
3920.2.a.p	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$-1$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{9}+6q^{11}-4q^{13}+\cdots$
3920.2.a.s	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$-1$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{9}-4q^{11}+2q^{13}-2q^{17}+\cdots$
3920.2.a.t	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-3q^{9}-4q^{11}+6q^{13}-2q^{17}+\cdots$
3920.2.a.w	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{9}-6q^{11}-2q^{13}+\cdots$
3920.2.a.z	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{9}+q^{11}+5q^{13}+\cdots$
3920.2.a.ba	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{9}+3q^{11}-5q^{13}+\cdots$
3920.2.a.bc	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{9}+6q^{11}+4q^{13}+\cdots$
3920.2.a.bd	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	None	✓	$1$	$0$	$0$	$2$	$-1$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots$
3920.2.a.be	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	None	✓	$1$	$0$	$0$	$2$	$-1$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{5}+q^{9}-3q^{11}+5q^{13}+\cdots$
3920.2.a.bi	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	None	✓	$1$	$0$	$0$	$3$	$-1$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-q^{5}+6q^{9}+2q^{11}-6q^{13}+\cdots$
3920.2.a.bj	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	None	✓	$1$	$0$	$0$	$3$	$1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+q^{5}+6q^{9}-q^{11}-3q^{13}+\cdots$
3920.2.a.bk	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	None	✓	$1$	$0$	$0$	$3$	$1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+q^{5}+6q^{9}+2q^{11}+3q^{15}+\cdots$
3920.2.a.bl	$3920$	$2$	3920.a	1.a	$1$	$1$	$1$	$31.301$	$\Q$	None	✓	$1$	$0$	$0$	$3$	$1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+q^{5}+6q^{9}+5q^{11}+3q^{13}+\cdots$
3920.2.a.bo	$3920$	$2$	3920.a	1.a	$1$	$2$	$2$	$31.301$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$-2$	$-2$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}-q^{5}-2\beta q^{9}+(1+2\beta )q^{11}+\cdots$
3920.2.a.bp	$3920$	$2$	3920.a	1.a	$1$	$2$	$2$	$31.301$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$-2$	$-2$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}-q^{5}-2\beta q^{9}+(2-2\beta )q^{11}+\cdots$
3920.2.a.bu	$3920$	$2$	3920.a	1.a	$1$	$2$	$2$	$31.301$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$0$	$1$	$-2$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}+(1+\beta )q^{9}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
3920.2.a.bw	$3920$	$2$	3920.a	1.a	$1$	$2$	$2$	$31.301$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$2$	$-2$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-q^{5}+2\beta q^{9}+(3+2\beta )q^{11}+\cdots$
3920.2.a.by	$3920$	$2$	3920.a	1.a	$1$	$2$	$2$	$31.301$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$2$	$2$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+q^{5}+2\beta q^{9}+q^{11}+(-1+\cdots)q^{13}+\cdots$
3920.2.a.bz	$3920$	$2$	3920.a	1.a	$1$	$2$	$2$	$31.301$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$2$	$2$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+q^{5}+2\beta q^{9}+(2+2\beta )q^{11}+\cdots$
3920.2.a.ca	$3920$	$2$	3920.a	1.a	$1$	$2$	$2$	$31.301$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$4$	$-2$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{3}-q^{5}+(3+4\beta )q^{9}+(-2+\cdots)q^{11}+\cdots$
3920.2.a.cb	$3920$	$2$	3920.a	1.a	$1$	$3$	$3$	$31.301$	3.3.1944.1	None	✓	$1$	$0$	$0$	$0$	$-3$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{5}+(3+\beta _{1}+\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots$
3920.2.a.cc	$3920$	$2$	3920.a	1.a	$1$	$3$	$3$	$31.301$	3.3.1944.1	None	✓	$1$	$0$	$0$	$0$	$3$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{5}+(3+\beta _{1}+\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots$
3920.2.a.cd	$3920$	$2$	3920.a	1.a	$1$	$4$	$4$	$31.301$	4.4.16448.2	None	✓	$1$	$0$	$0$	$-2$	$4$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.