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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	3	5	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
5445.2.a.a	$5445$	$2$	5445.a	1.a	$1$	$1$	$1$	$43.479$	$\Q$	None	✓	$1$	$2$	$-2$	$0$	$-1$	$-3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-q^{5}-3q^{7}+2q^{10}+\cdots$
5445.2.a.f	$5445$	$2$	5445.a	1.a	$1$	$1$	$1$	$43.479$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$1$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{5}-q^{7}+2q^{13}+4q^{16}+\cdots$
5445.2.a.g	$5445$	$2$	5445.a	1.a	$1$	$1$	$1$	$43.479$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$1$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{5}+q^{7}-2q^{13}+4q^{16}+\cdots$
5445.2.a.k	$5445$	$2$	5445.a	1.a	$1$	$1$	$1$	$43.479$	$\Q$	None	✓	$1$	$0$	$2$	$0$	$-1$	$3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-q^{5}+3q^{7}-2q^{10}+\cdots$
5445.2.a.m	$5445$	$2$	5445.a	1.a	$1$	$2$	$2$	$43.479$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$-2$	$0$	$2$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+(2+\cdots)q^{7}+\cdots$
5445.2.a.n	$5445$	$2$	5445.a	1.a	$1$	$2$	$2$	$43.479$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-1$	$0$	$-2$	$-4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}-q^{5}-2q^{7}+\cdots$
5445.2.a.o	$5445$	$2$	5445.a	1.a	$1$	$2$	$2$	$43.479$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-1$	$0$	$2$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(2-2\beta )q^{7}+\cdots$
5445.2.a.r	$5445$	$2$	5445.a	1.a	$1$	$2$	$2$	$43.479$	$\Q(\sqrt{3}) $	None	✓	$2$	$0$	$0$	$0$	$-2$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}-q^{5}-2\beta q^{7}-\beta q^{8}+\cdots$
5445.2.a.s	$5445$	$2$	5445.a	1.a	$1$	$2$	$2$	$43.479$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$0$	$2$	$-4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}+q^{5}-2q^{7}-\beta q^{8}+\beta q^{10}+\cdots$
5445.2.a.v	$5445$	$2$	5445.a	1.a	$1$	$2$	$2$	$43.479$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$1$	$0$	$-2$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}-q^{5}+2q^{7}+\cdots$
5445.2.a.x	$5445$	$2$	5445.a	1.a	$1$	$2$	$2$	$43.479$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$1$	$0$	$2$	$-2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(-2+2\beta )q^{7}+\cdots$
5445.2.a.y	$5445$	$2$	5445.a	1.a	$1$	$2$	$2$	$43.479$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$2$	$0$	$2$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+2\beta )q^{4}+q^{5}+2q^{7}+\cdots$
5445.2.a.bb	$5445$	$2$	5445.a	1.a	$1$	$3$	$3$	$43.479$	3.3.404.1	None	✓	$1$	$0$	$-1$	$0$	$3$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(3+\beta _{1}-\beta _{2})q^{4}+q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots$
5445.2.a.bd	$5445$	$2$	5445.a	1.a	$1$	$3$	$3$	$43.479$	3.3.404.1	None	✓	$1$	$0$	$1$	$0$	$3$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(3+\beta _{1}-\beta _{2})q^{4}+q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots$
5445.2.a.bg	$5445$	$2$	5445.a	1.a	$1$	$4$	$4$	$43.479$	4.4.2525.1	None	✓	$1$	$0$	$-3$	$0$	$-4$	$11$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{3})q^{2}+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{4}+\cdots$
5445.2.a.bi	$5445$	$2$	5445.a	1.a	$1$	$4$	$4$	$43.479$	4.4.725.1	None	✓	$1$	$0$	$-1$	$0$	$4$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots$
5445.2.a.bj	$5445$	$2$	5445.a	1.a	$1$	$4$	$4$	$43.479$	$\Q(\zeta_{15})^+$	None	✓	$1$	$0$	$-1$	$0$	$-4$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{2}+\beta _{3})q^{2}+\beta _{1}q^{4}-q^{5}+(-1+\cdots)q^{7}+\cdots$
5445.2.a.bn	$5445$	$2$	5445.a	1.a	$1$	$4$	$4$	$43.479$	4.4.27648.1	None	✓	$2$	$0$	$0$	$0$	$4$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}-\beta _{3}q^{7}+\cdots$
5445.2.a.bo	$5445$	$2$	5445.a	1.a	$1$	$4$	$4$	$43.479$	4.4.8112.1	None	✓	$2$	$0$	$0$	$0$	$-4$	$0$	$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(2-\beta _{3})q^{4}-q^{5}-\beta _{1}q^{7}+\cdots$
5445.2.a.br	$5445$	$2$	5445.a	1.a	$1$	$4$	$4$	$43.479$	4.4.5725.1	None	✓	$1$	$0$	$1$	$0$	$4$	$8$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}+\beta _{2})q^{2}+(3-\beta _{2}-\beta _{3})q^{4}+\cdots$
5445.2.a.bs	$5445$	$2$	5445.a	1.a	$1$	$4$	$4$	$43.479$	4.4.48704.2	None	✓	$1$	$0$	$2$	$0$	$-4$	$-4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(2+\beta _{2})q^{4}-q^{5}+(-1+\cdots)q^{7}+\cdots$
5445.2.a.bt	$5445$	$2$	5445.a	1.a	$1$	$4$	$4$	$43.479$	4.4.725.1	None	✓	$1$	$0$	$3$	$0$	$-4$	$-6$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots$
5445.2.a.bv	$5445$	$2$	5445.a	1.a	$1$	$4$	$4$	$43.479$	4.4.725.1	None	✓	$1$	$0$	$5$	$0$	$4$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(2-\beta _{1}-\beta _{2})q^{2}+(3-\beta _{1}-2\beta _{2}+\cdots)q^{4}+\cdots$
5445.2.a.bx	$5445$	$2$	5445.a	1.a	$1$	$6$	$6$	$43.479$	6.6.27433728.1	None	✓	$2$	$0$	$0$	$0$	$-6$	$0$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{7}+\cdots$
5445.2.a.by	$5445$	$2$	5445.a	1.a	$1$	$6$	$6$	$43.479$	6.6.74043072.1	None	✓	$2$	$0$	$0$	$0$	$6$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+\beta _{4}q^{7}+\cdots$
5445.2.a.bz	$5445$	$2$	5445.a	1.a	$1$	$6$	$6$	$43.479$	6.6.437199552.1	None	✓	$2$	$0$	$0$	$0$	$-6$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
5445.2.a.cc	$5445$	$2$	5445.a	1.a	$1$	$8$	$8$	$43.479$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$4$	$0$	$-8$	$-8$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(-\beta _{1}-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+\cdots$
5445.2.a.cd	$5445$	$2$	5445.a	1.a	$1$	$8$	$8$	$43.479$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$4$	$0$	$8$	$8$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(-\beta _{1}-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+\cdots$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
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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.