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 (28 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	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
5776.2.a.c	$5776$	$2$	5776.a	1.a	$1$	$1$	$1$	$46.122$	$\Q$	None	✓	$1$	$1$	$0$	$-2$	$3$	$1$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+3q^{5}+q^{7}+q^{9}-3q^{11}+\cdots$
5776.2.a.d	$5776$	$2$	5776.a	1.a	$1$	$1$	$1$	$46.122$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-4$	$-3$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{5}-3q^{7}-2q^{9}-2q^{11}+\cdots$
5776.2.a.e	$5776$	$2$	5776.a	1.a	$1$	$1$	$1$	$46.122$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-4$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{5}-2q^{9}-3q^{11}+2q^{13}+\cdots$
5776.2.a.f	$5776$	$2$	5776.a	1.a	$1$	$1$	$1$	$46.122$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-1$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{9}+4q^{11}+q^{13}+\cdots$
5776.2.a.h	$5776$	$2$	5776.a	1.a	$1$	$1$	$1$	$46.122$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$3$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}-2q^{9}+4q^{11}-5q^{13}+\cdots$
5776.2.a.m	$5776$	$2$	5776.a	1.a	$1$	$1$	$1$	$46.122$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$1$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}-2q^{9}+6q^{11}-5q^{13}+\cdots$
5776.2.a.n	$5776$	$2$	5776.a	1.a	$1$	$1$	$1$	$46.122$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$4$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{7}-2q^{9}-3q^{11}-2q^{13}+\cdots$
5776.2.a.p	$5776$	$2$	5776.a	1.a	$1$	$1$	$1$	$46.122$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$-1$	$3$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{5}+3q^{7}+q^{9}-5q^{11}+\cdots$
5776.2.a.r	$5776$	$2$	5776.a	1.a	$1$	$2$	$2$	$46.122$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$-4$	$1$	$2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+\beta q^{5}+(2-2\beta )q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots$
5776.2.a.s	$5776$	$2$	5776.a	1.a	$1$	$2$	$2$	$46.122$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$-3$	$2$	$-6$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+(2-2\beta )q^{5}-3q^{7}+\cdots$
5776.2.a.t	$5776$	$2$	5776.a	1.a	$1$	$2$	$2$	$46.122$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$-2$	$-5$	$2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2\beta q^{3}+(-3+\beta )q^{5}+(2-2\beta )q^{7}+\cdots$
5776.2.a.v	$5776$	$2$	5776.a	1.a	$1$	$2$	$2$	$46.122$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$0$	$-1$	$-3$	$-2$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-1-\beta )q^{5}-q^{7}+(1+\beta )q^{9}+\cdots$
5776.2.a.w	$5776$	$2$	5776.a	1.a	$1$	$2$	$2$	$46.122$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$-1$	$-2$	$-4$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}-2\beta q^{5}+(-1-2\beta )q^{7}+(-2+\cdots)q^{9}+\cdots$
5776.2.a.z	$5776$	$2$	5776.a	1.a	$1$	$2$	$2$	$46.122$	$\Q(\sqrt{7}) $	None	✓	$1$	$1$	$0$	$0$	$2$	$-2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(1-\beta )q^{5}+(-1-\beta )q^{7}+4q^{9}+\cdots$
5776.2.a.bb	$5776$	$2$	5776.a	1.a	$1$	$2$	$2$	$46.122$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$0$	$1$	$-3$	$-2$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-1-\beta )q^{5}-q^{7}+(1+\beta )q^{9}+\cdots$
5776.2.a.bc	$5776$	$2$	5776.a	1.a	$1$	$2$	$2$	$46.122$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$1$	$-2$	$-4$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-2\beta q^{5}+(-1-2\beta )q^{7}+(-2+\cdots)q^{9}+\cdots$
5776.2.a.be	$5776$	$2$	5776.a	1.a	$1$	$2$	$2$	$46.122$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$2$	$-5$	$2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{3}+(-3+\beta )q^{5}+(2-2\beta )q^{7}+\cdots$
5776.2.a.bg	$5776$	$2$	5776.a	1.a	$1$	$2$	$2$	$46.122$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$3$	$2$	$-6$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(2-2\beta )q^{5}-3q^{7}+(-1+\cdots)q^{9}+\cdots$
5776.2.a.bh	$5776$	$2$	5776.a	1.a	$1$	$2$	$2$	$46.122$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$4$	$1$	$2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+(1-\beta )q^{5}+2\beta q^{7}+q^{9}+(-4+\cdots)q^{11}+\cdots$
5776.2.a.bi	$5776$	$2$	5776.a	1.a	$1$	$3$	$3$	$46.122$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$0$	$-3$	$-3$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{3}+(-1+\beta _{1})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
5776.2.a.bj	$5776$	$2$	5776.a	1.a	$1$	$3$	$3$	$46.122$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$0$	$-3$	$-3$	$6$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-2\beta _{1}+\beta _{2})q^{3}+(-1-\beta _{2})q^{5}+\cdots$
5776.2.a.bk	$5776$	$2$	5776.a	1.a	$1$	$3$	$3$	$46.122$	3.3.316.1	None	✓	$1$	$1$	$0$	$-1$	$1$	$2$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}+\beta _{2})q^{3}+\beta _{1}q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots$
5776.2.a.bl	$5776$	$2$	5776.a	1.a	$1$	$3$	$3$	$46.122$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$0$	$0$	$0$	$3$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+(1+2\beta _{1})q^{7}+\cdots$
5776.2.a.bo	$5776$	$2$	5776.a	1.a	$1$	$3$	$3$	$46.122$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$0$	$0$	$6$	$-6$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+2q^{5}+(-2-2\beta _{2})q^{7}+(-1+\cdots)q^{9}+\cdots$
5776.2.a.by	$5776$	$2$	5776.a	1.a	$1$	$6$	$6$	$46.122$	6.6.20319417.1	None	✓	$1$	$1$	$0$	$3$	$-3$	$3$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{2}+\beta _{3})q^{3}-\beta _{4}q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots$
5776.2.a.ca	$5776$	$2$	5776.a	1.a	$1$	$8$	$8$	$46.122$	8.8.$\cdots$.1	None	✓	$1$	$1$	$0$	$-6$	$-2$	$2$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-1+\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots$
5776.2.a.cc	$5776$	$2$	5776.a	1.a	$1$	$8$	$8$	$46.122$	8.8.$\cdots$.1	None	✓	$1$	$1$	$0$	$6$	$-2$	$2$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(-1+\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots$
5776.2.a.cd	$5776$	$2$	5776.a	1.a	$1$	$9$	$9$	$46.122$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$0$	$-3$	$3$	$-9$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(\beta _{4}+\beta _{5})q^{5}+(-1-\beta _{6}+\cdots)q^{7}+\cdots$

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Elliptic 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.