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 51 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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
6552.2.a.a	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	$\Q$	None	✓				2184.2.a.h	$1$	$2$	$0$	$0$	$-4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}+q^{7}-6q^{11}-q^{13}-6q^{17}+\cdots$
6552.2.a.b	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	$\Q$	None	✓	✓			6552.2.a.b	$1$	$1$	$0$	$0$	$-4$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}+q^{7}+4q^{11}+q^{13}-6q^{17}+\cdots$
6552.2.a.c	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	$\Q$	None	✓				728.2.a.d	$1$	$0$	$0$	$0$	$-3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+q^{7}-q^{13}+2q^{17}+5q^{19}+\cdots$
6552.2.a.d	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	$\Q$	None	✓	✓			6552.2.a.d	$1$	$1$	$0$	$0$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}+q^{7}+3q^{11}-q^{13}-q^{17}+\cdots$
6552.2.a.e	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	$\Q$	None	✓				2184.2.a.f	$1$	$1$	$0$	$0$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{7}+q^{13}+6q^{17}-4q^{19}+\cdots$
6552.2.a.f	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	$\Q$	None	✓				2184.2.a.m	$1$	$1$	$0$	$0$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}-4q^{11}-q^{13}-6q^{17}+\cdots$
6552.2.a.g	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	$\Q$	None	✓	✓			6552.2.a.g	$1$	$0$	$0$	$0$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}+2q^{11}-q^{13}+6q^{17}+\cdots$
6552.2.a.h	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	$\Q$	None	✓				2184.2.a.g	$1$	$0$	$0$	$0$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{7}+4q^{11}-q^{13}-2q^{17}+\cdots$
6552.2.a.i	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	$\Q$	None	✓	✓			6552.2.a.i	$1$	$1$	$0$	$0$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-q^{7}-q^{11}+q^{13}+3q^{17}+\cdots$
6552.2.a.j	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	$\Q$	None	✓				2184.2.a.e	$1$	$0$	$0$	$0$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{7}-5q^{11}+q^{13}-3q^{17}+\cdots$
6552.2.a.k	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	$\Q$	None	✓				2184.2.a.d	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-2q^{11}-q^{13}+2q^{17}-5q^{25}+\cdots$
6552.2.a.l	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	$\Q$	None	✓				2184.2.a.k	$1$	$0$	$0$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+2q^{11}-q^{13}+2q^{17}+8q^{23}+\cdots$
6552.2.a.m	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	$\Q$	None	✓				728.2.a.b	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-3q^{11}-q^{13}-4q^{17}+2q^{19}+\cdots$
6552.2.a.n	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	$\Q$	None	✓	✓			6552.2.a.n	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-q^{13}-2q^{17}-4q^{19}-2q^{23}+\cdots$
6552.2.a.o	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	$\Q$	None	✓	✓			6552.2.a.n	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-q^{13}+2q^{17}-4q^{19}+2q^{23}+\cdots$
6552.2.a.p	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	$\Q$	None	✓				2184.2.a.l	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}+2q^{11}-q^{13}+6q^{17}-8q^{19}+\cdots$
6552.2.a.q	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	$\Q$	None	✓				728.2.a.c	$1$	$1$	$0$	$0$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{7}-2q^{11}+q^{13}-7q^{19}+\cdots$
6552.2.a.r	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	$\Q$	None	✓	✓			6552.2.a.i	$1$	$0$	$0$	$0$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{7}+q^{11}+q^{13}-3q^{17}+\cdots$
6552.2.a.s	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	$\Q$	None	✓				728.2.a.a	$1$	$1$	$0$	$0$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+q^{7}-4q^{11}-q^{13}+6q^{17}+\cdots$
6552.2.a.t	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	$\Q$	None	✓	✓			6552.2.a.g	$1$	$1$	$0$	$0$	$2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}-2q^{11}-q^{13}-6q^{17}+\cdots$
6552.2.a.u	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	$\Q$	None	✓				2184.2.a.j	$1$	$0$	$0$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}+4q^{11}+q^{13}-2q^{17}+\cdots$
6552.2.a.v	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	$\Q$	None	✓				2184.2.a.c	$1$	$0$	$0$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+q^{7}+4q^{11}+q^{13}+6q^{17}+\cdots$
6552.2.a.w	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	$\Q$	None	✓				2184.2.a.b	$1$	$0$	$0$	$0$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+q^{7}-6q^{11}-q^{13}+8q^{17}+\cdots$
6552.2.a.x	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	$\Q$	None	✓	✓			6552.2.a.d	$1$	$0$	$0$	$0$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+q^{7}-3q^{11}-q^{13}+q^{17}+\cdots$
6552.2.a.y	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	$\Q$	None	✓				2184.2.a.i	$1$	$0$	$0$	$0$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+q^{7}+2q^{11}-q^{13}+7q^{19}+\cdots$
6552.2.a.z	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	$\Q$	None	✓				2184.2.a.a	$1$	$0$	$0$	$0$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+q^{7}+5q^{11}-q^{13}-3q^{17}+\cdots$
6552.2.a.ba	$6552$	$2$	6552.a	1.a	$1$	$1$	$1$	$52.318$	$\Q$	None	✓	✓			6552.2.a.b	$1$	$0$	$0$	$0$	$4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}+q^{7}-4q^{11}+q^{13}+6q^{17}+\cdots$
6552.2.a.bb	$6552$	$2$	6552.a	1.a	$1$	$2$	$2$	$52.318$	$\Q(\sqrt{33}) $	None	✓	✓			6552.2.a.bb	$1$	$1$	$0$	$0$	$-3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}-q^{7}+(-3+\beta )q^{11}+\cdots$
6552.2.a.bc	$6552$	$2$	6552.a	1.a	$1$	$2$	$2$	$52.318$	$\Q(\sqrt{5}) $	None	✓	✓	✓		6552.2.a.bc	$1$	$1$	$0$	$0$	$-2$	$-2$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}-q^{7}+(-1-\beta )q^{11}+\cdots$
6552.2.a.bd	$6552$	$2$	6552.a	1.a	$1$	$2$	$2$	$52.318$	$\Q(\sqrt{33}) $	None	✓				2184.2.a.r	$1$	$1$	$0$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{5}-q^{7}+(2-\beta )q^{11}-q^{13}+(-2+\cdots)q^{17}+\cdots$
6552.2.a.be	$6552$	$2$	6552.a	1.a	$1$	$2$	$2$	$52.318$	$\Q(\sqrt{17}) $	None	✓				2184.2.a.p	$1$	$1$	$0$	$0$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{5}+q^{7}+2q^{11}-q^{13}+(-2+\cdots)q^{17}+\cdots$
6552.2.a.bf	$6552$	$2$	6552.a	1.a	$1$	$2$	$2$	$52.318$	$\Q(\sqrt{3}) $	None	✓				728.2.a.f	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}-q^{7}+(1-\beta )q^{11}-q^{13}+(-1+\cdots)q^{17}+\cdots$
6552.2.a.bg	$6552$	$2$	6552.a	1.a	$1$	$2$	$2$	$52.318$	$\Q(\sqrt{17}) $	None	✓				728.2.a.g	$1$	$0$	$0$	$0$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}-q^{7}+(-3+\beta )q^{11}+q^{13}+\cdots$
6552.2.a.bh	$6552$	$2$	6552.a	1.a	$1$	$2$	$2$	$52.318$	$\Q(\sqrt{17}) $	None	✓				2184.2.a.o	$1$	$0$	$0$	$0$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}-q^{7}+(-2+\beta )q^{11}-q^{13}+\cdots$
6552.2.a.bi	$6552$	$2$	6552.a	1.a	$1$	$2$	$2$	$52.318$	$\Q(\sqrt{5}) $	None	✓	✓	✓		6552.2.a.bc	$1$	$0$	$0$	$0$	$2$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}-q^{7}+(1+\beta )q^{11}+q^{13}+\cdots$
6552.2.a.bj	$6552$	$2$	6552.a	1.a	$1$	$2$	$2$	$52.318$	$\Q(\sqrt{2}) $	None	✓				728.2.a.e	$1$	$1$	$0$	$0$	$2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}+q^{7}+(2-3\beta )q^{11}+q^{13}+\cdots$
6552.2.a.bk	$6552$	$2$	6552.a	1.a	$1$	$2$	$2$	$52.318$	$\Q(\sqrt{17}) $	None	✓				2184.2.a.n	$1$	$1$	$0$	$0$	$3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}-q^{7}+(2-2\beta )q^{11}+q^{13}+\cdots$
6552.2.a.bl	$6552$	$2$	6552.a	1.a	$1$	$2$	$2$	$52.318$	$\Q(\sqrt{17}) $	None	✓				2184.2.a.q	$1$	$0$	$0$	$0$	$3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}-q^{7}+(2-2\beta )q^{11}+q^{13}+\cdots$
6552.2.a.bm	$6552$	$2$	6552.a	1.a	$1$	$2$	$2$	$52.318$	$\Q(\sqrt{33}) $	None	✓	✓			6552.2.a.bb	$1$	$0$	$0$	$0$	$3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}-q^{7}+(3-\beta )q^{11}-q^{13}+\cdots$
6552.2.a.bn	$6552$	$2$	6552.a	1.a	$1$	$3$	$3$	$52.318$	3.3.316.1	None	✓		✓		2184.2.a.u	$1$	$1$	$0$	$0$	$-3$	$3$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{5}+q^{7}+(-1-\beta _{1})q^{11}+\cdots$
6552.2.a.bo	$6552$	$2$	6552.a	1.a	$1$	$3$	$3$	$52.318$	3.3.961.1	None	✓		✓		2184.2.a.t	$1$	$1$	$0$	$0$	$-2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{5}-q^{7}+(-3+\beta _{1}-\beta _{2})q^{11}+\cdots$
6552.2.a.bp	$6552$	$2$	6552.a	1.a	$1$	$3$	$3$	$52.318$	3.3.2089.1	None	✓		✓		2184.2.a.s	$1$	$1$	$0$	$0$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}+q^{7}+(-\beta _{1}-\beta _{2})q^{11}-q^{13}+\cdots$
6552.2.a.bq	$6552$	$2$	6552.a	1.a	$1$	$4$	$4$	$52.318$	4.4.19664.1	None	✓	✓	✓		6552.2.a.bq	$1$	$0$	$0$	$0$	$-4$	$-4$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{3})q^{5}-q^{7}+(-1-\beta _{1})q^{11}+\cdots$
6552.2.a.br	$6552$	$2$	6552.a	1.a	$1$	$4$	$4$	$52.318$	4.4.64268.1	None	✓		✓		728.2.a.i	$1$	$0$	$0$	$0$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{5}-q^{7}+(\beta _{1}+2\beta _{3})q^{11}+\cdots$
6552.2.a.bs	$6552$	$2$	6552.a	1.a	$1$	$4$	$4$	$52.318$	4.4.138892.1	None	✓		✓		2184.2.a.v	$1$	$0$	$0$	$0$	$-2$	$-4$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{5}-q^{7}+(1-\beta _{2})q^{11}+\cdots$
6552.2.a.bt	$6552$	$2$	6552.a	1.a	$1$	$4$	$4$	$52.318$	4.4.183064.1	None	✓		✓		728.2.a.h	$1$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{5}+q^{7}-\beta _{1}q^{11}+q^{13}+(-1+\cdots)q^{17}+\cdots$
6552.2.a.bu	$6552$	$2$	6552.a	1.a	$1$	$4$	$4$	$52.318$	4.4.19664.1	None	✓	✓	✓		6552.2.a.bq	$1$	$1$	$0$	$0$	$4$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{3})q^{5}-q^{7}+(1+\beta _{1})q^{11}-q^{13}+\cdots$
6552.2.a.bv	$6552$	$2$	6552.a	1.a	$1$	$5$	$5$	$52.318$	5.5.9654428.1	None	✓	✓	✓		6552.2.a.bv	$1$	$1$	$0$	$0$	$-1$	$5$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{5}+q^{7}+(-2-\beta _{3})q^{11}+q^{13}+\cdots$
6552.2.a.bw	$6552$	$2$	6552.a	1.a	$1$	$5$	$5$	$52.318$	5.5.9654428.1	None	✓	✓	✓		6552.2.a.bv	$1$	$0$	$0$	$0$	$1$	$5$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}+q^{7}+(2+\beta _{3})q^{11}+q^{13}+\cdots$
6552.2.v.a	$6552$	$2$	6552.v	21.c	$2$	$48$	$48$	$52.318$		None		✓			6552.2.v.a	$2$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{2}]$

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Elliptic 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.