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 (32 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	37	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
5550.2.a.b	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓				1110.2.a.o	$1$	$1$	$-1$	$-1$	$0$	$-4$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-4q^{7}-q^{8}+\cdots$
5550.2.a.c	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓				1110.2.d.a	$1$	$1$	$-1$	$-1$	$0$	$-2$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots$
5550.2.a.d	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓				1110.2.d.c	$1$	$1$	$-1$	$-1$	$0$	$-1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots$
5550.2.a.e	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓	✓			5550.2.a.e	$1$	$1$	$-1$	$-1$	$0$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
5550.2.a.g	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓				1110.2.a.n	$1$	$1$	$-1$	$-1$	$0$	$1$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots$
5550.2.a.h	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓				222.2.a.e	$1$	$1$	$-1$	$-1$	$0$	$1$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots$
5550.2.a.i	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓	✓			5550.2.a.i	$1$	$1$	$-1$	$-1$	$0$	$2$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots$
5550.2.a.n	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓				222.2.a.d	$1$	$1$	$-1$	$1$	$0$	$-3$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-3q^{7}-q^{8}+\cdots$
5550.2.a.o	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓	✓			5550.2.a.o	$1$	$1$	$-1$	$1$	$0$	$-2$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-2q^{7}-q^{8}+\cdots$
5550.2.a.q	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓				1110.2.a.i	$1$	$1$	$-1$	$1$	$0$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
5550.2.a.t	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓				1110.2.a.j	$1$	$1$	$-1$	$1$	$0$	$3$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+3q^{7}-q^{8}+\cdots$
5550.2.a.u	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓	✓			5550.2.a.u	$1$	$1$	$-1$	$1$	$0$	$4$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+4q^{7}-q^{8}+\cdots$
5550.2.a.v	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓	✓			5550.2.a.u	$1$	$1$	$1$	$-1$	$0$	$-4$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots$
5550.2.a.w	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓				1110.2.a.g	$1$	$1$	$1$	$-1$	$0$	$-4$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots$
5550.2.a.y	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓				1110.2.a.f	$1$	$1$	$1$	$-1$	$0$	$-1$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots$
5550.2.a.z	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓				222.2.a.c	$1$	$1$	$1$	$-1$	$0$	$1$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots$
5550.2.a.bb	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓	✓			5550.2.a.o	$1$	$1$	$1$	$-1$	$0$	$2$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+2q^{7}+q^{8}+\cdots$
5550.2.a.bc	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓				1110.2.d.d	$1$	$1$	$1$	$-1$	$0$	$2$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+2q^{7}+q^{8}+\cdots$
5550.2.a.be	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓				1110.2.d.b	$1$	$1$	$1$	$1$	$0$	$-5$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-5q^{7}+q^{8}+\cdots$
5550.2.a.bf	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓				1110.2.a.d	$1$	$1$	$1$	$1$	$0$	$-3$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-3q^{7}+q^{8}+\cdots$
5550.2.a.bh	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓				222.2.a.a	$1$	$1$	$1$	$1$	$0$	$-3$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-3q^{7}+q^{8}+\cdots$
5550.2.a.bi	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓				1110.2.d.e	$1$	$1$	$1$	$1$	$0$	$-2$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots$
5550.2.a.bj	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓	✓			5550.2.a.i	$1$	$1$	$1$	$1$	$0$	$-2$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots$
5550.2.a.bl	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓				222.2.a.b	$1$	$1$	$1$	$1$	$0$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
5550.2.a.bm	$5550$	$2$	5550.a	1.a	$1$	$1$	$1$	$44.317$	$\Q$	None	✓	✓			5550.2.a.e	$1$	$1$	$1$	$1$	$0$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
5550.2.a.bt	$5550$	$2$	5550.a	1.a	$1$	$2$	$2$	$44.317$	$\Q(\sqrt{6}) $	None	✓		✓		1110.2.d.h	$1$	$1$	$-2$	$-2$	$0$	$-2$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+(-1+\beta )q^{7}+\cdots$
5550.2.a.bu	$5550$	$2$	5550.a	1.a	$1$	$2$	$2$	$44.317$	$\Q(\sqrt{5}) $	None	✓				1110.2.d.f	$1$	$1$	$-2$	$2$	$0$	$-4$	$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-2q^{7}-q^{8}+\cdots$
5550.2.a.bv	$5550$	$2$	5550.a	1.a	$1$	$2$	$2$	$44.317$	$\Q(\sqrt{33}) $	None	✓	✓	✓		5550.2.a.bv	$1$	$1$	$-2$	$2$	$0$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
5550.2.a.by	$5550$	$2$	5550.a	1.a	$1$	$2$	$2$	$44.317$	$\Q(\sqrt{33}) $	None	✓	✓			5550.2.a.bv	$1$	$1$	$2$	$-2$	$0$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
5550.2.a.cb	$5550$	$2$	5550.a	1.a	$1$	$2$	$2$	$44.317$	$\Q(\sqrt{2}) $	None	✓		✓		1110.2.d.g	$1$	$1$	$2$	$2$	$0$	$2$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+(1+\beta )q^{7}+\cdots$
5550.2.a.cf	$5550$	$2$	5550.a	1.a	$1$	$3$	$3$	$44.317$	3.3.568.1	None	✓		✓		1110.2.d.i	$1$	$1$	$-3$	$3$	$0$	$3$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+(1+\beta _{1}+\beta _{2})q^{7}+\cdots$
5550.2.a.cm	$5550$	$2$	5550.a	1.a	$1$	$4$	$4$	$44.317$	4.4.30056.1	None	✓		✓		1110.2.d.j	$1$	$1$	$4$	$-4$	$0$	$-3$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$

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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.