LMFDB - Newform search results

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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 (40 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	7	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
7623.2.a.a	$7623$	$2$	7623.a	1.a	$1$	$1$	$1$	$60.870$	$\Q$	None	✓	$1$	$0$	$-2$	$0$	$-1$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-q^{5}+q^{7}+2q^{10}+\cdots$
7623.2.a.c	$7623$	$2$	7623.a	1.a	$1$	$1$	$1$	$60.870$	$\Q$	None	✓	$1$	$0$	$-2$	$0$	$1$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+q^{5}-q^{7}-2q^{10}+\cdots$
7623.2.a.g	$7623$	$2$	7623.a	1.a	$1$	$1$	$1$	$60.870$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$2$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+2q^{5}+q^{7}+3q^{8}-2q^{10}+\cdots$
7623.2.a.h	$7623$	$2$	7623.a	1.a	$1$	$1$	$1$	$60.870$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$3$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+3q^{5}+q^{7}+3q^{8}-3q^{10}+\cdots$
7623.2.a.j	$7623$	$2$	7623.a	1.a	$1$	$1$	$1$	$60.870$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$1$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{5}+q^{7}+4q^{13}+4q^{16}+\cdots$
7623.2.a.l	$7623$	$2$	7623.a	1.a	$1$	$1$	$1$	$60.870$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$3$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+3q^{5}+q^{7}-4q^{13}+4q^{16}+\cdots$
7623.2.a.m	$7623$	$2$	7623.a	1.a	$1$	$1$	$1$	$60.870$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$-1$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{5}+q^{7}-3q^{8}-q^{10}+\cdots$
7623.2.a.n	$7623$	$2$	7623.a	1.a	$1$	$1$	$1$	$60.870$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$2$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+2q^{5}+q^{7}-3q^{8}+2q^{10}+\cdots$
7623.2.a.p	$7623$	$2$	7623.a	1.a	$1$	$1$	$1$	$60.870$	$\Q$	None	✓	$1$	$0$	$2$	$0$	$-1$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-q^{5}-q^{7}-2q^{10}+\cdots$
7623.2.a.s	$7623$	$2$	7623.a	1.a	$1$	$1$	$1$	$60.870$	$\Q$	None	✓	$1$	$0$	$2$	$0$	$3$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+3q^{5}+q^{7}+6q^{10}+\cdots$
7623.2.a.v	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-3$	$0$	$2$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+3\beta q^{4}+q^{5}-q^{7}+\cdots$
7623.2.a.z	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-1$	$0$	$1$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+(1-\beta )q^{5}+q^{7}+\cdots$
7623.2.a.bb	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-1$	$0$	$4$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+(1+2\beta )q^{5}+\cdots$
7623.2.a.be	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$-1$	$0$	$-2$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(2+\beta )q^{4}-q^{5}+q^{7}+(-4+\cdots)q^{8}+\cdots$
7623.2.a.bg	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	$\Q(\sqrt{13}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$-2$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-2q^{4}-\beta q^{5}-q^{7}+2q^{13}+4q^{16}+\cdots$
7623.2.a.bi	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	$\Q(\sqrt{3}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}+2\beta q^{5}-q^{7}-\beta q^{8}+\cdots$
7623.2.a.bn	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$1$	$0$	$0$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+(-1+2\beta )q^{5}+\cdots$
7623.2.a.bo	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$1$	$0$	$1$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+(1-\beta )q^{5}-q^{7}+\cdots$
7623.2.a.bs	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	$\Q(\sqrt{13}) $	None	✓	$1$	$0$	$1$	$0$	$0$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{4}+(1-2\beta )q^{5}+q^{7}+\cdots$
7623.2.a.bv	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$2$	$0$	$4$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(2+2\beta )q^{4}+(2+\beta )q^{5}+\cdots$
7623.2.a.bw	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$3$	$0$	$-2$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+3\beta q^{4}-q^{5}-q^{7}+(1+\cdots)q^{8}+\cdots$
7623.2.a.bx	$7623$	$2$	7623.a	1.a	$1$	$2$	$2$	$60.870$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$3$	$0$	$-2$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+3\beta q^{4}-q^{5}+q^{7}+(1+\cdots)q^{8}+\cdots$
7623.2.a.ca	$7623$	$2$	7623.a	1.a	$1$	$3$	$3$	$60.870$	3.3.316.1	None	✓	$1$	$0$	$-1$	$0$	$-1$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots$
7623.2.a.cb	$7623$	$2$	7623.a	1.a	$1$	$3$	$3$	$60.870$	3.3.837.1	None	✓	$1$	$0$	$0$	$0$	$0$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots$
7623.2.a.cd	$7623$	$2$	7623.a	1.a	$1$	$3$	$3$	$60.870$	3.3.229.1	None	✓	$1$	$0$	$2$	$0$	$-4$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}+(2+\beta _{1})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
7623.2.a.ce	$7623$	$2$	7623.a	1.a	$1$	$3$	$3$	$60.870$	3.3.568.1	None	✓	$1$	$0$	$2$	$0$	$-1$	$-3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(3+\beta _{2})q^{4}+\beta _{2}q^{5}+\cdots$
7623.2.a.cg	$7623$	$2$	7623.a	1.a	$1$	$4$	$4$	$60.870$	4.4.7488.1	None	✓	$1$	$0$	$-2$	$0$	$2$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(1+\beta _{3})q^{5}+\cdots$
7623.2.a.ch	$7623$	$2$	7623.a	1.a	$1$	$4$	$4$	$60.870$	4.4.2525.1	None	✓	$1$	$0$	$-2$	$0$	$6$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$
7623.2.a.ci	$7623$	$2$	7623.a	1.a	$1$	$4$	$4$	$60.870$	4.4.725.1	None	✓	$1$	$0$	$-1$	$0$	$4$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1}+\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{4}+\cdots$
7623.2.a.cj	$7623$	$2$	7623.a	1.a	$1$	$4$	$4$	$60.870$	$\Q(\sqrt{2}, \sqrt{7})$	None	✓	$2$	$0$	$0$	$0$	$0$	$-4$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{3}q^{5}-q^{7}-2\beta _{1}q^{8}-\beta _{2}q^{10}+\cdots$
7623.2.a.cl	$7623$	$2$	7623.a	1.a	$1$	$4$	$4$	$60.870$	4.4.725.1	None	✓	$1$	$0$	$1$	$0$	$4$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}-\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{4}+2\beta _{2}q^{5}+\cdots$
7623.2.a.cm	$7623$	$2$	7623.a	1.a	$1$	$4$	$4$	$60.870$	4.4.7488.1	None	✓	$1$	$0$	$2$	$0$	$-6$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(-1+\beta _{3})q^{5}+\cdots$
7623.2.a.co	$7623$	$2$	7623.a	1.a	$1$	$4$	$4$	$60.870$	4.4.2525.1	None	✓	$1$	$0$	$2$	$0$	$6$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$
7623.2.a.cr	$7623$	$2$	7623.a	1.a	$1$	$6$	$6$	$60.870$	6.6.3829849.1	None	✓	$2$	$0$	$0$	$0$	$0$	$6$	$+$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots$
7623.2.a.cs	$7623$	$2$	7623.a	1.a	$1$	$6$	$6$	$60.870$	6.6.7674048.1	None	✓	$1$	$0$	$4$	$0$	$4$	$-6$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
7623.2.a.cx	$7623$	$2$	7623.a	1.a	$1$	$10$	$10$	$60.870$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$0$	$0$	$-5$	$-10$	$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{6}q^{5}-q^{7}+\cdots$
7623.2.a.cy	$7623$	$2$	7623.a	1.a	$1$	$10$	$10$	$60.870$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$0$	$0$	$-5$	$10$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{6}q^{5}+q^{7}+\cdots$
7623.2.a.da	$7623$	$2$	7623.a	1.a	$1$	$12$	$12$	$60.870$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$2$	$0$	$0$	$0$	$0$	$12$	$+$	$-$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{8}q^{5}+q^{7}+\cdots$
7623.2.a.db	$7623$	$2$	7623.a	1.a	$1$	$16$	$16$	$60.870$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$2$	$0$	$0$	$0$	$0$	$-16$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{7}q^{5}-q^{7}+\cdots$
7623.2.a.dc	$7623$	$2$	7623.a	1.a	$1$	$16$	$16$	$60.870$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$2$	$0$	$0$	$0$	$0$	$16$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{7}q^{5}+q^{7}+\cdots$

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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.