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 69 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
3825.1.m.a	$3825$	$1$	3825.m	85.f	$4$	$2$	$1$	$1.909$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-15}) $	None		✓			3825.1.m.a	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q+(-i-1)q^{2}+i q^{4}+q^{16}-i q^{17}+\cdots$
3825.1.m.b	$3825$	$1$	3825.m	85.f	$4$	$2$	$1$	$1.909$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-15}) $	None		✓			3825.1.m.a	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+(i+1)q^{2}+i q^{4}+q^{16}+i q^{17}+\cdots$
3825.1.m.c	$3825$	$1$	3825.m	85.f	$4$	$4$	$2$	$1.909$	$\Q(\zeta_{8})$	$S_{4}$	None	None			✓		765.1.m.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{2}+\zeta_{8}^{2}q^{7}+\zeta_{8}q^{8}-\zeta_{8}q^{11}+\cdots$
3825.1.o.a	$3825$	$1$	3825.o	85.g	$4$	$4$	$2$	$1.909$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-51}) $	None					765.1.o.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{2}q^{4}+(\zeta_{8}+\zeta_{8}^{3})q^{11}+(-1-\zeta_{8}^{2}+\cdots)q^{13}+\cdots$
3825.1.o.b	$3825$	$1$	3825.o	85.g	$4$	$4$	$2$	$1.909$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-255}) $	$\Q(\sqrt{17}) $		✓			3825.1.o.b	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{2}-3\zeta_{8}^{2}q^{4}+2\zeta_{8}q^{8}+3q^{16}+\cdots$
3825.1.o.c	$3825$	$1$	3825.o	85.g	$4$	$8$	$4$	$1.909$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-255}) $	None		✓	✓		3825.1.o.c	$16$	$0$	$0$	$0$	$0$	$0$		$2^{4}$		$q-\zeta_{24}^{3}q^{2}+(-\zeta_{24}^{7}-\zeta_{24}^{11})q^{7}+\cdots$
3825.1.r.a	$3825$	$1$	3825.r	85.i	$4$	$2$	$1$	$1.909$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-15}) $	None		✓			3825.1.m.a	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q+(-i-1)q^{2}+i q^{4}+q^{16}-q^{17}+\cdots$
3825.1.r.b	$3825$	$1$	3825.r	85.i	$4$	$2$	$1$	$1.909$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-15}) $	None		✓			3825.1.m.a	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+(i+1)q^{2}+i q^{4}+q^{16}+q^{17}+\cdots$
3825.1.r.c	$3825$	$1$	3825.r	85.i	$4$	$4$	$2$	$1.909$	$\Q(\zeta_{8})$	$S_{4}$	None	None			✓		765.1.m.a	$4$	$0$	$0$	$0$	$0$	$4$		$1$		$q-\zeta_{8}^{3}q^{2}+q^{7}+\zeta_{8}q^{8}-\zeta_{8}^{3}q^{11}+\cdots$
3825.1.u.a	$3825$	$1$	3825.u	51.f	$4$	$4$	$2$	$1.909$	$\Q(\zeta_{8})$	$S_{4}$	None	None					765.1.j.a	$4$	$0$	$-4$	$0$	$0$	$0$		$1$		$q-q^{2}-\zeta_{8}^{3}q^{7}+q^{8}+\zeta_{8}q^{11}+(\zeta_{8}+\cdots)q^{13}+\cdots$
3825.1.u.b	$3825$	$1$	3825.u	51.f	$4$	$4$	$2$	$1.909$	$\Q(\zeta_{8})$	$S_{4}$	None	None					765.1.j.a	$4$	$0$	$4$	$0$	$0$	$0$		$1$		$q+q^{2}-\zeta_{8}^{3}q^{7}-q^{8}-\zeta_{8}q^{11}+(\zeta_{8}+\cdots)q^{13}+\cdots$
3825.1.bb.a	$3825$	$1$	3825.bb	153.i	$6$	$2$	$1$	$1.909$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{85}) $					765.1.v.a	$4$	$0$	$0$	$-1$	$0$	$-3$		$1$		$q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+(-1+\zeta_{6}^{2})q^{7}+\cdots$
3825.1.bb.b	$3825$	$1$	3825.bb	153.i	$6$	$2$	$1$	$1.909$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{85}) $					765.1.v.a	$4$	$0$	$0$	$1$	$0$	$3$		$1$		$q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+(1-\zeta_{6}^{2})q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
3825.1.bd.a	$3825$	$1$	3825.bd	85.k	$8$	$8$	$2$	$1.909$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-15}) $	None		✓	✓	✓	3825.1.bd.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{16}-\zeta_{16}^{7})q^{2}+(-1+\zeta_{16}^{2}+\cdots)q^{4}+\cdots$
3825.1.bk.a	$3825$	$1$	3825.bk	85.n	$8$	$8$	$2$	$1.909$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-15}) $	None		✓	✓	✓	3825.1.bd.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{16}^{3}+\zeta_{16}^{5})q^{2}+(1-\zeta_{16}^{2}+\cdots)q^{4}+\cdots$
3825.1.bv.a	$3825$	$1$	3825.bv	765.an	$12$	$4$	$1$	$1.909$	$\Q(\zeta_{12})$	$S_{4}$	None	None					765.1.bn.b	$4$	$0$	$0$	$2$	$0$	$-2$		$1$		$q-\zeta_{12}^{4}q^{3}-\zeta_{12}^{5}q^{4}+\zeta_{12}^{4}q^{7}+\cdots$
3825.1.bv.b	$3825$	$1$	3825.bv	765.an	$12$	$4$	$1$	$1.909$	$\Q(\zeta_{12})$	$S_{4}$	None	None					765.1.bn.a	$4$	$0$	$2$	$2$	$0$	$2$		$1$		$q+(-\zeta_{12}-\zeta_{12}^{4})q^{2}-\zeta_{12}^{4}q^{3}+\zeta_{12}^{5}q^{4}+\cdots$
3825.1.bz.a	$3825$	$1$	3825.bz	765.ar	$12$	$8$	$2$	$1.909$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓			3825.1.bz.a	$8$	$0$	$-4$	$0$	$0$	$0$		$1$		$q+(-\zeta_{24}^{4}+\zeta_{24}^{10})q^{2}-\zeta_{24}q^{3}+\cdots$
3825.1.bz.b	$3825$	$1$	3825.bz	765.ar	$12$	$8$	$2$	$1.909$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓			3825.1.bz.a	$8$	$0$	$4$	$0$	$0$	$0$		$1$		$q+(\zeta_{24}^{4}-\zeta_{24}^{10})q^{2}-\zeta_{24}q^{3}+\zeta_{24}^{2}q^{4}+\cdots$
3825.1.ca.a	$3825$	$1$	3825.ca	765.as	$12$	$4$	$1$	$1.909$	$\Q(\zeta_{12})$	$S_{4}$	None	None					765.1.bn.a	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q+(-\zeta_{12}^{2}-\zeta_{12}^{5})q^{2}+\zeta_{12}^{5}q^{3}+\cdots$
3825.1.ca.b	$3825$	$1$	3825.ca	765.as	$12$	$4$	$1$	$1.909$	$\Q(\zeta_{12})$	$S_{4}$	None	None					765.1.bn.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{3}+\zeta_{12}q^{4}+\zeta_{12}^{5}q^{7}-\zeta_{12}^{4}q^{9}+\cdots$
3825.1.ck.a	$3825$	$1$	3825.ck	17.e	$16$	$16$	$2$	$1.909$	$\Q(\zeta_{32})$	$D_{16}$	$\Q(\sqrt{-15}) $	None			✓	✓	765.1.bz.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{32}-\zeta_{32}^{3})q^{2}+(\zeta_{32}^{2}+\zeta_{32}^{4}+\cdots)q^{4}+\cdots$
3825.1.cu.a	$3825$	$1$	3825.cu	425.z	$20$	$16$	$2$	$1.909$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-51}) $	None		✓	✓	✓	3825.1.cu.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{40}^{2}q^{4}+\zeta_{40}^{5}q^{5}+(\zeta_{40}^{3}+\zeta_{40}^{9}+\cdots)q^{11}+\cdots$
3825.2.a.a	$3825$	$2$	3825.a	1.a	$1$	$1$	$1$	$30.543$	$\Q$	$_{}$	None	None	✓				1275.2.a.a	$1$	$1$	$-2$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-q^{7}-2q^{11}+7q^{13}+\cdots$
3825.2.a.b	$3825$	$2$	3825.a	1.a	$1$	$1$	$1$	$30.543$	$\Q$	$_{}$	None	None	✓				153.2.a.a	$1$	$1$	$-2$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+2q^{7}+3q^{11}+5q^{13}+\cdots$
3825.2.a.c	$3825$	$2$	3825.a	1.a	$1$	$1$	$1$	$30.543$	$\Q$	$_{}$	None	None	✓				255.2.b.a	$1$	$1$	$-1$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-4q^{7}+3q^{8}-6q^{11}+\cdots$
3825.2.a.d	$3825$	$2$	3825.a	1.a	$1$	$1$	$1$	$30.543$	$\Q$	$_{}$	None	None	✓				17.2.a.a	$1$	$1$	$-1$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-4q^{7}+3q^{8}+2q^{13}+\cdots$
3825.2.a.e	$3825$	$2$	3825.a	1.a	$1$	$1$	$1$	$30.543$	$\Q$	$_{}$	None	None	✓				765.2.a.b	$1$	$1$	$-1$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-4q^{7}+3q^{8}+2q^{11}+\cdots$
3825.2.a.f	$3825$	$2$	3825.a	1.a	$1$	$1$	$1$	$30.543$	$\Q$	$_{}$	None	None	✓				425.2.a.b	$1$	$1$	$-1$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{7}+3q^{8}+4q^{11}-q^{13}+\cdots$
3825.2.a.g	$3825$	$2$	3825.a	1.a	$1$	$1$	$1$	$30.543$	$\Q$	$_{}$	None	None	✓				1275.2.a.c	$1$	$1$	$0$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{7}-2q^{11}+q^{13}+4q^{16}+\cdots$
3825.2.a.h	$3825$	$2$	3825.a	1.a	$1$	$1$	$1$	$30.543$	$\Q$	$_{}$	None	None	✓				1275.2.a.c	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{7}-2q^{11}-q^{13}+4q^{16}+\cdots$
3825.2.a.i	$3825$	$2$	3825.a	1.a	$1$	$1$	$1$	$30.543$	$\Q$	$_{}$	None	None	✓				51.2.a.a	$1$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+4q^{7}+3q^{11}+q^{13}+4q^{16}+\cdots$
3825.2.a.j	$3825$	$2$	3825.a	1.a	$1$	$1$	$1$	$30.543$	$\Q$	$_{}$	None	None	✓				765.2.a.b	$1$	$0$	$1$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-4q^{7}-3q^{8}-2q^{11}+\cdots$
3825.2.a.k	$3825$	$2$	3825.a	1.a	$1$	$1$	$1$	$30.543$	$\Q$	$_{}$	None	None	✓				425.2.a.b	$1$	$1$	$1$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{7}-3q^{8}+4q^{11}+q^{13}+\cdots$
3825.2.a.l	$3825$	$2$	3825.a	1.a	$1$	$1$	$1$	$30.543$	$\Q$	$_{}$	None	None	✓				85.2.a.a	$1$	$1$	$1$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+2q^{7}-3q^{8}-2q^{11}+\cdots$
3825.2.a.m	$3825$	$2$	3825.a	1.a	$1$	$1$	$1$	$30.543$	$\Q$	$_{}$	None	None	✓				255.2.b.a	$1$	$0$	$1$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+4q^{7}-3q^{8}-6q^{11}+\cdots$
3825.2.a.n	$3825$	$2$	3825.a	1.a	$1$	$1$	$1$	$30.543$	$\Q$	$_{}$	None	None	✓				1275.2.a.a	$1$	$1$	$2$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+q^{7}-2q^{11}-7q^{13}+\cdots$
3825.2.a.o	$3825$	$2$	3825.a	1.a	$1$	$1$	$1$	$30.543$	$\Q$	$_{}$	None	None	✓				153.2.a.a	$1$	$0$	$2$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+2q^{7}-3q^{11}+5q^{13}+\cdots$
3825.2.a.p	$3825$	$2$	3825.a	1.a	$1$	$2$	$2$	$30.543$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				85.2.a.b	$1$	$0$	$-2$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+(2-\beta )q^{7}+\cdots$
3825.2.a.q	$3825$	$2$	3825.a	1.a	$1$	$2$	$2$	$30.543$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				255.2.b.b	$1$	$1$	$-1$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+q^{7}+(-1+2\beta )q^{8}+\cdots$
3825.2.a.r	$3825$	$2$	3825.a	1.a	$1$	$2$	$2$	$30.543$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				765.2.a.e	$1$	$0$	$-1$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+(1+2\beta )q^{7}+\cdots$
3825.2.a.s	$3825$	$2$	3825.a	1.a	$1$	$2$	$2$	$30.543$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				51.2.a.b	$1$	$1$	$-1$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(2+\beta )q^{4}+(-4-\beta )q^{8}+(1+\cdots)q^{11}+\cdots$
3825.2.a.t	$3825$	$2$	3825.a	1.a	$1$	$2$	$2$	$30.543$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				1275.2.a.k	$1$	$0$	$0$	$0$	$0$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-3-\beta )q^{7}-2\beta q^{8}+(2-2\beta )q^{11}+\cdots$
3825.2.a.u	$3825$	$2$	3825.a	1.a	$1$	$2$	$2$	$30.543$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				1275.2.a.k	$1$	$0$	$0$	$0$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(3-\beta )q^{7}-2\beta q^{8}+(2+2\beta )q^{11}+\cdots$
3825.2.a.v	$3825$	$2$	3825.a	1.a	$1$	$2$	$2$	$30.543$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				85.2.a.c	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}+(1-\beta )q^{7}-\beta q^{8}+(-3+\cdots)q^{11}+\cdots$
3825.2.a.w	$3825$	$2$	3825.a	1.a	$1$	$2$	$2$	$30.543$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				255.2.b.b	$1$	$0$	$1$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}-q^{7}+(1-2\beta )q^{8}+\cdots$
3825.2.a.x	$3825$	$2$	3825.a	1.a	$1$	$2$	$2$	$30.543$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				765.2.a.e	$1$	$1$	$1$	$0$	$0$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+(1+2\beta )q^{7}+\cdots$
3825.2.a.y	$3825$	$2$	3825.a	1.a	$1$	$2$	$2$	$30.543$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓				255.2.a.a	$1$	$1$	$1$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{4}+(1-2\beta )q^{7}+3q^{8}+\cdots$
3825.2.a.z	$3825$	$2$	3825.a	1.a	$1$	$2$	$2$	$30.543$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓				255.2.a.b	$1$	$0$	$3$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+3\beta q^{4}+(-1+2\beta )q^{7}+\cdots$
3825.2.a.ba	$3825$	$2$	3825.a	1.a	$1$	$3$	$3$	$30.543$	3.3.148.1	$_{}$	None	None	✓				1275.2.a.o	$1$	$0$	$-2$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$

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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.