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 86 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	5	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4400.2.a.a	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				88.2.a.a	$1$	$0$	$0$	$-3$	$0$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-2q^{7}+6q^{9}+q^{11}+6q^{17}+\cdots$
4400.2.a.b	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				110.2.b.c	$1$	$0$	$0$	$-3$	$0$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{7}+6q^{9}+q^{11}+5q^{17}+\cdots$
4400.2.a.c	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				440.2.b.b	$1$	$2$	$0$	$-2$	$0$	$-4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-4q^{7}+q^{9}-q^{11}-6q^{13}+\cdots$
4400.2.a.d	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				550.2.a.a	$1$	$1$	$0$	$-2$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-4q^{7}+q^{9}+q^{11}-5q^{13}+\cdots$
4400.2.a.e	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				220.2.a.a	$1$	$1$	$0$	$-2$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-4q^{7}+q^{9}+q^{11}+4q^{13}+\cdots$
4400.2.a.f	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				110.2.b.b	$1$	$1$	$0$	$-2$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{9}-q^{11}-2q^{13}+6q^{17}+\cdots$
4400.2.a.g	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				550.2.a.b	$1$	$1$	$0$	$-2$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{9}-q^{11}+3q^{13}-4q^{17}+\cdots$
4400.2.a.h	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				440.2.b.a	$1$	$1$	$0$	$-2$	$0$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{7}+q^{9}+q^{11}+4q^{17}+\cdots$
4400.2.a.i	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				11.2.a.a	$1$	$0$	$0$	$-1$	$0$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}-2q^{9}-q^{11}-4q^{13}+\cdots$
4400.2.a.j	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				440.2.b.c	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}-2q^{9}+q^{11}-q^{17}-q^{19}+\cdots$
4400.2.a.k	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				110.2.b.a	$1$	$1$	$0$	$-1$	$0$	$3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{7}-2q^{9}-q^{11}-4q^{13}+\cdots$
4400.2.a.l	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				110.2.a.b	$1$	$0$	$0$	$-1$	$0$	$3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{7}-2q^{9}-q^{11}+6q^{13}+\cdots$
4400.2.a.m	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				440.2.a.b	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-3q^{9}-q^{11}+4q^{13}+4q^{17}+\cdots$
4400.2.a.n	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				220.2.b.a	$1$	$0$	$0$	$0$	$0$	$-2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-3q^{9}+q^{11}-6q^{13}-2q^{17}+\cdots$
4400.2.a.o	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				440.2.a.a	$1$	$0$	$0$	$0$	$0$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-3q^{9}+q^{11}+8q^{19}-8q^{23}+\cdots$
4400.2.a.p	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				55.2.a.a	$1$	$1$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{9}+q^{11}-2q^{13}-6q^{17}+4q^{19}+\cdots$
4400.2.a.q	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				220.2.b.a	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-3q^{9}+q^{11}+6q^{13}+2q^{17}+\cdots$
4400.2.a.r	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				440.2.a.c	$1$	$0$	$0$	$0$	$0$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{7}-3q^{9}+q^{11}-6q^{13}+6q^{17}+\cdots$
4400.2.a.s	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				110.2.b.a	$1$	$1$	$0$	$1$	$0$	$-3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{7}-2q^{9}-q^{11}+4q^{13}+\cdots$
4400.2.a.t	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				110.2.a.c	$1$	$1$	$0$	$1$	$0$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}-2q^{9}+q^{11}-2q^{13}+\cdots$
4400.2.a.u	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				440.2.b.c	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}-2q^{9}+q^{11}+q^{17}-q^{19}+\cdots$
4400.2.a.v	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				44.2.a.a	$1$	$1$	$0$	$1$	$0$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{7}-2q^{9}+q^{11}+4q^{13}+\cdots$
4400.2.a.w	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				110.2.a.a	$1$	$0$	$0$	$1$	$0$	$5$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+5q^{7}-2q^{9}-q^{11}-2q^{13}+\cdots$
4400.2.a.x	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				440.2.b.a	$1$	$1$	$0$	$2$	$0$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{7}+q^{9}+q^{11}-4q^{17}+\cdots$
4400.2.a.y	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				550.2.a.b	$1$	$0$	$0$	$2$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{9}-q^{11}-3q^{13}+4q^{17}+\cdots$
4400.2.a.z	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				220.2.a.b	$1$	$0$	$0$	$2$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{9}-q^{11}+4q^{17}+4q^{19}+\cdots$
4400.2.a.ba	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				110.2.b.b	$1$	$1$	$0$	$2$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{9}-q^{11}+2q^{13}-6q^{17}+\cdots$
4400.2.a.bb	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				440.2.b.b	$1$	$0$	$0$	$2$	$0$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+4q^{7}+q^{9}-q^{11}+6q^{13}+\cdots$
4400.2.a.bc	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				550.2.a.a	$1$	$0$	$0$	$2$	$0$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+4q^{7}+q^{9}+q^{11}+5q^{13}+\cdots$
4400.2.a.bd	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				110.2.b.c	$1$	$0$	$0$	$3$	$0$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+q^{7}+6q^{9}+q^{11}-5q^{17}+\cdots$
4400.2.a.be	$4400$	$2$	4400.a	1.a	$1$	$1$	$1$	$35.134$	$\Q$	None	✓				440.2.a.d	$1$	$0$	$0$	$3$	$0$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+q^{7}+6q^{9}+q^{11}+6q^{13}+\cdots$
4400.2.a.bf	$4400$	$2$	4400.a	1.a	$1$	$2$	$2$	$35.134$	$\Q(\sqrt{13}) $	None	✓				1100.2.a.f	$1$	$1$	$0$	$-3$	$0$	$-5$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+(-2-\beta )q^{7}+(1+3\beta )q^{9}+\cdots$
4400.2.a.bg	$4400$	$2$	4400.a	1.a	$1$	$2$	$2$	$35.134$	$\Q(\sqrt{5}) $	None	✓				275.2.a.d	$1$	$0$	$0$	$-3$	$0$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+(-2+3\beta )q^{7}+(-1+\cdots)q^{9}+\cdots$
4400.2.a.bh	$4400$	$2$	4400.a	1.a	$1$	$2$	$2$	$35.134$	$\Q(\sqrt{13}) $	None	✓				275.2.a.e	$1$	$0$	$0$	$-1$	$0$	$-5$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-3+\beta )q^{7}+\beta q^{9}+q^{11}+\cdots$
4400.2.a.bi	$4400$	$2$	4400.a	1.a	$1$	$2$	$2$	$35.134$	$\Q(\sqrt{21}) $	None	✓				1100.2.a.g	$1$	$1$	$0$	$-1$	$0$	$-5$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-3+\beta )q^{7}+(2+\beta )q^{9}+q^{11}+\cdots$
4400.2.a.bj	$4400$	$2$	4400.a	1.a	$1$	$2$	$2$	$35.134$	$\Q(\sqrt{17}) $	None	✓				440.2.a.e	$1$	$1$	$0$	$-1$	$0$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}-\beta q^{7}+(1+\beta )q^{9}-q^{11}-2q^{13}+\cdots$
4400.2.a.bk	$4400$	$2$	4400.a	1.a	$1$	$2$	$2$	$35.134$	$\Q(\sqrt{5}) $	None	✓				2200.2.a.n	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(1-\beta )q^{7}+(-2+\beta )q^{9}+q^{11}+\cdots$
4400.2.a.bl	$4400$	$2$	4400.a	1.a	$1$	$2$	$2$	$35.134$	$\Q(\sqrt{33}) $	None	✓				110.2.a.d	$1$	$1$	$0$	$-1$	$0$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+\beta q^{7}+(5+\beta )q^{9}+q^{11}-2q^{13}+\cdots$
4400.2.a.bm	$4400$	$2$	4400.a	1.a	$1$	$2$	$2$	$35.134$	$\Q(\sqrt{5}) $	None	✓				2200.2.a.p	$1$	$0$	$0$	$-1$	$0$	$3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(1+\beta )q^{7}+(-2+\beta )q^{9}-q^{11}+\cdots$
4400.2.a.bn	$4400$	$2$	4400.a	1.a	$1$	$2$	$2$	$35.134$	$\Q(\sqrt{2}) $	None	✓				55.2.a.b	$1$	$0$	$0$	$0$	$0$	$-4$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{3}-2q^{7}+5q^{9}-q^{11}+(4+\beta )q^{13}+\cdots$
4400.2.a.bo	$4400$	$2$	4400.a	1.a	$1$	$2$	$2$	$35.134$	$\Q(\sqrt{5}) $	None	✓				2200.2.a.p	$1$	$1$	$0$	$1$	$0$	$-3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-1-\beta )q^{7}+(-2+\beta )q^{9}+\cdots$
4400.2.a.bp	$4400$	$2$	4400.a	1.a	$1$	$2$	$2$	$35.134$	$\Q(\sqrt{17}) $	None	✓				88.2.a.b	$1$	$0$	$0$	$1$	$0$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-2\beta q^{7}+(1+\beta )q^{9}+q^{11}+\cdots$
4400.2.a.bq	$4400$	$2$	4400.a	1.a	$1$	$2$	$2$	$35.134$	$\Q(\sqrt{5}) $	None	✓				2200.2.a.n	$1$	$0$	$0$	$1$	$0$	$-1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-1+\beta )q^{7}+(-2+\beta )q^{9}+\cdots$
4400.2.a.br	$4400$	$2$	4400.a	1.a	$1$	$2$	$2$	$35.134$	$\Q(\sqrt{17}) $	None	✓				440.2.a.f	$1$	$1$	$0$	$1$	$0$	$3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(2-\beta )q^{7}+(1+\beta )q^{9}-q^{11}+\cdots$
4400.2.a.bs	$4400$	$2$	4400.a	1.a	$1$	$2$	$2$	$35.134$	$\Q(\sqrt{13}) $	None	✓				275.2.a.e	$1$	$1$	$0$	$1$	$0$	$5$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(3-\beta )q^{7}+\beta q^{9}+q^{11}-5q^{13}+\cdots$
4400.2.a.bt	$4400$	$2$	4400.a	1.a	$1$	$2$	$2$	$35.134$	$\Q(\sqrt{17}) $	None	✓				440.2.a.g	$1$	$0$	$0$	$1$	$0$	$5$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(2+\beta )q^{7}+(1+\beta )q^{9}+q^{11}+\cdots$
4400.2.a.bu	$4400$	$2$	4400.a	1.a	$1$	$2$	$2$	$35.134$	$\Q(\sqrt{21}) $	None	✓				1100.2.a.g	$1$	$0$	$0$	$1$	$0$	$5$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(3-\beta )q^{7}+(2+\beta )q^{9}+q^{11}+\cdots$
4400.2.a.bv	$4400$	$2$	4400.a	1.a	$1$	$2$	$2$	$35.134$	$\Q(\sqrt{5}) $	None	✓				275.2.a.d	$1$	$1$	$0$	$3$	$0$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(2-3\beta )q^{7}+(-1+3\beta )q^{9}+\cdots$
4400.2.a.bw	$4400$	$2$	4400.a	1.a	$1$	$2$	$2$	$35.134$	$\Q(\sqrt{13}) $	None	✓				1100.2.a.f	$1$	$0$	$0$	$3$	$0$	$5$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(2+\beta )q^{7}+(1+3\beta )q^{9}+\cdots$
4400.2.a.bx	$4400$	$2$	4400.a	1.a	$1$	$3$	$3$	$35.134$	3.3.837.1	None	✓		✓		2200.2.a.t	$1$	$1$	$0$	$-3$	$0$	$-3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-1+\beta _{2})q^{7}+(2+\cdots)q^{9}+\cdots$

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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.