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 (22 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	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
10000.2.a.a	$10000$	$2$	10000.a	1.a	$1$	$2$	$2$	$79.850$	$\Q(\sqrt{5}) $	None	✓	$1$	$2$	$0$	$-3$	$0$	$-6$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}-3q^{7}+(-1+3\beta )q^{9}+\cdots$
10000.2.a.c	$10000$	$2$	10000.a	1.a	$1$	$2$	$2$	$79.850$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$-2$	$0$	$1$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{7}-2q^{9}+(4-2\beta )q^{11}+\cdots$
10000.2.a.d	$10000$	$2$	10000.a	1.a	$1$	$2$	$2$	$79.850$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$-2$	$0$	$1$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1-\beta )q^{7}-2q^{9}+3q^{11}+(3+\cdots)q^{13}+\cdots$
10000.2.a.h	$10000$	$2$	10000.a	1.a	$1$	$2$	$2$	$79.850$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$0$	$0$	$3$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-2\beta )q^{3}+(2-\beta )q^{7}+2q^{9}+(-5+\cdots)q^{11}+\cdots$
10000.2.a.j	$10000$	$2$	10000.a	1.a	$1$	$2$	$2$	$79.850$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-\beta q^{7}+(-2+\beta )q^{9}+(-2+\cdots)q^{11}+\cdots$
10000.2.a.l	$10000$	$2$	10000.a	1.a	$1$	$2$	$2$	$79.850$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$2$	$0$	$-1$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1+\beta )q^{7}-2q^{9}+(2+2\beta )q^{11}+\cdots$
10000.2.a.m	$10000$	$2$	10000.a	1.a	$1$	$2$	$2$	$79.850$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$3$	$0$	$1$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-1+3\beta )q^{7}+(-1+3\beta )q^{9}+\cdots$
10000.2.a.n	$10000$	$2$	10000.a	1.a	$1$	$2$	$2$	$79.850$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$3$	$0$	$6$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+3q^{7}+(-1+3\beta )q^{9}+\cdots$
10000.2.a.s	$10000$	$2$	10000.a	1.a	$1$	$4$	$4$	$79.850$	$\Q(\zeta_{15})^+$	None	✓	$1$	$0$	$0$	$-1$	$0$	$-2$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{2}+\beta _{3})q^{3}+(2\beta _{2}+2\beta _{3})q^{7}+(-1+\cdots)q^{9}+\cdots$
10000.2.a.t	$10000$	$2$	10000.a	1.a	$1$	$4$	$4$	$79.850$	4.4.7625.1	None	✓	$1$	$0$	$0$	$-1$	$0$	$-2$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1-\beta _{3})q^{7}+(2+\beta _{1}+\beta _{3})q^{9}+\cdots$
10000.2.a.u	$10000$	$2$	10000.a	1.a	$1$	$4$	$4$	$79.850$	4.4.18625.1	None	✓	$1$	$0$	$0$	$-1$	$0$	$3$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}-\beta _{2})q^{3}+(2-2\beta _{2}-\beta _{3})q^{7}+\cdots$
10000.2.a.x	$10000$	$2$	10000.a	1.a	$1$	$4$	$4$	$79.850$	4.4.7625.1	None	✓	$1$	$0$	$0$	$1$	$0$	$2$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1+\beta _{3})q^{7}+(2+\beta _{1}+\beta _{3})q^{9}+\cdots$
10000.2.a.y	$10000$	$2$	10000.a	1.a	$1$	$4$	$4$	$79.850$	4.4.108625.1	None	✓	$1$	$0$	$0$	$2$	$0$	$-3$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+(-\beta _{1}+\beta _{2})q^{7}+(-1+\cdots)q^{9}+\cdots$
10000.2.a.ba	$10000$	$2$	10000.a	1.a	$1$	$4$	$4$	$79.850$	4.4.7625.1	None	✓	$1$	$0$	$0$	$3$	$0$	$-2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+\beta _{2}q^{7}+(3-\beta _{1}+\beta _{3})q^{9}+\cdots$
10000.2.a.bc	$10000$	$2$	10000.a	1.a	$1$	$6$	$6$	$79.850$	6.6.103238125.1	None	✓	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1-\beta _{3}+\beta _{4})q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots$
10000.2.a.bd	$10000$	$2$	10000.a	1.a	$1$	$6$	$6$	$79.850$	6.6.103238125.1	None	✓	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1+\beta _{3}-\beta _{4})q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots$
10000.2.a.bf	$10000$	$2$	10000.a	1.a	$1$	$8$	$8$	$79.850$	8.8.$\cdots$.1	None	✓	$1$	$0$	$0$	$-5$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-\beta _{2}-\beta _{4}-\beta _{7})q^{7}+\cdots$
10000.2.a.bl	$10000$	$2$	10000.a	1.a	$1$	$8$	$8$	$79.850$	8.8.3266578125.1	None	✓	$1$	$0$	$0$	$3$	$0$	$2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}+\beta _{3})q^{3}+(-\beta _{4}+\beta _{5})q^{7}+\cdots$
10000.2.a.bn	$10000$	$2$	10000.a	1.a	$1$	$8$	$8$	$79.850$	8.8.6152203125.1	None	✓	$1$	$0$	$0$	$5$	$0$	$10$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{5})q^{3}+(1-\beta _{1}-\beta _{3}+\beta _{5}-\beta _{7})q^{7}+\cdots$
10000.2.a.bp	$10000$	$2$	10000.a	1.a	$1$	$12$	$12$	$79.850$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$0$	$4$	$0$	$0$	$+$	$-$	$-$	$5$	$\mathrm{SU}(2)$	$q+\beta _{6}q^{3}+(-1-\beta _{1}+\beta _{2}-\beta _{5})q^{7}+\cdots$
10000.2.a.bq	$10000$	$2$	10000.a	1.a	$1$	$16$	$16$	$79.850$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$1$	$0$	$0$	$-4$	$0$	$-8$	$+$	$-$	$-$	$5^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1+\beta _{8})q^{7}+(1+\beta _{2})q^{9}+\cdots$
10000.2.a.br	$10000$	$2$	10000.a	1.a	$1$	$16$	$16$	$79.850$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$1$	$0$	$0$	$4$	$0$	$8$	$+$	$-$	$-$	$5^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1-\beta _{8})q^{7}+(1+\beta _{2})q^{9}+\cdots$

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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.