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 (34 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	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
9072.2.a.e	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-2$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{7}+3q^{11}+2q^{17}+2q^{19}+\cdots$
9072.2.a.g	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-2$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}+q^{11}+2q^{17}-2q^{19}+\cdots$
9072.2.a.h	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-q^{7}+3q^{13}+7q^{17}-4q^{19}+\cdots$
9072.2.a.i	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-q^{7}+6q^{11}+6q^{13}-2q^{17}+\cdots$
9072.2.a.j	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{7}-2q^{11}-5q^{13}-3q^{17}+\cdots$
9072.2.a.k	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{7}+2q^{11}+3q^{13}+q^{17}+\cdots$
9072.2.a.o	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$1$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{7}+3q^{13}-7q^{17}-4q^{19}+\cdots$
9072.2.a.p	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$1$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+q^{7}-2q^{11}+3q^{13}-q^{17}+\cdots$
9072.2.a.q	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$1$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+q^{7}+2q^{11}-5q^{13}+3q^{17}+\cdots$
9072.2.a.r	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$2$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{7}-3q^{11}-2q^{17}+2q^{19}+\cdots$
9072.2.a.s	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$2$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-q^{7}+3q^{11}-6q^{13}+7q^{17}+\cdots$
9072.2.a.t	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$2$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}-q^{11}-6q^{13}-5q^{17}+\cdots$
9072.2.a.u	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$2$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}-q^{11}-2q^{17}-2q^{19}+\cdots$
9072.2.a.w	$9072$	$2$	9072.a	1.a	$1$	$1$	$1$	$72.440$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$3$	$-1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-q^{7}-6q^{11}+2q^{13}-6q^{17}+\cdots$
9072.2.a.z	$9072$	$2$	9072.a	1.a	$1$	$2$	$2$	$72.440$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$0$	$0$	$-4$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}+(2+\beta )q^{11}-4q^{13}+\cdots$
9072.2.a.ba	$9072$	$2$	9072.a	1.a	$1$	$2$	$2$	$72.440$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$0$	$0$	$-4$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-2+\beta )q^{5}+q^{7}+(3+\beta )q^{11}+(1+\cdots)q^{13}+\cdots$
9072.2.a.bb	$9072$	$2$	9072.a	1.a	$1$	$2$	$2$	$72.440$	$\Q(\sqrt{33}) $	None	✓	$1$	$1$	$0$	$0$	$-3$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}-q^{7}+(2-\beta )q^{11}+2q^{13}+\cdots$
9072.2.a.bf	$9072$	$2$	9072.a	1.a	$1$	$2$	$2$	$72.440$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$0$	$0$	$0$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}-q^{7}+(-3+\beta )q^{11}-q^{13}+\cdots$
9072.2.a.bg	$9072$	$2$	9072.a	1.a	$1$	$2$	$2$	$72.440$	$\Q(\sqrt{3}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{5}-q^{7}-\beta q^{11}-4q^{13}+2\beta q^{17}+\cdots$
9072.2.a.bh	$9072$	$2$	9072.a	1.a	$1$	$2$	$2$	$72.440$	$\Q(\sqrt{3}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}-q^{7}-2\beta q^{11}+5q^{13}+\beta q^{17}+\cdots$
9072.2.a.bi	$9072$	$2$	9072.a	1.a	$1$	$2$	$2$	$72.440$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$0$	$0$	$0$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}-q^{7}+(3+\beta )q^{11}-q^{13}+(-3+\cdots)q^{17}+\cdots$
9072.2.a.bk	$9072$	$2$	9072.a	1.a	$1$	$2$	$2$	$72.440$	$\Q(\sqrt{6}) $	None	✓	$1$	$1$	$0$	$0$	$2$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}+q^{7}-2q^{11}-2\beta q^{13}+\cdots$
9072.2.a.bn	$9072$	$2$	9072.a	1.a	$1$	$2$	$2$	$72.440$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$0$	$0$	$4$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{5}+q^{7}+(-3+\beta )q^{11}+(1+\cdots)q^{13}+\cdots$
9072.2.a.bo	$9072$	$2$	9072.a	1.a	$1$	$2$	$2$	$72.440$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$0$	$0$	$4$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}+(-2+\beta )q^{11}-4q^{13}+\cdots$
9072.2.a.bq	$9072$	$2$	9072.a	1.a	$1$	$3$	$3$	$72.440$	3.3.321.1	None	✓	$1$	$1$	$0$	$0$	$-5$	$3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-2-\beta _{2})q^{5}+q^{7}+(1-2\beta _{1}-\beta _{2})q^{11}+\cdots$
9072.2.a.br	$9072$	$2$	9072.a	1.a	$1$	$3$	$3$	$72.440$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$0$	$0$	$-3$	$-3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{5}-q^{7}+(-\beta _{1}+2\beta _{2})q^{11}+\cdots$
9072.2.a.bs	$9072$	$2$	9072.a	1.a	$1$	$3$	$3$	$72.440$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$0$	$0$	$-3$	$-3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{5}-q^{7}+(2+\beta _{1})q^{11}+\cdots$
9072.2.a.bw	$9072$	$2$	9072.a	1.a	$1$	$3$	$3$	$72.440$	3.3.837.1	None	✓	$1$	$1$	$0$	$0$	$0$	$-3$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{5}-q^{7}+(-1+\beta _{1})q^{11}+(-2+\cdots)q^{13}+\cdots$
9072.2.a.bx	$9072$	$2$	9072.a	1.a	$1$	$3$	$3$	$72.440$	3.3.837.1	None	✓	$1$	$1$	$0$	$0$	$0$	$-3$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{5}-q^{7}+(1-\beta _{1})q^{11}+(-2+\cdots)q^{13}+\cdots$
9072.2.a.by	$9072$	$2$	9072.a	1.a	$1$	$3$	$3$	$72.440$	3.3.321.1	None	✓	$1$	$1$	$0$	$0$	$1$	$3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}+q^{7}+(-1-\beta _{1}-2\beta _{2})q^{11}+\cdots$
9072.2.a.bz	$9072$	$2$	9072.a	1.a	$1$	$3$	$3$	$72.440$	3.3.321.1	None	✓	$1$	$1$	$0$	$0$	$3$	$-3$	$-$	$-$	$+$	$+$	$3$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{5}-q^{7}+(-2-\beta _{1})q^{11}+\cdots$
9072.2.a.ce	$9072$	$2$	9072.a	1.a	$1$	$4$	$4$	$72.440$	4.4.22545.1	None	✓	$1$	$1$	$0$	$0$	$-4$	$-4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}+\beta _{3})q^{5}-q^{7}+(-2+\beta _{1}+\cdots)q^{11}+\cdots$
9072.2.a.cg	$9072$	$2$	9072.a	1.a	$1$	$4$	$4$	$72.440$	4.4.45729.1	None	✓	$1$	$1$	$0$	$0$	$-3$	$4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{5}+q^{7}+(-2+\beta _{1})q^{11}+\cdots$
9072.2.a.cm	$9072$	$2$	9072.a	1.a	$1$	$5$	$5$	$72.440$	5.5.1425384.1	None	✓	$1$	$1$	$0$	$0$	$-3$	$5$	$+$	$-$	$-$	$+$	$3$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2})q^{5}+q^{7}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
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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.