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 118 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	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	Image	CM	RM	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
3060.1.f.a	$3060$	$1$	3060.f	340.d	$2$	$1$	$1$	$1.527$	$\Q$	$D_{2}$	$\Q(\sqrt{-15})$ , $\Q(\sqrt{-85})$	$\Q(\sqrt{51})$	✓	✓			3060.1.f.a	$4$	$0$	$-1$	$0$	$-1$	$0$		$1$		$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+q^{16}+\cdots$
3060.1.f.b	$3060$	$1$	3060.f	340.d	$2$	$1$	$1$	$1.527$	$\Q$	$D_{2}$	$\Q(\sqrt{-15})$ , $\Q(\sqrt{-85})$	$\Q(\sqrt{51})$	✓	✓			3060.1.f.a	$4$	$0$	$-1$	$0$	$1$	$0$		$1$		$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+q^{16}+\cdots$
3060.1.f.c	$3060$	$1$	3060.f	340.d	$2$	$1$	$1$	$1.527$	$\Q$	$D_{2}$	$\Q(\sqrt{-15})$ , $\Q(\sqrt{-85})$	$\Q(\sqrt{51})$	✓	✓			3060.1.f.a	$4$	$0$	$1$	$0$	$-1$	$0$		$1$		$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+q^{16}+\cdots$
3060.1.f.d	$3060$	$1$	3060.f	340.d	$2$	$1$	$1$	$1.527$	$\Q$	$D_{2}$	$\Q(\sqrt{-15})$ , $\Q(\sqrt{-85})$	$\Q(\sqrt{51})$	✓	✓			3060.1.f.a	$4$	$0$	$1$	$0$	$1$	$0$		$1$		$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+q^{16}+\cdots$
3060.1.f.e	$3060$	$1$	3060.f	340.d	$2$	$2$	$2$	$1.527$	$\Q(\sqrt{-1})$	$D_{2}$	$\Q(\sqrt{-1})$ , $\Q(\sqrt{-255})$	$\Q(\sqrt{255})$		✓			3060.1.f.e	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{2}-q^{4}-i q^{5}+i q^{8}-q^{10}+\cdots$
3060.1.f.f	$3060$	$1$	3060.f	340.d	$2$	$2$	$2$	$1.527$	$\Q(\sqrt{-1})$	$D_{2}$	$\Q(\sqrt{-1})$ , $\Q(\sqrt{-255})$	$\Q(\sqrt{255})$		✓			3060.1.f.e	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+i q^{2}-q^{4}-i q^{5}-i q^{8}+q^{10}+\cdots$
3060.1.f.g	$3060$	$1$	3060.f	340.d	$2$	$4$	$4$	$1.527$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-255})$	None		✓			3060.1.f.g	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{5}+(\zeta_{12}^{2}+\cdots)q^{7}+\cdots$
3060.1.f.h	$3060$	$1$	3060.f	340.d	$2$	$4$	$4$	$1.527$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-255})$	None		✓			3060.1.f.g	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{3}q^{5}+\cdots$
3060.1.r.a	$3060$	$1$	3060.r	1020.q	$4$	$4$	$2$	$1.527$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-1})$	None		✓			3060.1.r.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}q^{5}-\zeta_{8}^{3}q^{8}+\cdots$
3060.1.r.b	$3060$	$1$	3060.r	1020.q	$4$	$4$	$2$	$1.527$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-1})$	None		✓			3060.1.r.b	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+\zeta_{8}^{3}q^{8}+\cdots$
3060.1.v.a	$3060$	$1$	3060.v	85.g	$4$	$8$	$4$	$1.527$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-51})$	None		✓	✓	✓	3060.1.v.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{7}q^{5}+(\zeta_{24}^{5}+\zeta_{24}^{7})q^{11}+(-\zeta_{24}^{2}+\cdots)q^{13}+\cdots$
3060.1.y.a	$3060$	$1$	3060.y	1020.x	$4$	$4$	$2$	$1.527$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-1})$	None		✓			3060.1.y.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}q^{5}+\zeta_{8}^{3}q^{8}+\cdots$
3060.1.y.b	$3060$	$1$	3060.y	1020.x	$4$	$4$	$2$	$1.527$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-1})$	None		✓			3060.1.y.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}q^{5}-\zeta_{8}^{3}q^{8}+\cdots$
3060.1.bc.a	$3060$	$1$	3060.bc	340.n	$4$	$2$	$1$	$1.527$	$\Q(\sqrt{-1})$	$D_{4}$	$\Q(\sqrt{-1})$	None		✓			3060.1.bc.a	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-i q^{5}-q^{8}+i q^{10}+\cdots$
3060.1.bc.b	$3060$	$1$	3060.bc	340.n	$4$	$2$	$1$	$1.527$	$\Q(\sqrt{-1})$	$D_{4}$	$\Q(\sqrt{-1})$	None		✓			3060.1.bc.a	$4$	$0$	$-2$	$0$	$2$	$0$		$1$		$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-2 i q^{13}+\cdots$
3060.1.bc.c	$3060$	$1$	3060.bc	340.n	$4$	$2$	$1$	$1.527$	$\Q(\sqrt{-1})$	$D_{4}$	$\Q(\sqrt{-1})$	None		✓			3060.1.bc.a	$4$	$0$	$2$	$0$	$-2$	$0$		$1$		$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-2 i q^{13}+\cdots$
3060.1.bc.d	$3060$	$1$	3060.bc	340.n	$4$	$2$	$1$	$1.527$	$\Q(\sqrt{-1})$	$D_{4}$	$\Q(\sqrt{-1})$	None		✓			3060.1.bc.a	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+i q^{5}+q^{8}+i q^{10}+\cdots$
3060.1.bc.e	$3060$	$1$	3060.bc	340.n	$4$	$4$	$2$	$1.527$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-15})$	None		✓			3060.1.bc.e	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}q^{5}-\zeta_{8}^{3}q^{8}+\cdots$
3060.1.bc.f	$3060$	$1$	3060.bc	340.n	$4$	$4$	$2$	$1.527$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-15})$	None		✓			3060.1.bc.e	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}-\zeta_{8}q^{8}+\cdots$
3060.1.bm.a	$3060$	$1$	3060.bm	1020.al	$4$	$4$	$2$	$1.527$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-1})$	None		✓			3060.1.r.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{5}-\zeta_{8}q^{8}+\cdots$
3060.1.bm.b	$3060$	$1$	3060.bm	1020.al	$4$	$4$	$2$	$1.527$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-1})$	None		✓			3060.1.r.b	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}-\zeta_{8}q^{8}+\cdots$
3060.1.ck.a	$3060$	$1$	3060.ck	1020.au	$8$	$4$	$1$	$1.527$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1})$	None		✓			3060.1.ck.a	$4$	$0$	$0$	$0$	$-4$	$0$		$1$		$q+\zeta_{8}^{2}q^{2}-q^{4}-q^{5}-\zeta_{8}^{2}q^{8}-\zeta_{8}^{2}q^{10}+\cdots$
3060.1.ck.b	$3060$	$1$	3060.ck	1020.au	$8$	$4$	$1$	$1.527$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1})$	None		✓			3060.1.ck.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}^{3}q^{5}-\zeta_{8}^{2}q^{8}+\cdots$
3060.1.ck.c	$3060$	$1$	3060.ck	1020.au	$8$	$4$	$1$	$1.527$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1})$	None		✓			3060.1.ck.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{2}q^{2}-q^{4}+\zeta_{8}^{3}q^{5}+\zeta_{8}^{2}q^{8}+\cdots$
3060.1.ck.d	$3060$	$1$	3060.ck	1020.au	$8$	$4$	$1$	$1.527$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1})$	None		✓			3060.1.ck.a	$4$	$0$	$0$	$0$	$4$	$0$		$1$		$q-\zeta_{8}^{2}q^{2}-q^{4}+q^{5}+\zeta_{8}^{2}q^{8}-\zeta_{8}^{2}q^{10}+\cdots$
3060.1.cn.a	$3060$	$1$	3060.cn	1020.ax	$8$	$4$	$1$	$1.527$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1})$	None		✓			3060.1.ck.b	$4$	$0$	$-4$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}+\zeta_{8}^{2}q^{5}-q^{8}-\zeta_{8}^{2}q^{10}+\cdots$
3060.1.cn.b	$3060$	$1$	3060.cn	1020.ax	$8$	$4$	$1$	$1.527$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1})$	None		✓			3060.1.ck.a	$4$	$0$	$-4$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-\zeta_{8}^{3}q^{5}-q^{8}+\zeta_{8}^{3}q^{10}+\cdots$
3060.1.cn.c	$3060$	$1$	3060.cn	1020.ax	$8$	$4$	$1$	$1.527$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1})$	None		✓			3060.1.ck.b	$4$	$0$	$4$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}-\zeta_{8}^{2}q^{5}+q^{8}-\zeta_{8}^{2}q^{10}+\cdots$
3060.1.cn.d	$3060$	$1$	3060.cn	1020.ax	$8$	$4$	$1$	$1.527$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1})$	None		✓			3060.1.ck.a	$4$	$0$	$4$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+\zeta_{8}^{3}q^{5}+q^{8}+\zeta_{8}^{3}q^{10}+\cdots$
3060.1.cr.a	$3060$	$1$	3060.cr	340.aa	$8$	$4$	$1$	$1.527$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1})$	None					340.1.ba.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}^{2}q^{5}+\zeta_{8}q^{8}+\cdots$
3060.1.cr.b	$3060$	$1$	3060.cr	340.aa	$8$	$4$	$1$	$1.527$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1})$	None					340.1.ba.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}-\zeta_{8}q^{8}+\cdots$
3060.1.cr.c	$3060$	$1$	3060.cr	340.aa	$8$	$8$	$2$	$1.527$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-15})$	None		✓			3060.1.cr.c	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}-\zeta_{16}^{7}q^{5}+\cdots$
3060.1.cr.d	$3060$	$1$	3060.cr	340.aa	$8$	$8$	$2$	$1.527$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-15})$	None		✓			3060.1.cr.c	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{16}^{7}q^{2}-\zeta_{16}^{6}q^{4}+\zeta_{16}^{7}q^{5}+\cdots$
3060.1.di.a	$3060$	$1$	3060.di	3060.ci	$12$	$8$	$2$	$1.527$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓			3060.1.di.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{5}q^{2}-\zeta_{24}^{11}q^{3}+\zeta_{24}^{10}q^{4}+\cdots$
3060.1.di.b	$3060$	$1$	3060.di	3060.ci	$12$	$8$	$2$	$1.527$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓			3060.1.di.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{11}q^{2}+\zeta_{24}^{11}q^{3}-\zeta_{24}^{10}q^{4}+\cdots$
3060.1.ds.a	$3060$	$1$	3060.ds	340.ac	$16$	$8$	$1$	$1.527$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-1})$	None					340.1.bc.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}+\zeta_{16}^{6}q^{5}+\cdots$
3060.1.ds.b	$3060$	$1$	3060.ds	340.ac	$16$	$8$	$1$	$1.527$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-1})$	None		✓			3060.1.ds.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}-\zeta_{16}^{3}q^{5}+\cdots$
3060.1.ds.c	$3060$	$1$	3060.ds	340.ac	$16$	$8$	$1$	$1.527$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-1})$	None		✓			3060.1.ds.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}+\zeta_{16}^{3}q^{5}+\cdots$
3060.1.dz.a	$3060$	$1$	3060.dz	1020.bl	$16$	$8$	$1$	$1.527$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-1})$	None		✓			3060.1.dz.a	$4$	$0$	$0$	$0$	$-8$	$0$		$1$		$q-\zeta_{16}^{3}q^{2}+\zeta_{16}^{6}q^{4}-q^{5}+\zeta_{16}q^{8}+\cdots$
3060.1.dz.b	$3060$	$1$	3060.dz	1020.bl	$16$	$8$	$1$	$1.527$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-1})$	None		✓			3060.1.dz.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{16}^{3}q^{2}+\zeta_{16}^{6}q^{4}+\zeta_{16}q^{5}+\zeta_{16}q^{8}+\cdots$
3060.1.dz.c	$3060$	$1$	3060.dz	1020.bl	$16$	$8$	$1$	$1.527$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-1})$	None		✓			3060.1.dz.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}^{3}q^{2}+\zeta_{16}^{6}q^{4}-\zeta_{16}q^{5}-\zeta_{16}q^{8}+\cdots$
3060.1.dz.d	$3060$	$1$	3060.dz	1020.bl	$16$	$8$	$1$	$1.527$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-1})$	None		✓			3060.1.dz.a	$4$	$0$	$0$	$0$	$8$	$0$		$1$		$q+\zeta_{16}^{3}q^{2}+\zeta_{16}^{6}q^{4}+q^{5}-\zeta_{16}q^{8}+\cdots$
3060.1.eg.a	$3060$	$1$	3060.eg	340.aj	$16$	$8$	$1$	$1.527$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-1})$	None					340.1.bc.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}^{3}q^{2}+\zeta_{16}^{6}q^{4}+\zeta_{16}^{5}q^{5}+\cdots$
3060.1.eg.b	$3060$	$1$	3060.eg	340.aj	$16$	$8$	$1$	$1.527$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-1})$	None		✓			3060.1.ds.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{16}^{3}q^{2}+\zeta_{16}^{6}q^{4}+\zeta_{16}^{6}q^{5}+\cdots$
3060.1.eg.c	$3060$	$1$	3060.eg	340.aj	$16$	$8$	$1$	$1.527$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-1})$	None		✓			3060.1.ds.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}^{3}q^{2}+\zeta_{16}^{6}q^{4}-\zeta_{16}^{6}q^{5}+\cdots$
3060.2.a.a	$3060$	$2$	3060.a	1.a	$1$	$1$	$1$	$24.434$	$\Q$	$_{}$	None	None	✓				1020.2.a.h	$1$	$1$	$0$	$0$	$-1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-5q^{7}+5q^{11}-q^{17}+q^{19}+\cdots$
3060.2.a.b	$3060$	$2$	3060.a	1.a	$1$	$1$	$1$	$24.434$	$\Q$	$_{}$	None	None	✓				1020.2.a.b	$1$	$0$	$0$	$0$	$-1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{7}-3q^{11}-4q^{13}+q^{17}+\cdots$
3060.2.a.c	$3060$	$2$	3060.a	1.a	$1$	$1$	$1$	$24.434$	$\Q$	$_{}$	None	None	✓	✓			3060.2.a.c	$1$	$1$	$0$	$0$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-q^{7}-q^{11}+q^{17}-3q^{19}+\cdots$
3060.2.a.d	$3060$	$2$	3060.a	1.a	$1$	$1$	$1$	$24.434$	$\Q$	$_{}$	None	None	✓	✓			3060.2.a.d	$1$	$1$	$0$	$0$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-q^{7}+3q^{11}-4q^{13}+q^{17}+\cdots$
3060.2.a.e	$3060$	$2$	3060.a	1.a	$1$	$1$	$1$	$24.434$	$\Q$	$_{}$	None	None	✓				1020.2.a.c	$1$	$0$	$0$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+6q^{11}+2q^{13}+q^{17}-8q^{19}+\cdots$

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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.