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 (1-50 of 63 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	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4410.2.a.a	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				630.2.a.e	$1$	$0$	$-1$	$0$	$-1$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-4q^{11}+\cdots$
4410.2.a.b	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				70.2.a.a	$1$	$1$	$-1$	$0$	$-1$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-4q^{11}+\cdots$
4410.2.a.c	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				70.2.e.b	$1$	$1$	$-1$	$0$	$-1$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-3q^{11}+\cdots$
4410.2.a.d	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓	✓			4410.2.a.d	$1$	$0$	$-1$	$0$	$-1$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-2q^{11}+\cdots$
4410.2.a.e	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				1470.2.a.n	$1$	$1$	$-1$	$0$	$-1$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-2q^{11}+\cdots$
4410.2.a.f	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				210.2.a.d	$1$	$1$	$-1$	$0$	$-1$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-2q^{13}+\cdots$
4410.2.a.g	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				210.2.i.a	$1$	$0$	$-1$	$0$	$-1$	$0$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+q^{11}+\cdots$
4410.2.a.h	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				70.2.e.a	$1$	$1$	$-1$	$0$	$-1$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+2q^{11}+\cdots$
4410.2.a.i	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				490.2.a.f	$1$	$1$	$-1$	$0$	$-1$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+4q^{11}+\cdots$
4410.2.a.j	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				210.2.i.b	$1$	$0$	$-1$	$0$	$-1$	$0$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+5q^{11}+\cdots$
4410.2.a.k	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				90.2.a.a	$1$	$0$	$-1$	$0$	$-1$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+6q^{11}+\cdots$
4410.2.a.l	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				210.2.a.c	$1$	$0$	$-1$	$0$	$1$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-4q^{11}+\cdots$
4410.2.a.m	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				70.2.e.b	$1$	$1$	$-1$	$0$	$1$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-3q^{11}+\cdots$
4410.2.a.n	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				1470.2.a.n	$1$	$0$	$-1$	$0$	$1$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-2q^{11}+\cdots$
4410.2.a.o	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓	✓			4410.2.a.d	$1$	$1$	$-1$	$0$	$1$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-2q^{11}+\cdots$
4410.2.a.p	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				630.2.a.c	$1$	$1$	$-1$	$0$	$1$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-2q^{13}+\cdots$
4410.2.a.q	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				210.2.i.a	$1$	$0$	$-1$	$0$	$1$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+q^{11}+\cdots$
4410.2.a.r	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				70.2.e.a	$1$	$1$	$-1$	$0$	$1$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+2q^{11}+\cdots$
4410.2.a.s	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				490.2.a.f	$1$	$0$	$-1$	$0$	$1$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+4q^{11}+\cdots$
4410.2.a.t	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				210.2.a.e	$1$	$0$	$-1$	$0$	$1$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+4q^{11}+\cdots$
4410.2.a.u	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				210.2.i.b	$1$	$0$	$-1$	$0$	$1$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+5q^{11}+\cdots$
4410.2.a.v	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				1470.2.a.c	$1$	$0$	$1$	$0$	$-1$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-6q^{11}+\cdots$
4410.2.a.w	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				210.2.i.c	$1$	$0$	$1$	$0$	$-1$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-3q^{11}+\cdots$
4410.2.a.x	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				70.2.e.d	$1$	$1$	$1$	$0$	$-1$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-3q^{11}+\cdots$
4410.2.a.y	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				630.2.a.c	$1$	$1$	$1$	$0$	$-1$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-2q^{13}+\cdots$
4410.2.a.z	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				30.2.a.a	$1$	$0$	$1$	$0$	$-1$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-2q^{13}+\cdots$
4410.2.a.ba	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				210.2.i.d	$1$	$0$	$1$	$0$	$-1$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+q^{11}+\cdots$
4410.2.a.bb	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓	✓			4410.2.a.d	$1$	$1$	$1$	$0$	$-1$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+2q^{11}+\cdots$
4410.2.a.bc	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				210.2.a.a	$1$	$0$	$1$	$0$	$-1$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+4q^{11}+\cdots$
4410.2.a.bd	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				70.2.e.c	$1$	$0$	$1$	$0$	$-1$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+6q^{11}+\cdots$
4410.2.a.be	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				1470.2.a.c	$1$	$1$	$1$	$0$	$1$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-6q^{11}+\cdots$
4410.2.a.bf	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				90.2.a.a	$1$	$0$	$1$	$0$	$1$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-6q^{11}+\cdots$
4410.2.a.bg	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				70.2.e.d	$1$	$1$	$1$	$0$	$1$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-3q^{11}+\cdots$
4410.2.a.bh	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				210.2.i.c	$1$	$0$	$1$	$0$	$1$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-3q^{11}+\cdots$
4410.2.a.bi	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				210.2.a.b	$1$	$1$	$1$	$0$	$1$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-2q^{13}+\cdots$
4410.2.a.bj	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				210.2.i.d	$1$	$0$	$1$	$0$	$1$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+q^{11}+\cdots$
4410.2.a.bk	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓	✓			4410.2.a.d	$1$	$0$	$1$	$0$	$1$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+2q^{11}+\cdots$
4410.2.a.bl	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				630.2.a.e	$1$	$0$	$1$	$0$	$1$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+4q^{11}+\cdots$
4410.2.a.bm	$4410$	$2$	4410.a	1.a	$1$	$1$	$1$	$35.214$	$\Q$	None	✓				70.2.e.c	$1$	$0$	$1$	$0$	$1$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+6q^{11}+\cdots$
4410.2.a.bn	$4410$	$2$	4410.a	1.a	$1$	$2$	$2$	$35.214$	$\Q(\sqrt{2}) $	None	✓		✓		1470.2.a.u	$1$	$0$	$-2$	$0$	$-2$	$0$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+(-2+\cdots)q^{11}+\cdots$
4410.2.a.bo	$4410$	$2$	4410.a	1.a	$1$	$2$	$2$	$35.214$	$\Q(\sqrt{7}) $	None	✓		✓		630.2.k.i	$1$	$0$	$-2$	$0$	$-2$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+(-2+\cdots)q^{11}+\cdots$
4410.2.a.bp	$4410$	$2$	4410.a	1.a	$1$	$2$	$2$	$35.214$	$\Q(\sqrt{2}) $	None	✓	✓	✓	✓	4410.2.a.bp	$1$	$1$	$-2$	$0$	$-2$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+(2+\beta )q^{11}+\cdots$
4410.2.a.bq	$4410$	$2$	4410.a	1.a	$1$	$2$	$2$	$35.214$	$\Q(\sqrt{7}) $	None	✓				630.2.k.i	$1$	$0$	$-2$	$0$	$2$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+(-2+\cdots)q^{11}+\cdots$
4410.2.a.br	$4410$	$2$	4410.a	1.a	$1$	$2$	$2$	$35.214$	$\Q(\sqrt{2}) $	None	✓		✓		1470.2.a.u	$1$	$1$	$-2$	$0$	$2$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+(-2+\cdots)q^{11}+\cdots$
4410.2.a.bs	$4410$	$2$	4410.a	1.a	$1$	$2$	$2$	$35.214$	$\Q(\sqrt{2}) $	None	✓	✓			4410.2.a.bp	$1$	$0$	$-2$	$0$	$2$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+(2+\beta )q^{11}+\cdots$
4410.2.a.bt	$4410$	$2$	4410.a	1.a	$1$	$2$	$2$	$35.214$	$\Q(\sqrt{2}) $	None	✓				490.2.a.l	$1$	$1$	$2$	$0$	$-2$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+(-2+\cdots)q^{11}+\cdots$
4410.2.a.bu	$4410$	$2$	4410.a	1.a	$1$	$2$	$2$	$35.214$	$\Q(\sqrt{2}) $	None	✓	✓			4410.2.a.bp	$1$	$0$	$2$	$0$	$-2$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+(-2+\cdots)q^{11}+\cdots$
4410.2.a.bv	$4410$	$2$	4410.a	1.a	$1$	$2$	$2$	$35.214$	$\Q(\sqrt{7}) $	None	✓				630.2.k.i	$1$	$0$	$2$	$0$	$-2$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+(2+\beta )q^{11}+\cdots$
4410.2.a.bw	$4410$	$2$	4410.a	1.a	$1$	$2$	$2$	$35.214$	$\Q(\sqrt{2}) $	None	✓				1470.2.a.s	$1$	$1$	$2$	$0$	$-2$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+(2+3\beta )q^{11}+\cdots$
4410.2.a.bx	$4410$	$2$	4410.a	1.a	$1$	$2$	$2$	$35.214$	$\Q(\sqrt{2}) $	None	✓	✓	✓	✓	4410.2.a.bp	$1$	$1$	$2$	$0$	$2$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+(-2+\cdots)q^{11}+\cdots$

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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.