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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	7	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8281.2.a.a	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$1$	$-2$	$-2$	$-1$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-2q^{3}+2q^{4}-q^{5}+4q^{6}+\cdots$
8281.2.a.b	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$1$	$-2$	$2$	$1$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{3}+2q^{4}+q^{5}-4q^{6}+\cdots$
8281.2.a.c	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$1$	$-1$	$-3$	$-3$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-3q^{3}-q^{4}-3q^{5}+3q^{6}+3q^{8}+\cdots$
8281.2.a.f	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+3q^{8}-3q^{9}+3q^{11}+\cdots$
8281.2.a.i	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$1$	$1$	$-3$	$3$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}-q^{4}+3q^{5}-3q^{6}-3q^{8}+\cdots$
8281.2.a.k	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$1$	$2$	$-2$	$1$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-2q^{3}+2q^{4}+q^{5}-4q^{6}+\cdots$
8281.2.a.m	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$1$	$2$	$2$	$-1$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{3}+2q^{4}-q^{5}+4q^{6}+\cdots$
8281.2.a.q	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{3}) $	None	✓	$2$	$1$	$0$	$-4$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-2q^{3}+q^{4}+\beta q^{5}-2\beta q^{6}+\cdots$
8281.2.a.u	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{13}) $	$\Q(\sqrt{-91}) $	✓	$4$	$1$	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$2$	$N(\mathrm{U}(1))$	$q-2q^{4}-\beta q^{5}-3q^{9}+4q^{16}-\beta q^{19}+\cdots$
8281.2.a.w	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{3}) $	None	✓	$2$	$1$	$0$	$2$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+q^{4}+\beta q^{5}+\beta q^{6}-\beta q^{8}+\cdots$
8281.2.a.z	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$3$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1-2\beta )q^{3}+3\beta q^{4}+(1+\cdots)q^{5}+\cdots$
8281.2.a.bc	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	$\Q(\zeta_{14})^+$	$\Q(\sqrt{-7}) $	✓	$2$	$1$	$-4$	$0$	$0$	$0$	$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	$q+(-1-\beta _{1})q^{2}+(1+2\beta _{1}+\beta _{2})q^{4}+\cdots$
8281.2.a.be	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	3.3.148.1	None	✓	$1$	$1$	$-2$	$0$	$3$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
8281.2.a.bi	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	3.3.148.1	None	✓	$1$	$1$	$2$	$0$	$-3$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
8281.2.a.bj	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$2$	$2$	$-4$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1+\beta _{2})q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots$
8281.2.a.bl	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	$\Q(\zeta_{14})^+$	$\Q(\sqrt{-7}) $	✓	$2$	$1$	$3$	$0$	$0$	$0$	$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	$q+(1-\beta _{1}-\beta _{2})q^{2}+(4-\beta _{1})q^{4}+(5+\cdots)q^{8}+\cdots$
8281.2.a.bn	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	$\Q(\sqrt{2}, \sqrt{23})$	None	✓	$2$	$1$	$-4$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{2}q^{3}-q^{4}-\beta _{1}q^{5}-\beta _{2}q^{6}+\cdots$
8281.2.a.bq	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	$\Q(\sqrt{3}, \sqrt{7})$	None	✓	$2$	$1$	$0$	$-2$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+(-1-\beta _{2})q^{3}-\beta _{2}q^{4}-\beta _{3}q^{5}+\cdots$
8281.2.a.br	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	$\Q(\sqrt{3}, \sqrt{13})$	None	✓	$4$	$1$	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+q^{4}+\beta _{3}q^{5}+\beta _{2}q^{8}-3q^{9}+\cdots$
8281.2.a.bs	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	$\Q(\sqrt{3}, \sqrt{7})$	None	✓	$2$	$1$	$0$	$2$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+(1+\beta _{2})q^{3}-\beta _{2}q^{4}+\beta _{3}q^{5}+\cdots$
8281.2.a.bv	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	$\Q(\sqrt{2}, \sqrt{23})$	None	✓	$2$	$1$	$4$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{2}q^{3}-q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots$
8281.2.a.bw	$8281$	$2$	8281.a	1.a	$1$	$5$	$5$	$66.124$	5.5.746052.1	None	✓	$1$	$1$	$-4$	$0$	$-2$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-\beta _{4}q^{3}+(2-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$
8281.2.a.by	$8281$	$2$	8281.a	1.a	$1$	$6$	$6$	$66.124$	6.6.7674048.1	None	✓	$1$	$1$	$-4$	$0$	$6$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+\beta _{4}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
8281.2.a.bz	$8281$	$2$	8281.a	1.a	$1$	$6$	$6$	$66.124$	6.6.6995813.1	None	✓	$1$	$1$	$-2$	$-1$	$-1$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}+\beta _{4})q^{2}+\beta _{4}q^{3}+(1+\beta _{5})q^{4}+\cdots$
8281.2.a.cb	$8281$	$2$	8281.a	1.a	$1$	$6$	$6$	$66.124$	6.6.1279733.1	None	✓	$1$	$1$	$-2$	$4$	$2$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2}+\beta _{4})q^{2}+(\beta _{1}-\beta _{3})q^{3}+\cdots$
8281.2.a.cc	$8281$	$2$	8281.a	1.a	$1$	$6$	$6$	$66.124$	6.6.4507648.1	None	✓	$1$	$1$	$0$	$-8$	$6$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(-1-\beta _{1})q^{3}+(1-\beta _{1}-\beta _{3}+\cdots)q^{4}+\cdots$
8281.2.a.cd	$8281$	$2$	8281.a	1.a	$1$	$6$	$6$	$66.124$	6.6.4507648.1	None	✓	$1$	$1$	$0$	$8$	$-6$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(1+\beta _{1})q^{3}+(1-\beta _{1}-\beta _{3}+\cdots)q^{4}+\cdots$
8281.2.a.ce	$8281$	$2$	8281.a	1.a	$1$	$6$	$6$	$66.124$	6.6.6995813.1	None	✓	$1$	$1$	$2$	$-1$	$1$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}-\beta _{4})q^{2}+\beta _{4}q^{3}+(1+\beta _{5})q^{4}+\cdots$
8281.2.a.ch	$8281$	$2$	8281.a	1.a	$1$	$6$	$6$	$66.124$	6.6.7674048.1	None	✓	$1$	$1$	$4$	$0$	$-6$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+\beta _{4}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
8281.2.a.ci	$8281$	$2$	8281.a	1.a	$1$	$8$	$8$	$66.124$	8.8.8446345216.1	None	✓	$2$	$1$	$-4$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{5})q^{2}+(-\beta _{1}-\beta _{4})q^{3}+(1+\cdots)q^{4}+\cdots$
8281.2.a.cj	$8281$	$2$	8281.a	1.a	$1$	$8$	$8$	$66.124$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$2$	$1$	$0$	$-4$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots$
8281.2.a.cl	$8281$	$2$	8281.a	1.a	$1$	$8$	$8$	$66.124$	8.8.8446345216.1	None	✓	$2$	$1$	$4$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{5})q^{2}+(-\beta _{1}-\beta _{4})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots$
8281.2.a.cm	$8281$	$2$	8281.a	1.a	$1$	$12$	$12$	$66.124$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$2$	$1$	$-4$	$0$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+\beta _{1}q^{3}+(-\beta _{2}-\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots$
8281.2.a.cn	$8281$	$2$	8281.a	1.a	$1$	$12$	$12$	$66.124$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$-3$	$-8$	$-4$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(2-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots$
8281.2.a.co	$8281$	$2$	8281.a	1.a	$1$	$12$	$12$	$66.124$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$2$	$1$	$0$	$-6$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1-\beta _{8}+\beta _{9})q^{4}+\cdots$
8281.2.a.ct	$8281$	$2$	8281.a	1.a	$1$	$24$	$24$	$66.124$		None	✓	$1$	$1$	$-1$	$0$	$-13$	$0$	$-$	$-$	$+$		$\mathrm{SU}(2)$
8281.2.a.cv	$8281$	$2$	8281.a	1.a	$1$	$24$	$24$	$66.124$		None	✓	$1$	$1$	$1$	$0$	$-13$	$0$	$+$	$+$	$+$		$\mathrm{SU}(2)$
8281.2.a.cy	$8281$	$2$	8281.a	1.a	$1$	$36$	$36$	$66.124$		None	✓	$2$	$1$	$-14$	$0$	$0$	$0$	$+$	$+$	$+$		$\mathrm{SU}(2)$

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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.