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 56 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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	3	11	17	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
9537.2.a.a	$9537$	$2$	9537.a	1.a	$1$	$1$	$1$	$76.153$	$\Q$	None	✓				561.2.a.a	$1$	$1$	$-2$	$-1$	$0$	$3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}+2q^{6}+3q^{7}+\cdots$
9537.2.a.b	$9537$	$2$	9537.a	1.a	$1$	$1$	$1$	$76.153$	$\Q$	None	✓				561.2.a.b	$1$	$1$	$-1$	$-1$	$-2$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+3q^{8}+\cdots$
9537.2.a.c	$9537$	$2$	9537.a	1.a	$1$	$1$	$1$	$76.153$	$\Q$	None	✓	✓			9537.2.a.c	$1$	$1$	$-1$	$-1$	$-2$	$3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+3q^{7}+\cdots$
9537.2.a.d	$9537$	$2$	9537.a	1.a	$1$	$1$	$1$	$76.153$	$\Q$	None	✓	✓			9537.2.a.c	$1$	$0$	$-1$	$1$	$2$	$-3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}+2q^{5}-q^{6}-3q^{7}+\cdots$
9537.2.a.e	$9537$	$2$	9537.a	1.a	$1$	$1$	$1$	$76.153$	$\Q$	None	✓	✓			9537.2.a.e	$1$	$2$	$0$	$-1$	$-3$	$-2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-3q^{5}-2q^{7}+q^{9}+q^{11}+\cdots$
9537.2.a.f	$9537$	$2$	9537.a	1.a	$1$	$1$	$1$	$76.153$	$\Q$	None	✓	✓			9537.2.a.f	$1$	$1$	$0$	$-1$	$-1$	$-4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-q^{5}-4q^{7}+q^{9}-q^{11}+\cdots$
9537.2.a.g	$9537$	$2$	9537.a	1.a	$1$	$1$	$1$	$76.153$	$\Q$	None	✓	✓			9537.2.a.g	$1$	$1$	$0$	$-1$	$1$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+q^{5}+q^{9}+q^{11}+2q^{12}+\cdots$
9537.2.a.h	$9537$	$2$	9537.a	1.a	$1$	$1$	$1$	$76.153$	$\Q$	None	✓				561.2.a.d	$1$	$1$	$0$	$-1$	$2$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+2q^{5}-q^{7}+q^{9}-q^{11}+\cdots$
9537.2.a.i	$9537$	$2$	9537.a	1.a	$1$	$1$	$1$	$76.153$	$\Q$	None	✓	✓			9537.2.a.g	$1$	$0$	$0$	$1$	$-1$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-q^{5}+q^{9}-q^{11}-2q^{12}+\cdots$
9537.2.a.j	$9537$	$2$	9537.a	1.a	$1$	$1$	$1$	$76.153$	$\Q$	None	✓	✓			9537.2.a.f	$1$	$0$	$0$	$1$	$1$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+q^{5}+4q^{7}+q^{9}+q^{11}+\cdots$
9537.2.a.k	$9537$	$2$	9537.a	1.a	$1$	$1$	$1$	$76.153$	$\Q$	None	✓				561.2.a.c	$1$	$0$	$0$	$1$	$2$	$3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+2q^{5}+3q^{7}+q^{9}-q^{11}+\cdots$
9537.2.a.l	$9537$	$2$	9537.a	1.a	$1$	$1$	$1$	$76.153$	$\Q$	None	✓	✓			9537.2.a.e	$1$	$1$	$0$	$1$	$3$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}+3q^{5}+2q^{7}+q^{9}-q^{11}+\cdots$
9537.2.a.m	$9537$	$2$	9537.a	1.a	$1$	$1$	$1$	$76.153$	$\Q$	None	✓				33.2.a.a	$1$	$0$	$1$	$1$	$2$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+2q^{5}+q^{6}-4q^{7}+\cdots$
9537.2.a.n	$9537$	$2$	9537.a	1.a	$1$	$2$	$2$	$76.153$	$\Q(\sqrt{2}) $	None	✓				561.2.j.a	$1$	$1$	$-2$	$-2$	$4$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+(2-\beta )q^{5}+q^{6}+\cdots$
9537.2.a.o	$9537$	$2$	9537.a	1.a	$1$	$2$	$2$	$76.153$	$\Q(\sqrt{2}) $	None	✓				561.2.j.b	$1$	$0$	$-2$	$-2$	$4$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+(2+\beta )q^{5}+q^{6}+\cdots$
9537.2.a.p	$9537$	$2$	9537.a	1.a	$1$	$2$	$2$	$76.153$	$\Q(\sqrt{2}) $	None	✓				561.2.j.b	$1$	$0$	$-2$	$2$	$-4$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}+(-2-\beta )q^{5}-q^{6}+\cdots$
9537.2.a.q	$9537$	$2$	9537.a	1.a	$1$	$2$	$2$	$76.153$	$\Q(\sqrt{2}) $	None	✓				561.2.j.a	$1$	$1$	$-2$	$2$	$-4$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}+(-2-\beta )q^{5}-q^{6}+\cdots$
9537.2.a.r	$9537$	$2$	9537.a	1.a	$1$	$2$	$2$	$76.153$	$\Q(\sqrt{17}) $	None	✓	✓			9537.2.a.r	$1$	$0$	$-1$	$-2$	$3$	$5$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+(2+\beta )q^{4}+(1+\beta )q^{5}+\cdots$
9537.2.a.s	$9537$	$2$	9537.a	1.a	$1$	$2$	$2$	$76.153$	$\Q(\sqrt{17}) $	None	✓	✓			9537.2.a.r	$1$	$1$	$-1$	$2$	$-3$	$-5$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(2+\beta )q^{4}+(-1-\beta )q^{5}+\cdots$
9537.2.a.t	$9537$	$2$	9537.a	1.a	$1$	$2$	$2$	$76.153$	$\Q(\sqrt{2}) $	None	✓				561.2.a.e	$1$	$0$	$0$	$-2$	$4$	$6$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+(2+\beta )q^{5}-\beta q^{6}+3q^{7}+\cdots$
9537.2.a.u	$9537$	$2$	9537.a	1.a	$1$	$2$	$2$	$76.153$	$\Q(\sqrt{17}) $	None	✓				561.2.a.f	$1$	$0$	$1$	$2$	$-4$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(2+\beta )q^{4}-2q^{5}+\beta q^{6}+\cdots$
9537.2.a.v	$9537$	$2$	9537.a	1.a	$1$	$3$	$3$	$76.153$	3.3.148.1	None	✓				561.2.a.g	$1$	$1$	$-2$	$3$	$2$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
9537.2.a.w	$9537$	$2$	9537.a	1.a	$1$	$3$	$3$	$76.153$	3.3.148.1	None	✓				561.2.a.h	$1$	$0$	$0$	$3$	$4$	$7$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots$
9537.2.a.x	$9537$	$2$	9537.a	1.a	$1$	$3$	$3$	$76.153$	3.3.316.1	None	✓				561.2.a.i	$1$	$1$	$1$	$3$	$-4$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots$
9537.2.a.y	$9537$	$2$	9537.a	1.a	$1$	$4$	$4$	$76.153$	4.4.22676.1	None	✓				561.2.a.j	$1$	$1$	$1$	$-4$	$4$	$-9$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{3})q^{5}+\cdots$
9537.2.a.z	$9537$	$2$	9537.a	1.a	$1$	$5$	$5$	$76.153$	5.5.9338213.1	None	✓	✓			9537.2.a.z	$1$	$0$	$0$	$-5$	$2$	$8$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
9537.2.a.ba	$9537$	$2$	9537.a	1.a	$1$	$5$	$5$	$76.153$	5.5.9338213.1	None	✓	✓			9537.2.a.z	$1$	$1$	$0$	$5$	$-2$	$-8$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
9537.2.a.bb	$9537$	$2$	9537.a	1.a	$1$	$5$	$5$	$76.153$	5.5.81509.1	None	✓	✓			9537.2.a.bb	$1$	$1$	$1$	$-5$	$-3$	$-3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}-\beta _{4})q^{2}-q^{3}+(1-\beta _{3})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$
9537.2.a.bc	$9537$	$2$	9537.a	1.a	$1$	$5$	$5$	$76.153$	5.5.81509.1	None	✓	✓			9537.2.a.bb	$1$	$0$	$1$	$5$	$3$	$3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}-\beta _{4})q^{2}+q^{3}+(1-\beta _{3})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots$
9537.2.a.bd	$9537$	$2$	9537.a	1.a	$1$	$6$	$6$	$76.153$	6.6.24366928.1	None	✓				561.2.g.a	$1$	$1$	$-3$	$-6$	$6$	$1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
9537.2.a.be	$9537$	$2$	9537.a	1.a	$1$	$6$	$6$	$76.153$	6.6.24366928.1	None	✓				561.2.g.a	$1$	$1$	$-3$	$6$	$-6$	$-1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
9537.2.a.bf	$9537$	$2$	9537.a	1.a	$1$	$6$	$6$	$76.153$	6.6.6754732.1	None	✓	✓			9537.2.a.bf	$1$	$0$	$-1$	$-6$	$2$	$7$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{2}-q^{3}+(1-\beta _{4}-\beta _{5})q^{4}+(1+\cdots)q^{5}+\cdots$
9537.2.a.bg	$9537$	$2$	9537.a	1.a	$1$	$6$	$6$	$76.153$	6.6.78067472.1	None	✓				561.2.a.k	$1$	$0$	$-1$	$-6$	$-2$	$-7$	$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots$
9537.2.a.bh	$9537$	$2$	9537.a	1.a	$1$	$6$	$6$	$76.153$	6.6.6754732.1	None	✓	✓			9537.2.a.bf	$1$	$1$	$-1$	$6$	$-2$	$-7$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{2}+q^{3}+(1-\beta _{4}-\beta _{5})q^{4}+(-1+\cdots)q^{5}+\cdots$
9537.2.a.bi	$9537$	$2$	9537.a	1.a	$1$	$6$	$6$	$76.153$	6.6.1690398989.1	None	✓	✓			9537.2.a.bi	$1$	$1$	$2$	$-6$	$1$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots$
9537.2.a.bj	$9537$	$2$	9537.a	1.a	$1$	$6$	$6$	$76.153$	6.6.1690398989.1	None	✓	✓			9537.2.a.bi	$1$	$0$	$2$	$6$	$-1$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots$
9537.2.a.bk	$9537$	$2$	9537.a	1.a	$1$	$6$	$6$	$76.153$	6.6.7328637.1	None	✓	✓			9537.2.a.bk	$1$	$1$	$3$	$-6$	$0$	$-6$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{4})q^{2}-q^{3}+(1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
9537.2.a.bl	$9537$	$2$	9537.a	1.a	$1$	$6$	$6$	$76.153$	6.6.7328637.1	None	✓	✓			9537.2.a.bk	$1$	$0$	$3$	$6$	$0$	$6$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{4})q^{2}+q^{3}+(1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
9537.2.a.bm	$9537$	$2$	9537.a	1.a	$1$	$8$	$8$	$76.153$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓				561.2.g.b	$1$	$0$	$1$	$-8$	$-2$	$-1$	$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\beta _{6}+\cdots)q^{5}+\cdots$
9537.2.a.bn	$9537$	$2$	9537.a	1.a	$1$	$8$	$8$	$76.153$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓				561.2.g.b	$1$	$0$	$1$	$8$	$2$	$1$	$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
9537.2.a.bo	$9537$	$2$	9537.a	1.a	$1$	$10$	$10$	$76.153$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓				561.2.j.c	$1$	$1$	$0$	$-10$	$8$	$2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{6}+\cdots)q^{5}+\cdots$
9537.2.a.bp	$9537$	$2$	9537.a	1.a	$1$	$10$	$10$	$76.153$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓				561.2.j.c	$1$	$1$	$0$	$10$	$-8$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{6}+\cdots)q^{5}+\cdots$
9537.2.a.bq	$9537$	$2$	9537.a	1.a	$1$	$14$	$14$	$76.153$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓				561.2.j.d	$1$	$0$	$8$	$-14$	$-8$	$-2$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
9537.2.a.br	$9537$	$2$	9537.a	1.a	$1$	$14$	$14$	$76.153$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓				561.2.j.d	$1$	$0$	$8$	$14$	$8$	$2$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots$
9537.2.a.bs	$9537$	$2$	9537.a	1.a	$1$	$15$	$15$	$76.153$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	✓	✓		9537.2.a.bs	$1$	$1$	$0$	$-15$	$-6$	$-15$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{5}+\cdots)q^{5}+\cdots$
9537.2.a.bt	$9537$	$2$	9537.a	1.a	$1$	$15$	$15$	$76.153$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	✓			9537.2.a.bs	$1$	$0$	$0$	$15$	$6$	$15$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{5}+\cdots)q^{5}+\cdots$
9537.2.a.bu	$9537$	$2$	9537.a	1.a	$1$	$18$	$18$	$76.153$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	✓			9537.2.a.bu	$1$	$0$	$-3$	$-18$	$6$	$15$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{13}q^{5}+\cdots$
9537.2.a.bv	$9537$	$2$	9537.a	1.a	$1$	$18$	$18$	$76.153$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	✓	✓		9537.2.a.bu	$1$	$1$	$-3$	$18$	$-6$	$-15$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{13}q^{5}+\cdots$
9537.2.a.bw	$9537$	$2$	9537.a	1.a	$1$	$18$	$18$	$76.153$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	✓			9537.2.a.bw	$1$	$1$	$3$	$-18$	$-6$	$-15$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots$
9537.2.a.bx	$9537$	$2$	9537.a	1.a	$1$	$18$	$18$	$76.153$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	✓	✓		9537.2.a.bw	$1$	$0$	$3$	$18$	$6$	$15$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots$

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Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

L-functions

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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.