LMFDB - Newform search results

Note: Search results may be incomplete due to uncomputed quantities: atkin_lehner_string (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 (20 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	3	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
9408.2.a.bs	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-4$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{5}+q^{9}+6q^{11}+5q^{13}+\cdots$
9408.2.a.bw	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{9}-4q^{11}+6q^{13}+\cdots$
9408.2.a.bx	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{9}+2q^{11}-3q^{13}+\cdots$
9408.2.a.ca	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{9}+2q^{11}+4q^{13}+\cdots$
9408.2.a.cb	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{9}+4q^{11}-6q^{13}+\cdots$
9408.2.a.cc	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots$
9408.2.a.cj	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}-2q^{11}+5q^{13}+2q^{17}+\cdots$
9408.2.a.ck	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}-4q^{13}+4q^{17}-4q^{19}+\cdots$
9408.2.a.cp	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}+q^{11}+q^{15}+8q^{17}+\cdots$
9408.2.a.cr	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}+5q^{11}+q^{15}+4q^{17}+\cdots$
9408.2.a.cs	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{9}-6q^{11}-3q^{13}+\cdots$
9408.2.a.cz	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{9}+2q^{13}+2q^{15}+\cdots$
9408.2.a.da	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{9}+6q^{13}+2q^{15}+\cdots$
9408.2.a.dc	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$3$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}+q^{9}+q^{11}-4q^{13}+\cdots$
9408.2.a.de	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$4$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{5}+q^{9}-4q^{11}+4q^{13}+\cdots$
9408.2.a.df	$9408$	$2$	9408.a	1.a	$1$	$1$	$1$	$75.123$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$4$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{5}+q^{9}+2q^{11}-6q^{13}+\cdots$
9408.2.a.dw	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	$\Q(\sqrt{57}) $	None	✓	$1$	$0$	$0$	$2$	$-1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-\beta q^{5}+q^{9}-\beta q^{11}+(3-\beta )q^{13}+\cdots$
9408.2.a.dx	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$2$	$0$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}+q^{9}+(-2+\beta )q^{11}+\cdots$
9408.2.a.dz	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$0$	$2$	$0$	$0$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}+\beta q^{11}+\beta q^{13}-\beta q^{17}+\cdots$
9408.2.a.eb	$9408$	$2$	9408.a	1.a	$1$	$2$	$2$	$75.123$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$0$	$2$	$0$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}+q^{9}+\beta q^{11}+\beta q^{15}+\cdots$

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Classical	Maass
Hilbert	Bianchi

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.