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	3	5	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8550.2.a.b	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$-4$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-4q^{7}-q^{8}-2q^{13}+4q^{14}+\cdots$
8550.2.a.c	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$-4$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-4q^{7}-q^{8}+q^{11}+4q^{14}+\cdots$
8550.2.a.f	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$-2$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{7}-q^{8}+3q^{11}-6q^{13}+\cdots$
8550.2.a.g	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$-2$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{7}-q^{8}+6q^{11}+2q^{14}+\cdots$
8550.2.a.l	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{7}-q^{8}+3q^{13}-q^{14}+\cdots$
8550.2.a.p	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$2$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{7}-q^{8}+2q^{11}+4q^{13}+\cdots$
8550.2.a.r	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$4$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{7}-q^{8}+4q^{11}+6q^{13}+\cdots$
8550.2.a.s	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$-4$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-4q^{7}+q^{8}+6q^{13}-4q^{14}+\cdots$
8550.2.a.v	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$-2$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{7}+q^{8}-6q^{11}+4q^{13}+\cdots$
8550.2.a.w	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$-2$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{7}+q^{8}+4q^{11}-6q^{13}+\cdots$
8550.2.a.y	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}-2q^{11}+4q^{13}+\cdots$
8550.2.a.bb	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}+4q^{11}-2q^{13}+\cdots$
8550.2.a.bc	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}+4q^{11}+4q^{13}+\cdots$
8550.2.a.bd	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{7}+q^{8}+q^{13}+q^{14}+\cdots$
8550.2.a.bh	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$2$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{7}+q^{8}-6q^{13}+2q^{14}+\cdots$
8550.2.a.bi	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$2$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{7}+q^{8}+3q^{11}+6q^{13}+\cdots$
8550.2.a.bj	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$4$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{7}+q^{8}+4q^{13}+4q^{14}+\cdots$
8550.2.a.bk	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$4$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{7}+q^{8}+q^{11}+4q^{14}+\cdots$
8550.2.a.bl	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$4$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{7}+q^{8}+6q^{11}+4q^{14}+\cdots$
8550.2.a.bm	$8550$	$2$	8550.a	1.a	$1$	$1$	$1$	$68.272$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$5$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+5q^{7}+q^{8}+4q^{11}+q^{13}+\cdots$
8550.2.a.bo	$8550$	$2$	8550.a	1.a	$1$	$2$	$2$	$68.272$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$-2$	$0$	$0$	$-4$	$+$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{7}-q^{8}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
8550.2.a.bq	$8550$	$2$	8550.a	1.a	$1$	$2$	$2$	$68.272$	$\Q(\sqrt{10}) $	None	✓	$1$	$0$	$-2$	$0$	$0$	$0$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{7}-q^{8}+(-1-\beta )q^{11}+\cdots$
8550.2.a.br	$8550$	$2$	8550.a	1.a	$1$	$2$	$2$	$68.272$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$-2$	$0$	$0$	$1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{7}-q^{8}-4q^{11}+(2+\cdots)q^{13}+\cdots$
8550.2.a.bt	$8550$	$2$	8550.a	1.a	$1$	$2$	$2$	$68.272$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$-2$	$0$	$0$	$2$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta )q^{7}-q^{8}-3\beta q^{11}+\cdots$
8550.2.a.bx	$8550$	$2$	8550.a	1.a	$1$	$2$	$2$	$68.272$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$2$	$0$	$0$	$-2$	$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta )q^{7}+q^{8}-2q^{11}+\cdots$
8550.2.a.bz	$8550$	$2$	8550.a	1.a	$1$	$2$	$2$	$68.272$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$2$	$0$	$0$	$-2$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1+\beta )q^{7}+q^{8}+3\beta q^{11}+\cdots$
8550.2.a.ca	$8550$	$2$	8550.a	1.a	$1$	$2$	$2$	$68.272$	$\Q(\sqrt{10}) $	None	✓	$1$	$0$	$2$	$0$	$0$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{7}+q^{8}+(-1+\beta )q^{11}+\cdots$
8550.2.a.cb	$8550$	$2$	8550.a	1.a	$1$	$2$	$2$	$68.272$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$2$	$0$	$0$	$6$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(3+\beta )q^{7}+q^{8}+\beta q^{11}+\cdots$
8550.2.a.cc	$8550$	$2$	8550.a	1.a	$1$	$3$	$3$	$68.272$	3.3.788.1	None	✓	$1$	$0$	$-3$	$0$	$0$	$-2$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1+\beta _{1})q^{7}-q^{8}+(1+\cdots)q^{11}+\cdots$
8550.2.a.cd	$8550$	$2$	8550.a	1.a	$1$	$3$	$3$	$68.272$	3.3.564.1	None	✓	$1$	$0$	$-3$	$0$	$0$	$-2$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-\beta _{1}+\beta _{2})q^{7}-q^{8}+\cdots$
8550.2.a.ce	$8550$	$2$	8550.a	1.a	$1$	$3$	$3$	$68.272$	3.3.148.1	None	✓	$1$	$0$	$-3$	$0$	$0$	$0$	$+$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta _{2}q^{7}-q^{8}+(-3-\beta _{1}+\cdots)q^{11}+\cdots$
8550.2.a.ci	$8550$	$2$	8550.a	1.a	$1$	$3$	$3$	$68.272$	3.3.993.1	None	✓	$1$	$0$	$-3$	$0$	$0$	$2$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1-\beta _{2})q^{7}-q^{8}-2\beta _{1}q^{11}+\cdots$
8550.2.a.cj	$8550$	$2$	8550.a	1.a	$1$	$3$	$3$	$68.272$	3.3.257.1	None	✓	$1$	$0$	$-3$	$0$	$0$	$2$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1-\beta _{1}+2\beta _{2})q^{7}-q^{8}+\cdots$
8550.2.a.ck	$8550$	$2$	8550.a	1.a	$1$	$3$	$3$	$68.272$	3.3.568.1	None	✓	$1$	$0$	$-3$	$0$	$0$	$4$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta _{1})q^{7}-q^{8}+(\beta _{1}+\cdots)q^{11}+\cdots$
8550.2.a.co	$8550$	$2$	8550.a	1.a	$1$	$3$	$3$	$68.272$	3.3.257.1	None	✓	$1$	$0$	$3$	$0$	$0$	$-2$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1+\beta _{1}-2\beta _{2})q^{7}+\cdots$
8550.2.a.cp	$8550$	$2$	8550.a	1.a	$1$	$3$	$3$	$68.272$	3.3.993.1	None	✓	$1$	$0$	$3$	$0$	$0$	$-2$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1+\beta _{2})q^{7}+q^{8}-2\beta _{1}q^{11}+\cdots$
8550.2.a.cr	$8550$	$2$	8550.a	1.a	$1$	$3$	$3$	$68.272$	3.3.148.1	None	✓	$1$	$0$	$3$	$0$	$0$	$0$	$-$	$-$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-\beta _{2}q^{7}+q^{8}+(1-\beta _{1}+\cdots)q^{11}+\cdots$
8550.2.a.cs	$8550$	$2$	8550.a	1.a	$1$	$3$	$3$	$68.272$	3.3.564.1	None	✓	$1$	$0$	$3$	$0$	$0$	$2$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(\beta _{1}-\beta _{2})q^{7}+q^{8}+(2+\cdots)q^{11}+\cdots$
8550.2.a.ct	$8550$	$2$	8550.a	1.a	$1$	$3$	$3$	$68.272$	3.3.788.1	None	✓	$1$	$0$	$3$	$0$	$0$	$2$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1-\beta _{1})q^{7}+q^{8}+(1+\beta _{1}+\cdots)q^{11}+\cdots$
8550.2.a.cu	$8550$	$2$	8550.a	1.a	$1$	$4$	$4$	$68.272$	$\Q(\zeta_{24})^+$	None	✓	$2$	$0$	$-4$	$0$	$0$	$0$	$+$	$+$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta _{1}q^{7}-q^{8}-\beta _{3}q^{11}+\cdots$
8550.2.a.cx	$8550$	$2$	8550.a	1.a	$1$	$6$	$6$	$68.272$	6.6.3356224.1	None	✓	$2$	$0$	$6$	$0$	$0$	$0$	$-$	$+$	$-$	$-$	$-$	$2^{5}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta _{1}q^{7}+q^{8}+(\beta _{1}-\beta _{4}+\cdots)q^{11}+\cdots$

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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.