LMFDB - Newform search results

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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (43 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	3	17	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
6936.2.a.a	$6936$	$2$	6936.a	1.a	$1$	$1$	$1$	$55.384$	$\Q$	None	✓	✓			6936.2.a.a	$1$	$0$	$0$	$-1$	$-4$	$5$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{5}+5q^{7}+q^{9}-q^{13}+4q^{15}+\cdots$
6936.2.a.b	$6936$	$2$	6936.a	1.a	$1$	$1$	$1$	$55.384$	$\Q$	None	✓				408.2.a.d	$1$	$0$	$0$	$-1$	$-2$	$4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots$
6936.2.a.c	$6936$	$2$	6936.a	1.a	$1$	$1$	$1$	$55.384$	$\Q$	None	✓	✓			6936.2.a.c	$1$	$0$	$0$	$-1$	$-1$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-4q^{7}+q^{9}-3q^{11}+2q^{13}+\cdots$
6936.2.a.d	$6936$	$2$	6936.a	1.a	$1$	$1$	$1$	$55.384$	$\Q$	None	✓	✓			6936.2.a.d	$1$	$1$	$0$	$-1$	$0$	$-3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{7}+q^{9}+2q^{11}-3q^{13}+\cdots$
6936.2.a.e	$6936$	$2$	6936.a	1.a	$1$	$1$	$1$	$55.384$	$\Q$	None	✓				408.2.a.c	$1$	$1$	$0$	$-1$	$0$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}+q^{9}+2q^{13}+4q^{19}+\cdots$
6936.2.a.f	$6936$	$2$	6936.a	1.a	$1$	$1$	$1$	$55.384$	$\Q$	None	✓	✓			6936.2.a.f	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-4q^{11}-5q^{13}+\cdots$
6936.2.a.g	$6936$	$2$	6936.a	1.a	$1$	$1$	$1$	$55.384$	$\Q$	None	✓	✓			6936.2.a.g	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+6q^{11}+5q^{13}+\cdots$
6936.2.a.h	$6936$	$2$	6936.a	1.a	$1$	$1$	$1$	$55.384$	$\Q$	None	✓				408.2.a.b	$1$	$1$	$0$	$-1$	$3$	$4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}+4q^{7}+q^{9}-q^{11}-5q^{13}+\cdots$
6936.2.a.i	$6936$	$2$	6936.a	1.a	$1$	$1$	$1$	$55.384$	$\Q$	None	✓	✓			6936.2.a.i	$1$	$0$	$0$	$-1$	$4$	$1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{5}+q^{7}+q^{9}+2q^{11}-3q^{13}+\cdots$
6936.2.a.j	$6936$	$2$	6936.a	1.a	$1$	$1$	$1$	$55.384$	$\Q$	None	✓	✓			6936.2.a.i	$1$	$0$	$0$	$1$	$-4$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{5}-q^{7}+q^{9}-2q^{11}-3q^{13}+\cdots$
6936.2.a.k	$6936$	$2$	6936.a	1.a	$1$	$1$	$1$	$55.384$	$\Q$	None	✓				408.2.a.a	$1$	$1$	$0$	$1$	$-3$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}+q^{9}+q^{11}+3q^{13}+\cdots$
6936.2.a.l	$6936$	$2$	6936.a	1.a	$1$	$1$	$1$	$55.384$	$\Q$	None	✓	✓			6936.2.a.g	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-6q^{11}+5q^{13}+\cdots$
6936.2.a.m	$6936$	$2$	6936.a	1.a	$1$	$1$	$1$	$55.384$	$\Q$	None	✓	✓			6936.2.a.f	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+4q^{11}-5q^{13}+\cdots$
6936.2.a.n	$6936$	$2$	6936.a	1.a	$1$	$1$	$1$	$55.384$	$\Q$	None	✓	✓			6936.2.a.d	$1$	$1$	$0$	$1$	$0$	$3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{7}+q^{9}-2q^{11}-3q^{13}+\cdots$
6936.2.a.o	$6936$	$2$	6936.a	1.a	$1$	$1$	$1$	$55.384$	$\Q$	None	✓	✓			6936.2.a.c	$1$	$0$	$0$	$1$	$1$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+4q^{7}+q^{9}+3q^{11}+2q^{13}+\cdots$
6936.2.a.p	$6936$	$2$	6936.a	1.a	$1$	$1$	$1$	$55.384$	$\Q$	None	✓				24.2.a.a	$1$	$1$	$0$	$1$	$2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots$
6936.2.a.q	$6936$	$2$	6936.a	1.a	$1$	$1$	$1$	$55.384$	$\Q$	None	✓	✓			6936.2.a.a	$1$	$0$	$0$	$1$	$4$	$-5$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{5}-5q^{7}+q^{9}-q^{13}+4q^{15}+\cdots$
6936.2.a.r	$6936$	$2$	6936.a	1.a	$1$	$2$	$2$	$55.384$	$\Q(\sqrt{33}) $	None	✓				408.2.c.a	$1$	$1$	$0$	$-2$	$-3$	$-4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta )q^{5}-2q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
6936.2.a.s	$6936$	$2$	6936.a	1.a	$1$	$2$	$2$	$55.384$	$\Q(\sqrt{2}) $	None	✓				408.2.v.a	$1$	$0$	$0$	$-2$	$-2$	$4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+(2-\beta )q^{7}+q^{9}-3q^{11}+\cdots$
6936.2.a.t	$6936$	$2$	6936.a	1.a	$1$	$2$	$2$	$55.384$	$\Q(\sqrt{17}) $	None	✓	✓			6936.2.a.t	$1$	$0$	$0$	$-2$	$-1$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-\beta q^{5}+(1-\beta )q^{7}+q^{9}+(2-\beta )q^{11}+\cdots$
6936.2.a.u	$6936$	$2$	6936.a	1.a	$1$	$2$	$2$	$55.384$	$\Q(\sqrt{57}) $	None	✓				408.2.a.f	$1$	$0$	$0$	$-2$	$1$	$-8$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}-4q^{7}+q^{9}+(2-\beta )q^{11}+\cdots$
6936.2.a.v	$6936$	$2$	6936.a	1.a	$1$	$2$	$2$	$55.384$	$\Q(\sqrt{2}) $	None	✓				408.2.v.b	$1$	$0$	$0$	$-2$	$4$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(2+\beta )q^{5}-2q^{7}+q^{9}+4q^{11}+\cdots$
6936.2.a.w	$6936$	$2$	6936.a	1.a	$1$	$2$	$2$	$55.384$	$\Q(\sqrt{2}) $	None	✓				408.2.v.b	$1$	$1$	$0$	$2$	$-4$	$4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-2+\beta )q^{5}+2q^{7}+q^{9}-4q^{11}+\cdots$
6936.2.a.x	$6936$	$2$	6936.a	1.a	$1$	$2$	$2$	$55.384$	$\Q(\sqrt{17}) $	None	✓	✓			6936.2.a.t	$1$	$0$	$0$	$2$	$1$	$-1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}+(-1+\beta )q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots$
6936.2.a.y	$6936$	$2$	6936.a	1.a	$1$	$2$	$2$	$55.384$	$\Q(\sqrt{17}) $	None	✓				408.2.a.e	$1$	$0$	$0$	$2$	$1$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}+(2-2\beta )q^{7}+q^{9}+(4+\cdots)q^{11}+\cdots$
6936.2.a.z	$6936$	$2$	6936.a	1.a	$1$	$2$	$2$	$55.384$	$\Q(\sqrt{2}) $	None	✓				408.2.v.a	$1$	$1$	$0$	$2$	$2$	$-4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+(-2-\beta )q^{7}+q^{9}+3q^{11}+\cdots$
6936.2.a.ba	$6936$	$2$	6936.a	1.a	$1$	$2$	$2$	$55.384$	$\Q(\sqrt{33}) $	None	✓				408.2.c.a	$1$	$0$	$0$	$2$	$3$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta )q^{5}+2q^{7}+q^{9}+(1-\beta )q^{11}+\cdots$
6936.2.a.bb	$6936$	$2$	6936.a	1.a	$1$	$3$	$3$	$55.384$	3.3.316.1	None	✓				408.2.c.b	$1$	$0$	$0$	$-3$	$3$	$2$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta _{1})q^{5}+(1+\beta _{1}+\beta _{2})q^{7}+\cdots$
6936.2.a.bc	$6936$	$2$	6936.a	1.a	$1$	$3$	$3$	$55.384$	$\Q(\zeta_{18})^+$	None	✓	✓			6936.2.a.bc	$1$	$1$	$0$	$-3$	$3$	$3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1-\beta _{1})q^{5}+(1+\beta _{1}-\beta _{2})q^{7}+\cdots$
6936.2.a.bd	$6936$	$2$	6936.a	1.a	$1$	$3$	$3$	$55.384$	$\Q(\zeta_{18})^+$	None	✓	✓			6936.2.a.bc	$1$	$1$	$0$	$3$	$-3$	$-3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1+\beta _{1})q^{5}+(-1-\beta _{1}+\beta _{2})q^{7}+\cdots$
6936.2.a.be	$6936$	$2$	6936.a	1.a	$1$	$3$	$3$	$55.384$	3.3.316.1	None	✓				408.2.c.b	$1$	$1$	$0$	$3$	$-3$	$-2$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta _{1})q^{5}+(-1-\beta _{1}-\beta _{2})q^{7}+\cdots$
6936.2.a.bf	$6936$	$2$	6936.a	1.a	$1$	$6$	$6$	$55.384$	6.6.19952001.1	None	✓	✓			6936.2.a.bf	$1$	$0$	$0$	$-6$	$-3$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{1}q^{5}+(-\beta _{2}-\beta _{3}+\beta _{5})q^{7}+\cdots$
6936.2.a.bg	$6936$	$2$	6936.a	1.a	$1$	$6$	$6$	$55.384$	6.6.50874368.1	None	✓				408.2.v.c	$1$	$1$	$0$	$-6$	$-2$	$-4$	$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{5}q^{5}+(-1+\beta _{3})q^{7}+q^{9}+\cdots$
6936.2.a.bh	$6936$	$2$	6936.a	1.a	$1$	$6$	$6$	$55.384$	6.6.14178321.1	None	✓	✓			6936.2.a.bh	$1$	$1$	$0$	$-6$	$3$	$-3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1-\beta _{3})q^{5}+(-1-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$
6936.2.a.bi	$6936$	$2$	6936.a	1.a	$1$	$6$	$6$	$55.384$	6.6.14178321.1	None	✓	✓			6936.2.a.bh	$1$	$1$	$0$	$6$	$-3$	$3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1+\beta _{3})q^{5}+(1+\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots$
6936.2.a.bj	$6936$	$2$	6936.a	1.a	$1$	$6$	$6$	$55.384$	6.6.50874368.1	None	✓				408.2.v.c	$1$	$0$	$0$	$6$	$2$	$4$	$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{5}q^{5}+(1-\beta _{3})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots$
6936.2.a.bk	$6936$	$2$	6936.a	1.a	$1$	$6$	$6$	$55.384$	6.6.19952001.1	None	✓	✓			6936.2.a.bf	$1$	$0$	$0$	$6$	$3$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1-\beta _{1})q^{5}+\beta _{5}q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots$
6936.2.a.bl	$6936$	$2$	6936.a	1.a	$1$	$8$	$8$	$55.384$	8.8.$\cdots$.1	None	✓		✓		408.2.ba.a	$1$	$1$	$0$	$-8$	$-4$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-\beta _{1}-\beta _{2}-\beta _{3})q^{5}-\beta _{7}q^{7}+\cdots$
6936.2.a.bm	$6936$	$2$	6936.a	1.a	$1$	$8$	$8$	$55.384$	8.8.$\cdots$.1	None	✓		✓		408.2.ba.b	$1$	$0$	$0$	$-8$	$4$	$8$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(\beta _{2}+\beta _{3}-\beta _{7})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
6936.2.a.bn	$6936$	$2$	6936.a	1.a	$1$	$8$	$8$	$55.384$	8.8.$\cdots$.1	None	✓		✓		408.2.ba.b	$1$	$1$	$0$	$8$	$-4$	$-8$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-\beta _{2}-\beta _{3}+\beta _{7})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
6936.2.a.bo	$6936$	$2$	6936.a	1.a	$1$	$8$	$8$	$55.384$	8.8.$\cdots$.1	None	✓				408.2.ba.a	$1$	$0$	$0$	$8$	$4$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(\beta _{1}+\beta _{2}+\beta _{3})q^{5}+\beta _{7}q^{7}+\cdots$
6936.2.a.bp	$6936$	$2$	6936.a	1.a	$1$	$9$	$9$	$55.384$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓	✓		6936.2.a.bp	$1$	$0$	$0$	$-9$	$-3$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{1}q^{5}-\beta _{7}q^{7}+q^{9}+(-\beta _{3}+\cdots)q^{11}+\cdots$
6936.2.a.bq	$6936$	$2$	6936.a	1.a	$1$	$9$	$9$	$55.384$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓	✓		6936.2.a.bp	$1$	$0$	$0$	$9$	$3$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{1}q^{5}+\beta _{7}q^{7}+q^{9}+(\beta _{3}+\beta _{5}+\cdots)q^{11}+\cdots$

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