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	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 (22 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	5	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
3840.2.a.a	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	None	✓				960.2.k.a	$1$	$1$	$0$	$-1$	$-1$	$-4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-4q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots$
3840.2.a.c	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	None	✓				1920.2.k.b	$1$	$1$	$0$	$-1$	$-1$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots$
3840.2.a.d	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	None	✓				120.2.k.a	$1$	$1$	$0$	$-1$	$-1$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{7}+q^{9}+4q^{11}+q^{15}+\cdots$
3840.2.a.f	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	None	✓				1920.2.k.c	$1$	$1$	$0$	$-1$	$-1$	$2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots$
3840.2.a.h	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	None	✓				1920.2.k.c	$1$	$1$	$0$	$-1$	$1$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots$
3840.2.a.j	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	None	✓				960.2.k.b	$1$	$1$	$0$	$-1$	$1$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}-6q^{13}-q^{15}+2q^{19}+\cdots$
3840.2.a.l	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	None	✓				1920.2.k.b	$1$	$1$	$0$	$-1$	$1$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots$
3840.2.a.m	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	None	✓				120.2.k.a	$1$	$1$	$0$	$-1$	$1$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+2q^{7}+q^{9}+4q^{11}-q^{15}+\cdots$
3840.2.a.o	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	None	✓				1920.2.k.d	$1$	$1$	$0$	$1$	$-1$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{7}+q^{9}-6q^{11}+6q^{13}+\cdots$
3840.2.a.r	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	None	✓				120.2.k.a	$1$	$1$	$0$	$1$	$-1$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+2q^{7}+q^{9}-4q^{11}-q^{15}+\cdots$
3840.2.a.s	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	None	✓				1920.2.k.a	$1$	$1$	$0$	$1$	$-1$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+2q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots$
3840.2.a.u	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	None	✓				960.2.k.a	$1$	$1$	$0$	$1$	$-1$	$4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+4q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots$
3840.2.a.w	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	None	✓				120.2.k.a	$1$	$1$	$0$	$1$	$1$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{7}+q^{9}-4q^{11}+q^{15}+\cdots$
3840.2.a.x	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	None	✓				1920.2.k.a	$1$	$1$	$0$	$1$	$1$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots$
3840.2.a.z	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	None	✓				960.2.k.b	$1$	$1$	$0$	$1$	$1$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+q^{9}-6q^{13}+q^{15}-2q^{19}+\cdots$
3840.2.a.ba	$3840$	$2$	3840.a	1.a	$1$	$1$	$1$	$30.663$	$\Q$	None	✓				1920.2.k.d	$1$	$1$	$0$	$1$	$1$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+2q^{7}+q^{9}-6q^{11}-6q^{13}+\cdots$
3840.2.a.bc	$3840$	$2$	3840.a	1.a	$1$	$2$	$2$	$30.663$	$\Q(\sqrt{2}) $	None	✓				1920.2.k.i	$1$	$1$	$0$	$-2$	$-2$	$-4$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+(-2+\beta )q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots$
3840.2.a.be	$3840$	$2$	3840.a	1.a	$1$	$2$	$2$	$30.663$	$\Q(\sqrt{3}) $	None	✓				960.2.k.e	$1$	$1$	$0$	$-2$	$-2$	$4$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+2q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots$
3840.2.a.bg	$3840$	$2$	3840.a	1.a	$1$	$2$	$2$	$30.663$	$\Q(\sqrt{2}) $	None	✓		✓		1920.2.k.j	$1$	$1$	$0$	$-2$	$2$	$-4$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots$
3840.2.a.bi	$3840$	$2$	3840.a	1.a	$1$	$2$	$2$	$30.663$	$\Q(\sqrt{3}) $	None	✓				960.2.k.e	$1$	$1$	$0$	$2$	$-2$	$-4$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{7}+q^{9}+(2-\beta )q^{11}+\cdots$
3840.2.a.bj	$3840$	$2$	3840.a	1.a	$1$	$2$	$2$	$30.663$	$\Q(\sqrt{2}) $	None	✓				1920.2.k.j	$1$	$1$	$0$	$2$	$-2$	$-4$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{7}+q^{9}+(2+\beta )q^{11}+\cdots$
3840.2.a.bl	$3840$	$2$	3840.a	1.a	$1$	$2$	$2$	$30.663$	$\Q(\sqrt{2}) $	None	✓		✓		1920.2.k.i	$1$	$1$	$0$	$2$	$2$	$-4$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+(-2+\beta )q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots$

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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.