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 (33 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	7	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
5824.2.a.b	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	$\Q$	None	✓	$1$	$0$	$0$	$-3$	$4$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+4q^{5}-q^{7}+6q^{9}-q^{11}+\cdots$
5824.2.a.f	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	$\Q$	None	✓	$1$	$0$	$0$	$-2$	$3$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+3q^{5}-q^{7}+q^{9}-q^{13}-6q^{15}+\cdots$
5824.2.a.i	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$0$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}-2q^{9}+q^{11}-q^{13}+4q^{17}+\cdots$
5824.2.a.k	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$0$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}-2q^{9}+3q^{11}-q^{13}+\cdots$
5824.2.a.l	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$-2$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{7}-3q^{9}-4q^{11}+q^{13}+\cdots$
5824.2.a.m	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$-2$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}-3q^{9}+4q^{11}+q^{13}+\cdots$
5824.2.a.q	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$2$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}-3q^{9}-4q^{11}-q^{13}+\cdots$
5824.2.a.s	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$3$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-q^{7}-3q^{9}+6q^{11}+q^{13}+\cdots$
5824.2.a.t	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$3$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+q^{7}-3q^{9}-6q^{11}+q^{13}+\cdots$
5824.2.a.v	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-4$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{5}-q^{7}-2q^{9}+5q^{11}+\cdots$
5824.2.a.x	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}-2q^{9}-3q^{11}-q^{13}+\cdots$
5824.2.a.bd	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	$\Q$	None	✓	$1$	$0$	$0$	$2$	$3$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+3q^{5}+q^{7}+q^{9}-q^{13}+6q^{15}+\cdots$
5824.2.a.bf	$5824$	$2$	5824.a	1.a	$1$	$1$	$1$	$46.505$	$\Q$	None	✓	$1$	$0$	$0$	$3$	$4$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+4q^{5}+q^{7}+6q^{9}+q^{11}+\cdots$
5824.2.a.bg	$5824$	$2$	5824.a	1.a	$1$	$2$	$2$	$46.505$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$-4$	$2$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-2+\beta )q^{3}+(1-\beta )q^{5}-q^{7}+(3+\cdots)q^{9}+\cdots$
5824.2.a.bh	$5824$	$2$	5824.a	1.a	$1$	$2$	$2$	$46.505$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$-2$	$0$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}-\beta q^{5}+q^{7}+(1-2\beta )q^{9}+\cdots$
5824.2.a.bi	$5824$	$2$	5824.a	1.a	$1$	$2$	$2$	$46.505$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$-2$	$0$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+\beta q^{5}+q^{7}+(1-2\beta )q^{9}+\cdots$
5824.2.a.bm	$5824$	$2$	5824.a	1.a	$1$	$2$	$2$	$46.505$	$\Q(\sqrt{6}) $	None	✓	$1$	$0$	$0$	$0$	$2$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(1+\beta )q^{5}-q^{7}+3q^{9}+(-4+\cdots)q^{11}+\cdots$
5824.2.a.bn	$5824$	$2$	5824.a	1.a	$1$	$2$	$2$	$46.505$	$\Q(\sqrt{6}) $	None	✓	$1$	$0$	$0$	$0$	$2$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(1-\beta )q^{5}+q^{7}+3q^{9}+(4+\cdots)q^{11}+\cdots$
5824.2.a.bp	$5824$	$2$	5824.a	1.a	$1$	$2$	$2$	$46.505$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$2$	$0$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-\beta q^{5}-q^{7}+(1+2\beta )q^{9}+\cdots$
5824.2.a.bq	$5824$	$2$	5824.a	1.a	$1$	$2$	$2$	$46.505$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$2$	$0$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+\beta q^{5}-q^{7}+(1+2\beta )q^{9}+\cdots$
5824.2.a.br	$5824$	$2$	5824.a	1.a	$1$	$2$	$2$	$46.505$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$4$	$2$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{3}+(1+\beta )q^{5}+q^{7}+(3+4\beta )q^{9}+\cdots$
5824.2.a.bt	$5824$	$2$	5824.a	1.a	$1$	$3$	$3$	$46.505$	3.3.564.1	None	✓	$1$	$0$	$0$	$-2$	$-1$	$-3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots$
5824.2.a.bu	$5824$	$2$	5824.a	1.a	$1$	$3$	$3$	$46.505$	3.3.148.1	None	✓	$1$	$0$	$0$	$0$	$-1$	$-3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}-\beta _{1}q^{5}-q^{7}+(-\beta _{1}-\beta _{2})q^{9}+\cdots$
5824.2.a.bx	$5824$	$2$	5824.a	1.a	$1$	$3$	$3$	$46.505$	3.3.148.1	None	✓	$1$	$0$	$0$	$0$	$5$	$3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(2-\beta _{1})q^{5}+q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots$
5824.2.a.cb	$5824$	$2$	5824.a	1.a	$1$	$4$	$4$	$46.505$	4.4.64268.1	None	✓	$1$	$0$	$0$	$-1$	$-2$	$-4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1-\beta _{2})q^{5}-q^{7}+(3+\beta _{1}+\cdots)q^{9}+\cdots$
5824.2.a.cc	$5824$	$2$	5824.a	1.a	$1$	$4$	$4$	$46.505$	4.4.183064.1	None	✓	$1$	$0$	$0$	$-1$	$0$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+\beta _{3}q^{5}+q^{7}+(2+\beta _{2})q^{9}+\cdots$
5824.2.a.cd	$5824$	$2$	5824.a	1.a	$1$	$4$	$4$	$46.505$	4.4.33844.1	None	✓	$1$	$0$	$0$	$-1$	$1$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-\beta _{3}q^{5}+q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots$
5824.2.a.ce	$5824$	$2$	5824.a	1.a	$1$	$4$	$4$	$46.505$	4.4.64268.1	None	✓	$1$	$0$	$0$	$1$	$-2$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+q^{7}+(3+\beta _{1}+\cdots)q^{9}+\cdots$
5824.2.a.cf	$5824$	$2$	5824.a	1.a	$1$	$4$	$4$	$46.505$	4.4.183064.1	None	✓	$1$	$0$	$0$	$1$	$0$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{3}q^{5}-q^{7}+(2+\beta _{2})q^{9}+\cdots$
5824.2.a.ch	$5824$	$2$	5824.a	1.a	$1$	$4$	$4$	$46.505$	4.4.11348.1	None	✓	$1$	$0$	$0$	$2$	$1$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+\beta _{1}q^{5}-q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
5824.2.a.ck	$5824$	$2$	5824.a	1.a	$1$	$5$	$5$	$46.505$	5.5.6329476.1	None	✓	$1$	$0$	$0$	$0$	$-3$	$5$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1+\beta _{3})q^{5}+q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
5824.2.a.cl	$5824$	$2$	5824.a	1.a	$1$	$5$	$5$	$46.505$	5.5.1025428.1	None	✓	$1$	$0$	$0$	$5$	$3$	$5$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{3}+(1-\beta _{4})q^{5}+q^{7}+(1+\cdots)q^{9}+\cdots$
5824.2.a.cn	$5824$	$2$	5824.a	1.a	$1$	$6$	$6$	$46.505$	6.6.153499364.1	None	✓	$1$	$0$	$0$	$4$	$-3$	$-6$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+\beta _{5}q^{5}-q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots$

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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.