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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	3	5	47	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
3525.2.a.a	$3525$	$2$	3525.a	1.a	$1$	$1$	$1$	$28.147$	$\Q$	None	✓	$1$	$2$	$-2$	$-1$	$0$	$-4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}+2q^{6}-4q^{7}+\cdots$
3525.2.a.c	$3525$	$2$	3525.a	1.a	$1$	$1$	$1$	$28.147$	$\Q$	None	✓	$1$	$0$	$-2$	$-1$	$0$	$3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}+2q^{6}+3q^{7}+\cdots$
3525.2.a.f	$3525$	$2$	3525.a	1.a	$1$	$1$	$1$	$28.147$	$\Q$	None	✓	$1$	$2$	$0$	$-1$	$0$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-2q^{7}+q^{9}-6q^{11}+\cdots$
3525.2.a.j	$3525$	$2$	3525.a	1.a	$1$	$1$	$1$	$28.147$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{6}-3q^{8}+q^{9}+\cdots$
3525.2.a.k	$3525$	$2$	3525.a	1.a	$1$	$1$	$1$	$28.147$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$0$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}-4q^{7}-3q^{8}+\cdots$
3525.2.a.l	$3525$	$2$	3525.a	1.a	$1$	$1$	$1$	$28.147$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$0$	$5$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}+5q^{7}-3q^{8}+\cdots$
3525.2.a.n	$3525$	$2$	3525.a	1.a	$1$	$1$	$1$	$28.147$	$\Q$	None	✓	$1$	$0$	$2$	$1$	$0$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}+2q^{6}+q^{7}+q^{9}+\cdots$
3525.2.a.o	$3525$	$2$	3525.a	1.a	$1$	$1$	$1$	$28.147$	$\Q$	None	✓	$1$	$0$	$2$	$1$	$0$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}+2q^{6}+4q^{7}+\cdots$
3525.2.a.q	$3525$	$2$	3525.a	1.a	$1$	$2$	$2$	$28.147$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$1$	$2$	$0$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(2+\beta )q^{4}+\beta q^{6}+(-1+\cdots)q^{7}+\cdots$
3525.2.a.r	$3525$	$2$	3525.a	1.a	$1$	$2$	$2$	$28.147$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$1$	$2$	$0$	$3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(2+\beta )q^{4}+\beta q^{6}+(2+\cdots)q^{7}+\cdots$
3525.2.a.s	$3525$	$2$	3525.a	1.a	$1$	$2$	$2$	$28.147$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$2$	$-2$	$0$	$6$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}+(-1+\cdots)q^{6}+\cdots$
3525.2.a.u	$3525$	$2$	3525.a	1.a	$1$	$4$	$4$	$28.147$	4.4.14656.1	None	✓	$1$	$0$	$-2$	$4$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
3525.2.a.w	$3525$	$2$	3525.a	1.a	$1$	$6$	$6$	$28.147$	6.6.414764096.1	None	✓	$1$	$0$	$-2$	$-6$	$0$	$-4$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
3525.2.a.z	$3525$	$2$	3525.a	1.a	$1$	$7$	$7$	$28.147$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$-1$	$7$	$0$	$7$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2}+\beta _{3})q^{4}-\beta _{1}q^{6}+\cdots$
3525.2.a.bb	$3525$	$2$	3525.a	1.a	$1$	$7$	$7$	$28.147$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$1$	$-7$	$0$	$11$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
3525.2.a.bc	$3525$	$2$	3525.a	1.a	$1$	$7$	$7$	$28.147$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$3$	$7$	$0$	$5$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
3525.2.a.be	$3525$	$2$	3525.a	1.a	$1$	$8$	$8$	$28.147$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$3$	$-8$	$0$	$8$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots$
3525.2.a.bh	$3525$	$2$	3525.a	1.a	$1$	$13$	$13$	$28.147$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$0$	$-3$	$-13$	$0$	$4$	$+$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$
3525.2.a.bi	$3525$	$2$	3525.a	1.a	$1$	$13$	$13$	$28.147$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$0$	$3$	$13$	$0$	$-4$	$-$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots$

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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.