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 (31 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	5	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
5070.2.a.d	$5070$	$2$	5070.a	1.a	$1$	$1$	$1$	$40.484$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$1$	$-2$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots$
5070.2.a.e	$5070$	$2$	5070.a	1.a	$1$	$1$	$1$	$40.484$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$1$	$-2$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots$
5070.2.a.f	$5070$	$2$	5070.a	1.a	$1$	$1$	$1$	$40.484$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$1$	$-2$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots$
5070.2.a.i	$5070$	$2$	5070.a	1.a	$1$	$1$	$1$	$40.484$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$-1$	$-5$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-5q^{7}+\cdots$
5070.2.a.j	$5070$	$2$	5070.a	1.a	$1$	$1$	$1$	$40.484$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$-1$	$2$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots$
5070.2.a.n	$5070$	$2$	5070.a	1.a	$1$	$1$	$1$	$40.484$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$-1$	$2$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots$
5070.2.a.o	$5070$	$2$	5070.a	1.a	$1$	$1$	$1$	$40.484$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$-1$	$2$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots$
5070.2.a.p	$5070$	$2$	5070.a	1.a	$1$	$1$	$1$	$40.484$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$-1$	$2$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots$
5070.2.a.u	$5070$	$2$	5070.a	1.a	$1$	$1$	$1$	$40.484$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$1$	$-4$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-4q^{7}+\cdots$
5070.2.a.v	$5070$	$2$	5070.a	1.a	$1$	$1$	$1$	$40.484$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$1$	$-2$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots$
5070.2.a.w	$5070$	$2$	5070.a	1.a	$1$	$1$	$1$	$40.484$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$1$	$4$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots$
5070.2.a.x	$5070$	$2$	5070.a	1.a	$1$	$1$	$1$	$40.484$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$1$	$5$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+5q^{7}+\cdots$
5070.2.a.y	$5070$	$2$	5070.a	1.a	$1$	$2$	$2$	$40.484$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$-2$	$-2$	$-2$	$-4$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots$
5070.2.a.z	$5070$	$2$	5070.a	1.a	$1$	$2$	$2$	$40.484$	$\Q(\sqrt{13}) $	None	✓	$1$	$0$	$-2$	$-2$	$-2$	$-2$	$+$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots$
5070.2.a.bb	$5070$	$2$	5070.a	1.a	$1$	$2$	$2$	$40.484$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$-2$	$2$	$-2$	$-3$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$
5070.2.a.bc	$5070$	$2$	5070.a	1.a	$1$	$2$	$2$	$40.484$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$-2$	$2$	$-2$	$0$	$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+\beta q^{7}+\cdots$
5070.2.a.bd	$5070$	$2$	5070.a	1.a	$1$	$2$	$2$	$40.484$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$-2$	$2$	$2$	$2$	$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(1+\beta )q^{7}+\cdots$
5070.2.a.bf	$5070$	$2$	5070.a	1.a	$1$	$2$	$2$	$40.484$	$\Q(\sqrt{13}) $	None	✓	$1$	$0$	$2$	$-2$	$2$	$2$	$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(1+\beta )q^{7}+\cdots$
5070.2.a.bg	$5070$	$2$	5070.a	1.a	$1$	$2$	$2$	$40.484$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$2$	$-2$	$2$	$4$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots$
5070.2.a.bh	$5070$	$2$	5070.a	1.a	$1$	$2$	$2$	$40.484$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$2$	$2$	$-2$	$-2$	$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots$
5070.2.a.bi	$5070$	$2$	5070.a	1.a	$1$	$2$	$2$	$40.484$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$2$	$2$	$2$	$3$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(1+\beta )q^{7}+\cdots$
5070.2.a.bk	$5070$	$2$	5070.a	1.a	$1$	$3$	$3$	$40.484$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$-3$	$-3$	$-3$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots$
5070.2.a.bm	$5070$	$2$	5070.a	1.a	$1$	$3$	$3$	$40.484$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$-3$	$-3$	$3$	$8$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(3-\beta _{1}+\cdots)q^{7}+\cdots$
5070.2.a.bo	$5070$	$2$	5070.a	1.a	$1$	$3$	$3$	$40.484$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$-3$	$3$	$-3$	$10$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(3+\beta _{1}+\cdots)q^{7}+\cdots$
5070.2.a.bq	$5070$	$2$	5070.a	1.a	$1$	$3$	$3$	$40.484$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$-3$	$3$	$3$	$6$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(2+\beta _{1}+\cdots)q^{7}+\cdots$
5070.2.a.bs	$5070$	$2$	5070.a	1.a	$1$	$3$	$3$	$40.484$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$3$	$-3$	$-3$	$-8$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(-3+\cdots)q^{7}+\cdots$
5070.2.a.bu	$5070$	$2$	5070.a	1.a	$1$	$3$	$3$	$40.484$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$3$	$-3$	$3$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(1-2\beta _{1}+\cdots)q^{7}+\cdots$
5070.2.a.bw	$5070$	$2$	5070.a	1.a	$1$	$3$	$3$	$40.484$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$3$	$3$	$-3$	$6$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+(2-\beta _{1}+\cdots)q^{7}+\cdots$
5070.2.a.by	$5070$	$2$	5070.a	1.a	$1$	$3$	$3$	$40.484$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$3$	$3$	$3$	$2$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(1-\beta _{1}+\cdots)q^{7}+\cdots$
5070.2.a.bz	$5070$	$2$	5070.a	1.a	$1$	$4$	$4$	$40.484$	4.4.131472.2	None	✓	$1$	$0$	$-4$	$4$	$4$	$-2$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-\beta _{1}q^{7}+\cdots$
5070.2.a.ca	$5070$	$2$	5070.a	1.a	$1$	$4$	$4$	$40.484$	4.4.131472.2	None	✓	$1$	$0$	$4$	$4$	$-4$	$2$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+\beta _{1}q^{7}+\cdots$

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Elliptic curves over $\Q$
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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.