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 (38 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	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8112.2.a.a	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$-4$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{5}+2q^{7}+q^{9}-2q^{11}+\cdots$
8112.2.a.c	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$-3$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}+2q^{7}+q^{9}+6q^{11}+\cdots$
8112.2.a.e	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓	$1$	$2$	$0$	$-1$	$-2$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots$
8112.2.a.i	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$0$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}+q^{9}-6q^{17}+2q^{19}+\cdots$
8112.2.a.k	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$2$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots$
8112.2.a.m	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$3$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}-2q^{7}+q^{9}-6q^{11}+\cdots$
8112.2.a.p	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$4$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{5}-2q^{7}+q^{9}+2q^{11}+\cdots$
8112.2.a.q	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-4$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{5}+q^{9}-2q^{11}-4q^{15}+\cdots$
8112.2.a.r	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-3$	$-4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots$
8112.2.a.t	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-2$	$-1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-q^{7}+q^{9}+6q^{11}-2q^{15}+\cdots$
8112.2.a.y	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$-4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{7}+q^{9}-2q^{11}-6q^{17}+\cdots$
8112.2.a.be	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$2$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{9}+4q^{11}+2q^{15}+\cdots$
8112.2.a.bf	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$2$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{7}+q^{9}-6q^{11}+2q^{15}+\cdots$
8112.2.a.bg	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$2$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+4q^{7}+q^{9}+2q^{15}+\cdots$
8112.2.a.bh	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$3$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots$
8112.2.a.bk	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$0$	$-2$	$-3$	$3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta )q^{5}+(2-\beta )q^{7}+q^{9}+\cdots$
8112.2.a.bm	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$-2$	$0$	$0$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}+\beta q^{7}+q^{9}-2q^{11}+\cdots$
8112.2.a.bo	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$0$	$-2$	$3$	$-3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta )q^{5}+(-2+\beta )q^{7}+q^{9}+\cdots$
8112.2.a.bq	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$2$	$0$	$-6$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}+(-3+\beta )q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots$
8112.2.a.bs	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	$\Q(\sqrt{3}) $	None	✓	$2$	$0$	$0$	$2$	$0$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}+q^{9}+\beta q^{11}+\beta q^{15}+\cdots$
8112.2.a.bt	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	$\Q(\sqrt{3}) $	None	✓	$2$	$0$	$0$	$2$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}+2\beta q^{7}+q^{9}-2\beta q^{11}+\cdots$
8112.2.a.bu	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	$\Q(\sqrt{3}) $	None	✓	$2$	$0$	$0$	$2$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2\beta q^{5}-\beta q^{7}+q^{9}+2\beta q^{11}+\cdots$
8112.2.a.bv	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	$\Q(\sqrt{3}) $	None	✓	$2$	$0$	$0$	$2$	$0$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}-\beta q^{7}+q^{9}-\beta q^{11}+6q^{17}+\cdots$
8112.2.a.bx	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$2$	$0$	$6$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}+(3+\beta )q^{7}+q^{9}+(3+\beta )q^{11}+\cdots$
8112.2.a.cc	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$0$	$-3$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1-2\beta _{1}+\beta _{2})q^{5}+(1-2\beta _{1}+\cdots)q^{7}+\cdots$
8112.2.a.cd	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$0$	$-3$	$0$	$6$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1-2\beta _{1}+\beta _{2})q^{5}+(3-2\beta _{1}+\cdots)q^{7}+\cdots$
8112.2.a.ce	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$0$	$-3$	$3$	$3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta _{1}+\beta _{2})q^{5}+(\beta _{1}-2\beta _{2})q^{7}+\cdots$
8112.2.a.cf	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$0$	$-3$	$4$	$-10$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta _{1})q^{5}+(-3-\beta _{1})q^{7}+\cdots$
8112.2.a.cj	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$0$	$3$	$-1$	$9$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1-3\beta _{1}+\beta _{2})q^{5}+(4-\beta _{1}+\cdots)q^{7}+\cdots$
8112.2.a.ck	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	3.3.837.1	None	✓	$1$	$0$	$0$	$3$	$0$	$-3$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}-\beta _{2}q^{5}+(-1+\beta _{1})q^{7}+q^{9}+\cdots$
8112.2.a.cl	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	3.3.837.1	None	✓	$1$	$0$	$0$	$3$	$0$	$3$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{2}q^{5}+(1-\beta _{1})q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots$
8112.2.a.cn	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$0$	$3$	$2$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1-\beta _{1})q^{5}+(1-\beta _{1}+2\beta _{2})q^{7}+\cdots$
8112.2.a.co	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$0$	$3$	$2$	$6$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1-\beta _{1})q^{5}+(3-\beta _{1}+2\beta _{2})q^{7}+\cdots$
8112.2.a.cp	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$0$	$3$	$6$	$-2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(2-\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots$
8112.2.a.cq	$8112$	$2$	8112.a	1.a	$1$	$4$	$4$	$64.775$	4.4.25488.1	None	✓	$1$	$0$	$0$	$-4$	$-4$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
8112.2.a.cs	$8112$	$2$	8112.a	1.a	$1$	$4$	$4$	$64.775$	4.4.25488.1	None	✓	$1$	$0$	$0$	$-4$	$4$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
8112.2.a.cu	$8112$	$2$	8112.a	1.a	$1$	$6$	$6$	$64.775$	6.6.27700337.1	None	✓	$1$	$0$	$0$	$-6$	$1$	$5$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-\beta _{1}+\beta _{3})q^{5}+(1-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots$
8112.2.a.cv	$8112$	$2$	8112.a	1.a	$1$	$6$	$6$	$64.775$	6.6.27700337.1	None	✓	$1$	$0$	$0$	$6$	$-1$	$7$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-\beta _{5}q^{5}+(1+\beta _{1})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots$

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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.