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 52 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	53	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
7632.2.a.a	$7632$	$2$	7632.a	1.a	$1$	$1$	$1$	$60.942$	$\Q$	None	✓				1272.2.a.b	$1$	$2$	$0$	$0$	$-4$	$-1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}-q^{7}-5q^{11}-2q^{17}-5q^{19}+\cdots$
7632.2.a.b	$7632$	$2$	7632.a	1.a	$1$	$1$	$1$	$60.942$	$\Q$	None	✓				318.2.a.b	$1$	$1$	$0$	$0$	$-4$	$-1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}-q^{7}-q^{11}-4q^{13}-6q^{17}+\cdots$
7632.2.a.c	$7632$	$2$	7632.a	1.a	$1$	$1$	$1$	$60.942$	$\Q$	None	✓				106.2.a.c	$1$	$2$	$0$	$0$	$-3$	$-2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{5}-2q^{7}-3q^{11}-4q^{13}-3q^{17}+\cdots$
7632.2.a.d	$7632$	$2$	7632.a	1.a	$1$	$1$	$1$	$60.942$	$\Q$	None	✓				954.2.a.b	$1$	$1$	$0$	$0$	$-2$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-4q^{7}-2q^{11}+2q^{13}+4q^{19}+\cdots$
7632.2.a.e	$7632$	$2$	7632.a	1.a	$1$	$1$	$1$	$60.942$	$\Q$	None	✓				212.2.a.b	$1$	$0$	$0$	$0$	$-2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-4q^{11}-2q^{13}-2q^{17}-2q^{19}+\cdots$
7632.2.a.f	$7632$	$2$	7632.a	1.a	$1$	$1$	$1$	$60.942$	$\Q$	None	✓				954.2.a.e	$1$	$1$	$0$	$0$	$-2$	$3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+3q^{7}-q^{11}-2q^{13}-2q^{17}+\cdots$
7632.2.a.g	$7632$	$2$	7632.a	1.a	$1$	$1$	$1$	$60.942$	$\Q$	None	✓				106.2.a.b	$1$	$1$	$0$	$0$	$-1$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}+5q^{11}-4q^{13}-3q^{17}+\cdots$
7632.2.a.h	$7632$	$2$	7632.a	1.a	$1$	$1$	$1$	$60.942$	$\Q$	None	✓				318.2.a.c	$1$	$2$	$0$	$0$	$0$	$-5$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-5q^{7}-3q^{11}-4q^{13}-6q^{17}-5q^{19}+\cdots$
7632.2.a.i	$7632$	$2$	7632.a	1.a	$1$	$1$	$1$	$60.942$	$\Q$	None	✓				318.2.a.e	$1$	$0$	$0$	$0$	$0$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{7}+5q^{11}-2q^{17}+q^{19}+3q^{23}+\cdots$
7632.2.a.j	$7632$	$2$	7632.a	1.a	$1$	$1$	$1$	$60.942$	$\Q$	None	✓				53.2.a.a	$1$	$0$	$0$	$0$	$0$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{7}-3q^{13}+3q^{17}+5q^{19}+7q^{23}+\cdots$
7632.2.a.k	$7632$	$2$	7632.a	1.a	$1$	$1$	$1$	$60.942$	$\Q$	None	✓				106.2.a.d	$1$	$0$	$0$	$0$	$0$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{7}+5q^{13}+3q^{17}+q^{19}+3q^{23}+\cdots$
7632.2.a.l	$7632$	$2$	7632.a	1.a	$1$	$1$	$1$	$60.942$	$\Q$	None	✓				318.2.a.a	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{11}-2q^{13}+7q^{17}-2q^{19}+\cdots$
7632.2.a.m	$7632$	$2$	7632.a	1.a	$1$	$1$	$1$	$60.942$	$\Q$	None	✓				954.2.a.b	$1$	$0$	$0$	$0$	$2$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{7}+2q^{11}+2q^{13}+4q^{19}+\cdots$
7632.2.a.n	$7632$	$2$	7632.a	1.a	$1$	$1$	$1$	$60.942$	$\Q$	None	✓				212.2.a.a	$1$	$1$	$0$	$0$	$2$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+2q^{7}+2q^{11}-7q^{13}+3q^{17}+\cdots$
7632.2.a.o	$7632$	$2$	7632.a	1.a	$1$	$1$	$1$	$60.942$	$\Q$	None	✓				954.2.a.e	$1$	$0$	$0$	$0$	$2$	$3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+3q^{7}+q^{11}-2q^{13}+2q^{17}+\cdots$
7632.2.a.p	$7632$	$2$	7632.a	1.a	$1$	$1$	$1$	$60.942$	$\Q$	None	✓				1272.2.a.a	$1$	$0$	$0$	$0$	$3$	$-4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-4q^{7}+3q^{11}-2q^{13}+7q^{17}+\cdots$
7632.2.a.q	$7632$	$2$	7632.a	1.a	$1$	$1$	$1$	$60.942$	$\Q$	None	✓				318.2.a.d	$1$	$1$	$0$	$0$	$3$	$4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+4q^{7}-5q^{11}-2q^{13}-5q^{17}+\cdots$
7632.2.a.r	$7632$	$2$	7632.a	1.a	$1$	$1$	$1$	$60.942$	$\Q$	None	✓				106.2.a.a	$1$	$0$	$0$	$0$	$4$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}-4q^{11}+q^{13}-5q^{17}+7q^{19}+\cdots$
7632.2.a.s	$7632$	$2$	7632.a	1.a	$1$	$2$	$2$	$60.942$	$\Q(\sqrt{13}) $	None	✓				1908.2.a.c	$1$	$1$	$0$	$0$	$-5$	$-5$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-2-\beta )q^{5}+(-3+\beta )q^{7}+(2-2\beta )q^{11}+\cdots$
7632.2.a.t	$7632$	$2$	7632.a	1.a	$1$	$2$	$2$	$60.942$	$\Q(\sqrt{17}) $	None	✓				318.2.a.g	$1$	$1$	$0$	$0$	$-1$	$-1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{5}+(-1+\beta )q^{7}-q^{11}-2\beta q^{13}+\cdots$
7632.2.a.u	$7632$	$2$	7632.a	1.a	$1$	$2$	$2$	$60.942$	$\Q(\sqrt{5}) $	None	✓				636.2.a.d	$1$	$1$	$0$	$0$	$-1$	$-1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{5}+(-1+\beta )q^{7}+2q^{11}+\beta q^{13}+\cdots$
7632.2.a.v	$7632$	$2$	7632.a	1.a	$1$	$2$	$2$	$60.942$	$\Q(\sqrt{41}) $	None	✓				318.2.a.f	$1$	$0$	$0$	$0$	$-1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{5}+(2-\beta )q^{11}+6q^{13}+(4+\beta )q^{17}+\cdots$
7632.2.a.w	$7632$	$2$	7632.a	1.a	$1$	$2$	$2$	$60.942$	$\Q(\sqrt{13}) $	None	✓				636.2.a.b	$1$	$1$	$0$	$0$	$-1$	$3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{5}+(1+\beta )q^{7}+(-2-2\beta )q^{11}+\cdots$
7632.2.a.x	$7632$	$2$	7632.a	1.a	$1$	$2$	$2$	$60.942$	$\Q(\sqrt{13}) $	None	✓				1908.2.a.d	$1$	$0$	$0$	$0$	$-1$	$3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{5}+(1+\beta )q^{7}+2\beta q^{11}+(2-3\beta )q^{13}+\cdots$
7632.2.a.y	$7632$	$2$	7632.a	1.a	$1$	$2$	$2$	$60.942$	$\Q(\sqrt{37}) $	None	✓				636.2.a.a	$1$	$0$	$0$	$0$	$1$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(-1+\beta )q^{7}+2q^{11}+\beta q^{13}+\cdots$
7632.2.a.z	$7632$	$2$	7632.a	1.a	$1$	$2$	$2$	$60.942$	$\Q(\sqrt{5}) $	None	✓				1272.2.a.d	$1$	$0$	$0$	$0$	$1$	$3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(1+\beta )q^{7}+(-4+2\beta )q^{11}+\cdots$
7632.2.a.ba	$7632$	$2$	7632.a	1.a	$1$	$2$	$2$	$60.942$	$\Q(\sqrt{13}) $	None	✓				1908.2.a.d	$1$	$1$	$0$	$0$	$1$	$3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(1+\beta )q^{7}-2\beta q^{11}+(2-3\beta )q^{13}+\cdots$
7632.2.a.bb	$7632$	$2$	7632.a	1.a	$1$	$2$	$2$	$60.942$	$\Q(\sqrt{5}) $	None	✓				1272.2.a.c	$1$	$1$	$0$	$0$	$3$	$3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{5}+(2-\beta )q^{7}+(-3-\beta )q^{13}+\cdots$
7632.2.a.bc	$7632$	$2$	7632.a	1.a	$1$	$2$	$2$	$60.942$	$\Q(\sqrt{2}) $	None	✓				424.2.a.a	$1$	$1$	$0$	$0$	$4$	$-4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+(-2+2\beta )q^{7}+(-2-2\beta )q^{11}+\cdots$
7632.2.a.bd	$7632$	$2$	7632.a	1.a	$1$	$2$	$2$	$60.942$	$\Q(\sqrt{13}) $	None	✓				1908.2.a.c	$1$	$0$	$0$	$0$	$5$	$-5$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(3-\beta )q^{5}+(-2-\beta )q^{7}-2\beta q^{11}+\cdots$
7632.2.a.be	$7632$	$2$	7632.a	1.a	$1$	$2$	$2$	$60.942$	$\Q(\sqrt{5}) $	None	✓				636.2.a.c	$1$	$0$	$0$	$0$	$5$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(3-\beta )q^{5}+3\beta q^{7}+(-4+2\beta )q^{11}+\cdots$
7632.2.a.bf	$7632$	$2$	7632.a	1.a	$1$	$3$	$3$	$60.942$	3.3.229.1	None	✓				1272.2.a.h	$1$	$1$	$0$	$0$	$-5$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-2-\beta _{2})q^{5}+(-1+2\beta _{1}-\beta _{2})q^{7}+\cdots$
7632.2.a.bg	$7632$	$2$	7632.a	1.a	$1$	$3$	$3$	$60.942$	3.3.316.1	None	✓				424.2.a.c	$1$	$1$	$0$	$0$	$-3$	$-6$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2})q^{5}-2q^{7}+(1+2\beta _{1}-\beta _{2})q^{11}+\cdots$
7632.2.a.bh	$7632$	$2$	7632.a	1.a	$1$	$3$	$3$	$60.942$	3.3.1229.1	None	✓				1272.2.a.i	$1$	$0$	$0$	$0$	$-1$	$3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{5}+(1+\beta _{2})q^{7}+2\beta _{1}q^{11}+(4+\cdots)q^{13}+\cdots$
7632.2.a.bi	$7632$	$2$	7632.a	1.a	$1$	$3$	$3$	$60.942$	3.3.756.1	None	✓				212.2.a.c	$1$	$0$	$0$	$0$	$0$	$-6$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{5}+(-2-\beta _{2})q^{7}+(2+2\beta _{1}+\cdots)q^{11}+\cdots$
7632.2.a.bj	$7632$	$2$	7632.a	1.a	$1$	$3$	$3$	$60.942$	3.3.621.1	None	✓				1272.2.a.g	$1$	$1$	$0$	$0$	$0$	$3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}+(1-\beta _{1})q^{7}+(-1+\beta _{2})q^{11}+\cdots$
7632.2.a.bk	$7632$	$2$	7632.a	1.a	$1$	$3$	$3$	$60.942$	3.3.3132.1	None	✓				954.2.a.p	$1$	$0$	$0$	$0$	$0$	$3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}+(1+\beta _{1})q^{7}+(-1+\beta _{2})q^{11}+\cdots$
7632.2.a.bl	$7632$	$2$	7632.a	1.a	$1$	$3$	$3$	$60.942$	3.3.3132.1	None	✓				954.2.a.p	$1$	$1$	$0$	$0$	$0$	$3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{5}+(1+\beta _{1})q^{7}+(1-\beta _{2})q^{11}+\cdots$
7632.2.a.bm	$7632$	$2$	7632.a	1.a	$1$	$3$	$3$	$60.942$	3.3.469.1	None	✓				1272.2.a.f	$1$	$0$	$0$	$0$	$1$	$-2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{5}+(-1-\beta _{2})q^{7}+(3-\beta _{1}+\beta _{2})q^{11}+\cdots$
7632.2.a.bn	$7632$	$2$	7632.a	1.a	$1$	$3$	$3$	$60.942$	3.3.148.1	None	✓				53.2.a.b	$1$	$1$	$0$	$0$	$2$	$-4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}-\beta _{2})q^{5}+(-1-\beta _{1}-\beta _{2})q^{7}+\cdots$
7632.2.a.bo	$7632$	$2$	7632.a	1.a	$1$	$3$	$3$	$60.942$	3.3.148.1	None	✓				424.2.a.b	$1$	$0$	$0$	$0$	$2$	$8$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}+\beta _{2})q^{5}+(3-\beta _{1}-\beta _{2})q^{7}+\cdots$
7632.2.a.bp	$7632$	$2$	7632.a	1.a	$1$	$3$	$3$	$60.942$	3.3.229.1	None	✓				1272.2.a.e	$1$	$0$	$0$	$0$	$4$	$-1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{2})q^{5}+(-2\beta _{1}+\beta _{2})q^{7}+(-3\beta _{1}+\cdots)q^{11}+\cdots$
7632.2.a.bq	$7632$	$2$	7632.a	1.a	$1$	$4$	$4$	$60.942$	4.4.1957.1	None	✓		✓		477.2.a.c	$1$	$0$	$0$	$0$	$-4$	$0$	$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2})q^{5}+\beta _{2}q^{7}+(2-\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots$
7632.2.a.br	$7632$	$2$	7632.a	1.a	$1$	$4$	$4$	$60.942$	4.4.1957.1	None	✓		✓		159.2.a.a	$1$	$0$	$0$	$0$	$-2$	$4$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{3})q^{5}+(1-\beta _{1})q^{7}+(1+\beta _{1}+\cdots)q^{11}+\cdots$
7632.2.a.bs	$7632$	$2$	7632.a	1.a	$1$	$4$	$4$	$60.942$	4.4.1957.1	None	✓		✓		477.2.a.c	$1$	$1$	$0$	$0$	$4$	$0$	$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1-\beta _{2})q^{5}+\beta _{2}q^{7}+(-2+\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots$
7632.2.a.bt	$7632$	$2$	7632.a	1.a	$1$	$5$	$5$	$60.942$	5.5.4321108.1	None	✓		✓		424.2.a.d	$1$	$0$	$0$	$0$	$-5$	$6$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{3})q^{5}+(1+\beta _{2}+\beta _{4})q^{7}+\cdots$
7632.2.a.bu	$7632$	$2$	7632.a	1.a	$1$	$5$	$5$	$60.942$	5.5.7329029.1	None	✓		✓		1272.2.a.j	$1$	$1$	$0$	$0$	$-2$	$-6$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{5}+(-1-\beta _{1}-\beta _{3}+\beta _{4})q^{7}+\cdots$
7632.2.a.bv	$7632$	$2$	7632.a	1.a	$1$	$5$	$5$	$60.942$	5.5.81509.1	None	✓				3816.2.a.n	$1$	$1$	$0$	$0$	$-2$	$1$	$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{5}-\beta _{2}q^{7}+(\beta _{1}+\beta _{2}-\beta _{3})q^{11}+\cdots$
7632.2.a.bw	$7632$	$2$	7632.a	1.a	$1$	$5$	$5$	$60.942$	5.5.1054013.1	None	✓		✓		159.2.a.b	$1$	$1$	$0$	$0$	$0$	$-4$	$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{5}+(-1-\beta _{1}+\beta _{3})q^{7}+(\beta _{2}+\cdots)q^{11}+\cdots$
7632.2.a.bx	$7632$	$2$	7632.a	1.a	$1$	$5$	$5$	$60.942$	5.5.81509.1	None	✓				3816.2.a.n	$1$	$0$	$0$	$0$	$2$	$1$	$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{5}-\beta _{2}q^{7}+(-\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{11}+\cdots$

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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.