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 (41 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
2450.4.a.a	$2450$	$4$	2450.a	1.a	$1$	$1$	$1$	$144.555$	$\Q$	None	✓	$1$	$0$	$-2$	$-10$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-10q^{3}+4q^{4}+20q^{6}-8q^{8}+\cdots$
2450.4.a.c	$2450$	$4$	2450.a	1.a	$1$	$1$	$1$	$144.555$	$\Q$	None	✓	$1$	$0$	$-2$	$-7$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-7q^{3}+4q^{4}+14q^{6}-8q^{8}+\cdots$
2450.4.a.f	$2450$	$4$	2450.a	1.a	$1$	$1$	$1$	$144.555$	$\Q$	None	✓	$1$	$0$	$-2$	$-4$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-4q^{3}+4q^{4}+8q^{6}-8q^{8}+\cdots$
2450.4.a.g	$2450$	$4$	2450.a	1.a	$1$	$1$	$1$	$144.555$	$\Q$	None	✓	$1$	$0$	$-2$	$-3$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}+6q^{6}-8q^{8}+\cdots$
2450.4.a.j	$2450$	$4$	2450.a	1.a	$1$	$1$	$1$	$144.555$	$\Q$	None	✓	$1$	$0$	$-2$	$-1$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+4q^{4}+2q^{6}-8q^{8}+\cdots$
2450.4.a.l	$2450$	$4$	2450.a	1.a	$1$	$1$	$1$	$144.555$	$\Q$	None	✓	$1$	$0$	$-2$	$1$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+4q^{4}-2q^{6}-8q^{8}+\cdots$
2450.4.a.o	$2450$	$4$	2450.a	1.a	$1$	$1$	$1$	$144.555$	$\Q$	None	✓	$1$	$0$	$-2$	$2$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{3}+4q^{4}-4q^{6}-8q^{8}+\cdots$
2450.4.a.q	$2450$	$4$	2450.a	1.a	$1$	$1$	$1$	$144.555$	$\Q$	None	✓	$1$	$0$	$-2$	$5$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+5q^{3}+4q^{4}-10q^{6}-8q^{8}+\cdots$
2450.4.a.u	$2450$	$4$	2450.a	1.a	$1$	$1$	$1$	$144.555$	$\Q$	None	✓	$1$	$0$	$-2$	$8$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+8q^{3}+4q^{4}-2^{4}q^{6}-8q^{8}+\cdots$
2450.4.a.w	$2450$	$4$	2450.a	1.a	$1$	$1$	$1$	$144.555$	$\Q$	None	✓	$1$	$0$	$2$	$-8$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-8q^{3}+4q^{4}-2^{4}q^{6}+8q^{8}+\cdots$
2450.4.a.x	$2450$	$4$	2450.a	1.a	$1$	$1$	$1$	$144.555$	$\Q$	None	✓	$1$	$0$	$2$	$-8$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-8q^{3}+4q^{4}-2^{4}q^{6}+8q^{8}+\cdots$
2450.4.a.ba	$2450$	$4$	2450.a	1.a	$1$	$1$	$1$	$144.555$	$\Q$	None	✓	$1$	$0$	$2$	$-3$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+8q^{8}+\cdots$
2450.4.a.bc	$2450$	$4$	2450.a	1.a	$1$	$1$	$1$	$144.555$	$\Q$	None	✓	$1$	$0$	$2$	$-1$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+4q^{4}-2q^{6}+8q^{8}+\cdots$
2450.4.a.bd	$2450$	$4$	2450.a	1.a	$1$	$1$	$1$	$144.555$	$\Q$	None	✓	$1$	$0$	$2$	$-1$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+4q^{4}-2q^{6}+8q^{8}+\cdots$
2450.4.a.be	$2450$	$4$	2450.a	1.a	$1$	$1$	$1$	$144.555$	$\Q$	None	✓	$1$	$0$	$2$	$-1$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+4q^{4}-2q^{6}+8q^{8}+\cdots$
2450.4.a.bf	$2450$	$4$	2450.a	1.a	$1$	$1$	$1$	$144.555$	$\Q$	None	✓	$1$	$0$	$2$	$-1$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-q^{3}+4q^{4}-2q^{6}+8q^{8}+\cdots$
2450.4.a.bj	$2450$	$4$	2450.a	1.a	$1$	$1$	$1$	$144.555$	$\Q$	None	✓	$1$	$0$	$2$	$3$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}+6q^{6}+8q^{8}+\cdots$
2450.4.a.bl	$2450$	$4$	2450.a	1.a	$1$	$1$	$1$	$144.555$	$\Q$	None	✓	$1$	$0$	$2$	$4$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{3}+4q^{4}+8q^{6}+8q^{8}+\cdots$
2450.4.a.bm	$2450$	$4$	2450.a	1.a	$1$	$1$	$1$	$144.555$	$\Q$	None	✓	$1$	$0$	$2$	$4$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{3}+4q^{4}+8q^{6}+8q^{8}+\cdots$
2450.4.a.bo	$2450$	$4$	2450.a	1.a	$1$	$1$	$1$	$144.555$	$\Q$	None	✓	$1$	$0$	$2$	$8$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+8q^{3}+4q^{4}+2^{4}q^{6}+8q^{8}+\cdots$
2450.4.a.bp	$2450$	$4$	2450.a	1.a	$1$	$1$	$1$	$144.555$	$\Q$	None	✓	$1$	$0$	$2$	$10$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+10q^{3}+4q^{4}+20q^{6}+8q^{8}+\cdots$
2450.4.a.bq	$2450$	$4$	2450.a	1.a	$1$	$1$	$1$	$144.555$	$\Q$	None	✓	$1$	$0$	$2$	$10$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+10q^{3}+4q^{4}+20q^{6}+8q^{8}+\cdots$
2450.4.a.bt	$2450$	$4$	2450.a	1.a	$1$	$2$	$2$	$144.555$	$\Q(\sqrt{177}) $	None	✓	$1$	$0$	$4$	$-5$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-2-\beta )q^{3}+4q^{4}+(-4+\cdots)q^{6}+\cdots$
2450.4.a.bv	$2450$	$4$	2450.a	1.a	$1$	$2$	$2$	$144.555$	$\Q(\sqrt{46}) $	None	✓	$1$	$0$	$4$	$-2$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-1+\beta )q^{3}+4q^{4}+(-2+\cdots)q^{6}+\cdots$
2450.4.a.ca	$2450$	$4$	2450.a	1.a	$1$	$2$	$2$	$144.555$	$\Q(\sqrt{177}) $	None	✓	$1$	$0$	$4$	$5$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(3-\beta )q^{3}+4q^{4}+(6-2\beta )q^{6}+\cdots$
2450.4.a.cb	$2450$	$4$	2450.a	1.a	$1$	$3$	$3$	$144.555$	3.3.115880.1	None	✓	$1$	$0$	$-6$	$-4$	$0$	$0$	$+$	$+$	$+$	$+$	$3$	$\mathrm{SU}(2)$	$q-2q^{2}+(-1-\beta _{1})q^{3}+4q^{4}+(2+2\beta _{1}+\cdots)q^{6}+\cdots$
2450.4.a.cd	$2450$	$4$	2450.a	1.a	$1$	$3$	$3$	$144.555$	3.3.238585.1	None	✓	$1$	$0$	$-6$	$3$	$0$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(-2+2\beta _{1}+\cdots)q^{6}+\cdots$
2450.4.a.cf	$2450$	$4$	2450.a	1.a	$1$	$3$	$3$	$144.555$	3.3.51960.1	None	✓	$1$	$0$	$-6$	$7$	$0$	$0$	$+$	$-$	$-$	$+$	$5$	$\mathrm{SU}(2)$	$q-2q^{2}+(2+\beta _{1})q^{3}+4q^{4}+(-4-2\beta _{1}+\cdots)q^{6}+\cdots$
2450.4.a.ch	$2450$	$4$	2450.a	1.a	$1$	$3$	$3$	$144.555$	3.3.238585.1	None	✓	$1$	$0$	$6$	$-3$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+(-2+\cdots)q^{6}+\cdots$
2450.4.a.cj	$2450$	$4$	2450.a	1.a	$1$	$4$	$4$	$144.555$	$\Q(\sqrt{2}, \sqrt{113})$	None	✓	$1$	$0$	$-8$	$-10$	$0$	$0$	$+$	$+$	$+$	$+$	$7$	$\mathrm{SU}(2)$	$q-2q^{2}+(-3-\beta _{1})q^{3}+4q^{4}+(6+2\beta _{1}+\cdots)q^{6}+\cdots$
2450.4.a.cm	$2450$	$4$	2450.a	1.a	$1$	$4$	$4$	$144.555$	4.4.10197128.1	None	✓	$2$	$0$	$-8$	$0$	$0$	$0$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-2q^{2}+\beta _{1}q^{3}+4q^{4}-2\beta _{1}q^{6}-8q^{8}+\cdots$
2450.4.a.cn	$2450$	$4$	2450.a	1.a	$1$	$4$	$4$	$144.555$	4.4.1555279308.1	None	✓	$2$	$0$	$-8$	$0$	$0$	$0$	$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-2q^{2}+\beta _{1}q^{3}+4q^{4}-2\beta _{1}q^{6}-8q^{8}+\cdots$
2450.4.a.co	$2450$	$4$	2450.a	1.a	$1$	$4$	$4$	$144.555$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	$1$	$0$	$-8$	$1$	$0$	$0$	$+$	$+$	$+$	$+$	$3^{2}$	$\mathrm{SU}(2)$	$q-2q^{2}+\beta _{2}q^{3}+4q^{4}-2\beta _{2}q^{6}-8q^{8}+\cdots$
2450.4.a.cp	$2450$	$4$	2450.a	1.a	$1$	$4$	$4$	$144.555$	$\Q(\sqrt{2}, \sqrt{113})$	None	✓	$1$	$0$	$-8$	$10$	$0$	$0$	$+$	$+$	$+$	$+$	$7$	$\mathrm{SU}(2)$	$q-2q^{2}+(2-\beta _{1})q^{3}+4q^{4}+(-4+2\beta _{1}+\cdots)q^{6}+\cdots$
2450.4.a.cq	$2450$	$4$	2450.a	1.a	$1$	$4$	$4$	$144.555$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	$1$	$0$	$8$	$-1$	$0$	$0$	$-$	$-$	$+$	$+$	$3^{2}$	$\mathrm{SU}(2)$	$q+2q^{2}-\beta _{2}q^{3}+4q^{4}-2\beta _{2}q^{6}+8q^{8}+\cdots$
2450.4.a.ct	$2450$	$4$	2450.a	1.a	$1$	$4$	$4$	$144.555$	4.4.1555279308.1	None	✓	$2$	$0$	$8$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+2q^{2}+\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+8q^{8}+\cdots$
2450.4.a.cw	$2450$	$4$	2450.a	1.a	$1$	$6$	$6$	$144.555$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	$1$	$0$	$-12$	$7$	$0$	$0$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-2q^{2}+(1+\beta _{1})q^{3}+4q^{4}+(-2-2\beta _{1}+\cdots)q^{6}+\cdots$
2450.4.a.cy	$2450$	$4$	2450.a	1.a	$1$	$6$	$6$	$144.555$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	$1$	$0$	$12$	$7$	$0$	$0$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+2q^{2}+(1+\beta _{1})q^{3}+4q^{4}+(2+2\beta _{1}+\cdots)q^{6}+\cdots$
2450.4.a.cz	$2450$	$4$	2450.a	1.a	$1$	$8$	$8$	$144.555$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$2$	$0$	$-16$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$2\cdot 7^{2}\cdot 11^{2}$	$\mathrm{SU}(2)$	$q-2q^{2}-\beta _{3}q^{3}+4q^{4}+2\beta _{3}q^{6}-8q^{8}+\cdots$
2450.4.a.da	$2450$	$4$	2450.a	1.a	$1$	$8$	$8$	$144.555$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$2$	$0$	$16$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$2\cdot 7^{2}\cdot 11^{2}$	$\mathrm{SU}(2)$	$q+2q^{2}-\beta _{3}q^{3}+4q^{4}-2\beta _{3}q^{6}+8q^{8}+\cdots$
2450.4.a.dc	$2450$	$4$	2450.a	1.a	$1$	$10$	$10$	$144.555$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$2$	$0$	$20$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$2^{6}\cdot 5^{2}\cdot 7^{2}$	$\mathrm{SU}(2)$	$q+2q^{2}+\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+8q^{8}+\cdots$

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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.