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 (28 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.a	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	$\Q$	None	✓	$1$	$0$	$0$	$-3$	$0$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{7}+6q^{9}+q^{11}+q^{13}+\cdots$
5600.2.a.c	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	$\Q$	None	✓	$1$	$0$	$0$	$-2$	$0$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{7}+q^{9}+4q^{11}+4q^{13}+\cdots$
5600.2.a.e	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$0$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}-2q^{9}-3q^{11}+7q^{13}+\cdots$
5600.2.a.h	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$0$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}-2q^{9}+3q^{11}-2q^{13}+\cdots$
5600.2.a.k	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$0$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-3q^{9}+4q^{11}-2q^{13}-6q^{17}+\cdots$
5600.2.a.l	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$0$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-3q^{9}-4q^{11}-2q^{13}-6q^{17}+\cdots$
5600.2.a.m	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$0$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-3q^{9}+2q^{13}-2q^{17}-8q^{19}+\cdots$
5600.2.a.n	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}-2q^{9}-5q^{11}-5q^{13}+\cdots$
5600.2.a.o	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}-2q^{9}-3q^{11}-2q^{13}+\cdots$
5600.2.a.q	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}-2q^{9}+q^{11}+q^{13}-q^{17}+\cdots$
5600.2.a.s	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}-2q^{9}+3q^{11}+7q^{13}+\cdots$
5600.2.a.u	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	$\Q$	None	✓	$1$	$0$	$0$	$3$	$0$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+q^{7}+6q^{9}-3q^{11}-q^{13}+\cdots$
5600.2.a.v	$5600$	$2$	5600.a	1.a	$1$	$1$	$1$	$44.716$	$\Q$	None	✓	$1$	$0$	$0$	$3$	$0$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+q^{7}+6q^{9}-q^{11}+q^{13}+\cdots$
5600.2.a.z	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$-2$	$0$	$2$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+q^{7}+(3+2\beta )q^{9}+(2+\cdots)q^{11}+\cdots$
5600.2.a.bb	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$0$	$-1$	$0$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+q^{7}+(1+\beta )q^{9}+(4-\beta )q^{11}+\cdots$
5600.2.a.bd	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	$\Q(\sqrt{6}) $	None	✓	$1$	$0$	$0$	$0$	$0$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{7}+3q^{9}+(1+\beta )q^{11}+(4+\cdots)q^{13}+\cdots$
5600.2.a.be	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	$\Q(\sqrt{6}) $	None	✓	$1$	$0$	$0$	$0$	$0$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+q^{7}+3q^{9}+(-1+\beta )q^{11}+\cdots$
5600.2.a.bi	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$2$	$0$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-q^{7}+(1+2\beta )q^{9}+(-2+\cdots)q^{11}+\cdots$
5600.2.a.bj	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$2$	$0$	$-2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-q^{7}+(1+2\beta )q^{9}+(2-\beta )q^{11}+\cdots$
5600.2.a.bk	$5600$	$2$	5600.a	1.a	$1$	$2$	$2$	$44.716$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$2$	$0$	$-2$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-q^{7}+(3+2\beta )q^{9}+(-2+\cdots)q^{11}+\cdots$
5600.2.a.bm	$5600$	$2$	5600.a	1.a	$1$	$3$	$3$	$44.716$	3.3.1016.1	None	✓	$1$	$0$	$0$	$-1$	$0$	$-3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+(-3+\cdots)q^{11}+\cdots$
5600.2.a.bp	$5600$	$2$	5600.a	1.a	$1$	$3$	$3$	$44.716$	3.3.1016.1	None	✓	$1$	$0$	$0$	$1$	$0$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+(3+\cdots)q^{11}+\cdots$
5600.2.a.bs	$5600$	$2$	5600.a	1.a	$1$	$4$	$4$	$44.716$	4.4.48396.1	None	✓	$1$	$0$	$0$	$2$	$0$	$4$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+(-1+\cdots)q^{11}+\cdots$
5600.2.a.bt	$5600$	$2$	5600.a	1.a	$1$	$4$	$4$	$44.716$	4.4.48396.1	None	✓	$1$	$0$	$0$	$2$	$0$	$4$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots$
5600.2.a.bv	$5600$	$2$	5600.a	1.a	$1$	$5$	$5$	$44.716$	5.5.504568.1	None	✓	$1$	$0$	$0$	$-2$	$0$	$5$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+q^{7}+(1+\beta _{2}+\beta _{3})q^{9}+(1+\cdots)q^{11}+\cdots$
5600.2.a.bx	$5600$	$2$	5600.a	1.a	$1$	$5$	$5$	$44.716$	5.5.504568.1	None	✓	$1$	$0$	$0$	$2$	$0$	$-5$	$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}-q^{7}+(1+\beta _{2}+\beta _{3})q^{9}+(1+\cdots)q^{11}+\cdots$
5600.2.a.by	$5600$	$2$	5600.a	1.a	$1$	$6$	$6$	$44.716$	6.6.29935424.1	None	✓	$2$	$0$	$0$	$-2$	$0$	$-6$	$+$	$-$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{7}+(1+\beta _{1}-\beta _{2})q^{9}+\beta _{4}q^{11}+\cdots$
5600.2.a.bz	$5600$	$2$	5600.a	1.a	$1$	$6$	$6$	$44.716$	6.6.29935424.1	None	✓	$2$	$0$	$0$	$2$	$0$	$6$	$-$	$-$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{7}+(1+\beta _{1}-\beta _{2})q^{9}+\beta _{4}q^{11}+\cdots$

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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.