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 (44 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1160.1.o.a	$1160$	$1$	1160.o	1160.o	$2$	$2$	$2$	$0.579$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-290}) $	None	✓	✓			1160.1.o.a	$2$	$0$	$-2$	$1$	$-2$	$1$		$1$		$q-q^{2}+\beta q^{3}+q^{4}-q^{5}-\beta q^{6}+(1+\cdots)q^{7}+\cdots$
1160.1.o.b	$1160$	$1$	1160.o	1160.o	$2$	$2$	$2$	$0.579$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-290}) $	None	✓	✓			1160.1.o.a	$2$	$0$	$-2$	$1$	$2$	$-1$		$1$		$q-q^{2}+(1-\beta )q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots$
1160.1.o.c	$1160$	$1$	1160.o	1160.o	$2$	$2$	$2$	$0.579$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-290}) $	None	✓	✓			1160.1.o.a	$2$	$0$	$2$	$-1$	$-2$	$1$		$1$		$q+q^{2}+(-1+\beta )q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots$
1160.1.o.d	$1160$	$1$	1160.o	1160.o	$2$	$2$	$2$	$0.579$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-290}) $	None	✓	✓			1160.1.o.a	$2$	$0$	$2$	$-1$	$2$	$-1$		$1$		$q+q^{2}-\beta q^{3}+q^{4}+q^{5}-\beta q^{6}+(-1+\cdots)q^{7}+\cdots$
1160.1.o.e	$1160$	$1$	1160.o	1160.o	$2$	$4$	$4$	$0.579$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{145}) $		✓	✓		1160.1.o.e	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+(-\zeta_{8}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$
1160.2.a.a	$1160$	$2$	1160.a	1.a	$1$	$1$	$1$	$9.263$	$\Q$	$_{}$	None	None	✓	✓			1160.2.a.a	$1$	$1$	$0$	$-2$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots$
1160.2.a.b	$1160$	$2$	1160.a	1.a	$1$	$1$	$1$	$9.263$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1160.2.a.b	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-3q^{9}-2q^{13}-6q^{17}-8q^{19}+\cdots$
1160.2.a.c	$1160$	$2$	1160.a	1.a	$1$	$1$	$1$	$9.263$	$\Q$	$_{}$	None	None	✓	✓			1160.2.a.c	$1$	$1$	$0$	$2$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{5}-4q^{7}+q^{9}-2q^{13}+\cdots$
1160.2.a.d	$1160$	$2$	1160.a	1.a	$1$	$1$	$1$	$9.263$	$\Q$	$_{}$	None	None	✓	✓			1160.2.a.d	$1$	$0$	$0$	$2$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{5}+4q^{7}+q^{9}+6q^{13}+\cdots$
1160.2.a.e	$1160$	$2$	1160.a	1.a	$1$	$3$	$3$	$9.263$	3.3.148.1	$_{}$	None	None	✓	✓	✓	✓	1160.2.a.e	$1$	$1$	$0$	$-2$	$-3$	$2$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}-q^{5}+(1-\beta _{2})q^{7}+\cdots$
1160.2.a.f	$1160$	$2$	1160.a	1.a	$1$	$3$	$3$	$9.263$	3.3.148.1	$_{}$	None	None	✓	✓	✓	✓	1160.2.a.f	$1$	$1$	$0$	$-2$	$3$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+q^{5}+(-1-\beta _{1})q^{7}+\cdots$
1160.2.a.g	$1160$	$2$	1160.a	1.a	$1$	$3$	$3$	$9.263$	3.3.229.1	$_{}$	None	None	✓	✓	✓		1160.2.a.g	$1$	$0$	$0$	$1$	$-3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}-q^{5}+(-1+\beta _{1})q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots$
1160.2.a.h	$1160$	$2$	1160.a	1.a	$1$	$5$	$5$	$9.263$	5.5.3145252.1	$_{}$	None	None	✓	✓	✓	✓	1160.2.a.h	$1$	$0$	$0$	$-1$	$-5$	$7$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}-q^{5}+(1-\beta _{2})q^{7}+(2-\beta _{2}+\cdots)q^{9}+\cdots$
1160.2.a.i	$1160$	$2$	1160.a	1.a	$1$	$5$	$5$	$9.263$	5.5.6083172.1	$_{}$	None	None	✓	✓	✓	✓	1160.2.a.i	$1$	$0$	$0$	$-1$	$5$	$-1$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+q^{5}+(-\beta _{2}+\beta _{3})q^{7}+(2+\cdots)q^{9}+\cdots$
1160.2.a.j	$1160$	$2$	1160.a	1.a	$1$	$5$	$5$	$9.263$	5.5.580484.1	$_{}$	None	None	✓	✓	✓	✓	1160.2.a.j	$1$	$0$	$0$	$3$	$5$	$7$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1-\beta _{3})q^{3}+q^{5}+(1-\beta _{2}+\beta _{3})q^{7}+\cdots$
1160.2.d.a	$1160$	$2$	1160.d	5.b	$2$	$2$	$2$	$9.263$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1160.2.d.a	$2$	$0$	$0$	$0$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+(-\beta-1)q^{5}+\beta q^{7}-q^{9}+\cdots$
1160.2.d.b	$1160$	$2$	1160.d	5.b	$2$	$2$	$2$	$9.263$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1160.2.d.b	$2$	$0$	$0$	$0$	$2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta+1)q^{5}+\beta q^{7}+3 q^{9}-3\beta q^{17}+\cdots$
1160.2.d.c	$1160$	$2$	1160.d	5.b	$2$	$16$	$16$	$9.263$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓			1160.2.d.c	$2$	$0$	$0$	$0$	$-2$	$0$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{5}q^{5}-\beta _{13}q^{7}+(-1+\beta _{9}+\cdots)q^{9}+\cdots$
1160.2.d.d	$1160$	$2$	1160.d	5.b	$2$	$22$	$22$	$9.263$		$_{}$	None	None		✓	✓		1160.2.d.d	$2$	$0$	$0$	$0$	$2$	$0$			$\mathrm{SU}(2)[C_{2}]$
1160.2.g.a	$1160$	$2$	1160.g	29.b	$2$	$2$	$2$	$9.263$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1160.2.g.a	$2$	$0$	$0$	$0$	$2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{3}+q^{5}-q^{9}-\beta q^{11}-2 q^{13}+\cdots$
1160.2.g.b	$1160$	$2$	1160.g	29.b	$2$	$14$	$14$	$9.263$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		✓			1160.2.g.b	$2$	$0$	$0$	$0$	$-14$	$6$		$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{3}-q^{5}+\beta _{6}q^{7}+(-1+\beta _{3}+\cdots)q^{9}+\cdots$
1160.2.g.c	$1160$	$2$	1160.g	29.b	$2$	$14$	$14$	$9.263$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		✓			1160.2.g.c	$2$	$0$	$0$	$0$	$14$	$-6$		$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+q^{5}-\beta _{5}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots$
1160.2.j.a	$1160$	$2$	1160.j	145.d	$2$	$22$	$22$	$9.263$		$_{}$	None	None		✓			1160.2.j.a	$2$	$0$	$0$	$0$	$-1$	$0$			$\mathrm{SU}(2)[C_{2}]$
1160.2.j.b	$1160$	$2$	1160.j	145.d	$2$	$22$	$22$	$9.263$		$_{}$	None	None		✓			1160.2.j.a	$2$	$0$	$0$	$0$	$-1$	$0$			$\mathrm{SU}(2)[C_{2}]$
1160.2.s.a	$1160$	$2$	1160.s	145.j	$4$	$2$	$1$	$9.263$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1160.2.s.a	$2$	$0$	$0$	$0$	$2$	$-2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+2 i q^{3}+(-2 i+1)q^{5}+(i-1)q^{7}+\cdots$
1160.2.s.b	$1160$	$2$	1160.s	145.j	$4$	$4$	$2$	$9.263$	$\Q(i, \sqrt{7})$	$_{}$	None	None		✓			1160.2.s.b	$2$	$0$	$0$	$0$	$-4$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q-2\beta _{1}q^{3}+(-1-2\beta _{1})q^{5}+\beta _{2}q^{7}+\cdots$
1160.2.s.c	$1160$	$2$	1160.s	145.j	$4$	$42$	$21$	$9.263$		$_{}$	None	None		✓			1160.2.s.c	$2$	$0$	$0$	$0$	$0$	$-2$			$\mathrm{SU}(2)[C_{4}]$
1160.2.s.d	$1160$	$2$	1160.s	145.j	$4$	$42$	$21$	$9.263$		$_{}$	None	None		✓			1160.2.s.d	$2$	$0$	$0$	$0$	$2$	$4$			$\mathrm{SU}(2)[C_{4}]$
1160.2.bl.a	$1160$	$2$	1160.bl	145.e	$4$	$2$	$1$	$9.263$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1160.2.s.a	$2$	$0$	$0$	$4$	$-2$	$-2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+2 q^{3}+(-2 i-1)q^{5}+(-i-1)q^{7}+\cdots$
1160.2.bl.b	$1160$	$2$	1160.bl	145.e	$4$	$4$	$2$	$9.263$	$\Q(i, \sqrt{7})$	$_{}$	None	None		✓			1160.2.s.b	$2$	$0$	$0$	$8$	$4$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q+2q^{3}+(1+2\beta _{1})q^{5}+\beta _{2}q^{7}+q^{9}+\cdots$
1160.2.bl.c	$1160$	$2$	1160.bl	145.e	$4$	$42$	$21$	$9.263$		$_{}$	None	None		✓			1160.2.s.d	$2$	$0$	$0$	$-8$	$-2$	$4$			$\mathrm{SU}(2)[C_{4}]$
1160.2.bl.d	$1160$	$2$	1160.bl	145.e	$4$	$42$	$21$	$9.263$		$_{}$	None	None		✓			1160.2.s.c	$2$	$0$	$0$	$-4$	$0$	$-2$			$\mathrm{SU}(2)[C_{4}]$
1160.4.a.a	$1160$	$4$	1160.a	1.a	$1$	$1$	$1$	$68.442$	$\Q$	$_{}$	None	None	✓	✓			1160.4.a.a	$1$	$2$	$0$	$-8$	$-5$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-8q^{3}-5q^{5}-6q^{7}+37q^{9}-58q^{11}+\cdots$
1160.4.a.b	$1160$	$4$	1160.a	1.a	$1$	$3$	$3$	$68.442$	3.3.1556.1	$_{}$	None	None	✓	✓			1160.4.a.b	$1$	$1$	$0$	$-8$	$-15$	$-42$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-3+\beta _{2})q^{3}-5q^{5}+(-15-2\beta _{1}+\cdots)q^{7}+\cdots$
1160.4.a.c	$1160$	$4$	1160.a	1.a	$1$	$7$	$7$	$68.442$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓	✓		1160.4.a.c	$1$	$1$	$0$	$1$	$-35$	$65$	$-$	$2^{5}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-5q^{5}+(9-\beta _{5})q^{7}+(7+\beta _{1}+\cdots)q^{9}+\cdots$
1160.4.a.d	$1160$	$4$	1160.a	1.a	$1$	$9$	$9$	$68.442$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1160.4.a.d	$1$	$1$	$0$	$-7$	$45$	$-39$	$-$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+5q^{5}+(-4-\beta _{1}+\cdots)q^{7}+\cdots$
1160.4.a.e	$1160$	$4$	1160.a	1.a	$1$	$9$	$9$	$68.442$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1160.4.a.e	$1$	$1$	$0$	$-3$	$-45$	$-27$	$-$	$2^{7}\cdot 7$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-5q^{5}+(-3-\beta _{1}-\beta _{4})q^{7}+\cdots$
1160.4.a.f	$1160$	$4$	1160.a	1.a	$1$	$9$	$9$	$68.442$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1160.4.a.f	$1$	$1$	$0$	$-3$	$45$	$9$	$-$	$2^{7}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+5q^{5}+(1+\beta _{1}+\beta _{2})q^{7}+\cdots$
1160.4.a.g	$1160$	$4$	1160.a	1.a	$1$	$11$	$11$	$68.442$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓	✓	✓		1160.4.a.g	$1$	$0$	$0$	$2$	$-55$	$56$	$+$	$2^{12}\cdot 3$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-5q^{5}+(5+\beta _{7})q^{7}+(6+\beta _{2}+\cdots)q^{9}+\cdots$
1160.4.a.h	$1160$	$4$	1160.a	1.a	$1$	$11$	$11$	$68.442$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1160.4.a.h	$1$	$0$	$0$	$8$	$-55$	$16$	$+$	$2^{9}\cdot 3^{3}\cdot 43$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}-5q^{5}+(1+\beta _{1}-\beta _{5}+\cdots)q^{7}+\cdots$
1160.4.a.i	$1160$	$4$	1160.a	1.a	$1$	$11$	$11$	$68.442$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1160.4.a.i	$1$	$0$	$0$	$8$	$55$	$38$	$+$	$2^{9}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+5q^{5}+(4-\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots$
1160.4.a.j	$1160$	$4$	1160.a	1.a	$1$	$13$	$13$	$68.442$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	1160.4.a.j	$1$	$0$	$0$	$-6$	$65$	$2$	$+$	$2^{15}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+5q^{5}+(1-\beta _{1}-\beta _{3})q^{7}+\cdots$
1160.4.g.a	$1160$	$4$	1160.g	29.b	$2$	$44$	$44$	$68.442$		$_{}$	None	None		✓			1160.4.g.a	$2$	$0$	$0$	$0$	$220$	$42$			$\mathrm{SU}(2)[C_{2}]$
1160.4.g.b	$1160$	$4$	1160.g	29.b	$2$	$46$	$46$	$68.442$		$_{}$	None	None		✓	✓		1160.4.g.b	$2$	$0$	$0$	$0$	$-230$	$-42$			$\mathrm{SU}(2)[C_{2}]$

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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.