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 222 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
1872.1.i.a	$1872$	$1$	1872.i	52.b	$2$	$1$	$1$	$0.934$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-13}) $	$\Q(\sqrt{39}) $	✓	✓			1872.1.i.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-2q^{7}+q^{13}+2q^{19}+q^{25}+2q^{31}+\cdots$
1872.1.i.b	$1872$	$1$	1872.i	52.b	$2$	$1$	$1$	$0.934$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-13}) $	$\Q(\sqrt{13}) $	✓				208.1.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{13}+2q^{17}+q^{25}+2q^{29}-q^{49}+\cdots$
1872.1.i.c	$1872$	$1$	1872.i	52.b	$2$	$1$	$1$	$0.934$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-13}) $	$\Q(\sqrt{39}) $	✓	✓			1872.1.i.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+2q^{7}+q^{13}-2q^{19}+q^{25}-2q^{31}+\cdots$
1872.1.bb.a	$1872$	$1$	1872.bb	208.o	$4$	$8$	$4$	$0.934$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-39}) $	None		✓	✓	✓	1872.1.bb.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}+(\zeta_{16}^{5}+\zeta_{16}^{7}+\cdots)q^{5}+\cdots$
1872.1.bd.a	$1872$	$1$	1872.bd	13.d	$4$	$2$	$1$	$0.934$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None			✓	✓	117.1.j.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+(-i+1)q^{7}+i q^{13}+(i+1)q^{19}+\cdots$
1872.1.bg.a	$1872$	$1$	1872.bg	156.l	$4$	$4$	$2$	$0.934$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	1872.1.bg.a	$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q-\zeta_{8}^{3}q^{5}-q^{13}+(\zeta_{8}-\zeta_{8}^{3})q^{17}+\cdots$
1872.1.bs.a	$1872$	$1$	1872.bs	52.i	$6$	$2$	$1$	$0.934$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			1872.1.bs.a	$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{13}+\zeta_{6}^{2}q^{19}+q^{25}+\cdots$
1872.1.bs.b	$1872$	$1$	1872.bs	52.i	$6$	$2$	$1$	$0.934$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None					208.1.y.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{5}+\zeta_{6}q^{13}-\zeta_{6}^{2}q^{17}+\cdots$
1872.1.bs.c	$1872$	$1$	1872.bs	52.i	$6$	$2$	$1$	$0.934$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			1872.1.bs.a	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{13}-\zeta_{6}^{2}q^{19}+q^{25}+\cdots$
1872.1.bv.a	$1872$	$1$	1872.bv	39.i	$6$	$4$	$2$	$0.934$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None			✓	✓	468.1.r.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+\beta _{3}q^{5}+(1-\beta _{2})q^{7}+(\beta _{1}-\beta _{3})q^{11}+\cdots$
1872.1.cm.a	$1872$	$1$	1872.cm	117.n	$6$	$2$	$1$	$0.934$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{13}) $			✓	✓	468.1.z.a	$4$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{13}+(-\zeta_{6}+\cdots)q^{17}+\cdots$
1872.1.dc.a	$1872$	$1$	1872.dc	468.ag	$6$	$2$	$1$	$0.934$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{13}) $		✓			1872.1.dc.a	$4$	$0$	$0$	$-1$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{13}+q^{17}+\cdots$
1872.1.dc.b	$1872$	$1$	1872.dc	468.ag	$6$	$2$	$1$	$0.934$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{13}) $		✓			1872.1.dc.a	$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{13}+q^{17}+\cdots$
1872.1.dy.a	$1872$	$1$	1872.dy	52.j	$6$	$2$	$1$	$0.934$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			1872.1.dy.a	$4$	$0$	$0$	$0$	$0$	$-3$		$1$		$q+(-1-\zeta_{6})q^{7}-\zeta_{6}^{2}q^{13}-q^{25}+\cdots$
1872.1.dy.b	$1872$	$1$	1872.dy	52.j	$6$	$2$	$1$	$0.934$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		✓			1872.1.dy.a	$4$	$0$	$0$	$0$	$0$	$3$		$1$		$q+(1+\zeta_{6})q^{7}-\zeta_{6}^{2}q^{13}-q^{25}+(\zeta_{6}+\cdots)q^{31}+\cdots$
1872.1.dy.c	$1872$	$1$	1872.dy	52.j	$6$	$4$	$2$	$0.934$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-1}) $	None		✓	✓		1872.1.dy.c	$8$	$0$	$0$	$0$	$0$	$0$		$3$		$q+(\zeta_{12}-\zeta_{12}^{5})q^{5}-\zeta_{12}^{4}q^{13}+(-\zeta_{12}+\cdots)q^{17}+\cdots$
1872.1.fi.a	$1872$	$1$	1872.fi	117.y	$12$	$4$	$1$	$0.934$	$\Q(\zeta_{12})$	$S_{4}$	None	None					936.1.dm.b	$4$	$0$	$0$	$-2$	$2$	$0$		$1$		$q-\zeta_{12}^{2}q^{3}+(\zeta_{12}^{2}-\zeta_{12}^{5})q^{5}+\zeta_{12}^{4}q^{9}+\cdots$
1872.1.fi.b	$1872$	$1$	1872.fi	117.y	$12$	$4$	$1$	$0.934$	$\Q(\zeta_{12})$	$S_{4}$	None	None					936.1.dm.a	$4$	$0$	$0$	$2$	$0$	$2$		$1$		$q+\zeta_{12}^{2}q^{3}+(\zeta_{12}-\zeta_{12}^{4})q^{7}+\zeta_{12}^{4}q^{9}+\cdots$
1872.1.fr.a	$1872$	$1$	1872.fr	156.v	$12$	$8$	$2$	$0.934$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		✓	✓	✓	1872.1.fr.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}^{3}q^{5}-\zeta_{24}^{8}q^{13}+(\zeta_{24}^{9}-\zeta_{24}^{11}+\cdots)q^{17}+\cdots$
1872.1.gc.a	$1872$	$1$	1872.gc	13.f	$12$	$4$	$1$	$0.934$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None			✓	✓	468.1.cd.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+(-\zeta_{12}^{2}-\zeta_{12}^{3})q^{7}-\zeta_{12}q^{13}+\cdots$
1872.2.a.a	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	$\Q$	$_{}$	None	None	✓				468.2.a.a	$1$	$0$	$0$	$0$	$-4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}-4q^{7}-4q^{11}-q^{13}-8q^{23}+\cdots$
1872.2.a.b	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	$\Q$	$_{}$	None	None	✓				312.2.a.c	$1$	$0$	$0$	$0$	$-4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}-2q^{11}-q^{13}-2q^{17}-8q^{19}+\cdots$
1872.2.a.c	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	$\Q$	$_{}$	None	None	✓				78.2.a.a	$1$	$0$	$0$	$0$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-4q^{7}-4q^{11}+q^{13}-2q^{17}+\cdots$
1872.2.a.d	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	$\Q$	$_{}$	None	None	✓				936.2.a.c	$1$	$1$	$0$	$0$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-2q^{7}+4q^{11}-q^{13}+2q^{19}+\cdots$
1872.2.a.e	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	$\Q$	$_{}$	None	None	✓				312.2.a.f	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+q^{13}-2q^{17}+4q^{19}-q^{25}+\cdots$
1872.2.a.f	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	$\Q$	$_{}$	None	None	✓				52.2.a.a	$1$	$1$	$0$	$0$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+2q^{7}-2q^{11}-q^{13}-6q^{17}+\cdots$
1872.2.a.g	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	$\Q$	$_{}$	None	None	✓				234.2.a.a	$1$	$0$	$0$	$0$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+2q^{7}+4q^{11}-q^{13}+6q^{19}+\cdots$
1872.2.a.h	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	$\Q$	$_{}$	None	None	✓				39.2.a.a	$1$	$0$	$0$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+4q^{7}+4q^{11}+q^{13}-2q^{17}+\cdots$
1872.2.a.i	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	$\Q$	$_{}$	None	None	✓				156.2.a.b	$1$	$0$	$0$	$0$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}+q^{13}+6q^{17}-2q^{19}-5q^{25}+\cdots$
1872.2.a.j	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	$\Q$	$_{}$	None	None	✓				312.2.a.e	$1$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+6q^{11}-q^{13}-2q^{17}+4q^{23}-5q^{25}+\cdots$
1872.2.a.k	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	$\Q$	$_{}$	None	None	✓				312.2.a.b	$1$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{7}-2q^{11}-q^{13}+6q^{17}+4q^{19}+\cdots$
1872.2.a.l	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	$\Q$	$_{}$	None	None	✓				104.2.a.a	$1$	$0$	$0$	$0$	$1$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-5q^{7}-2q^{11}-q^{13}+3q^{17}+\cdots$
1872.2.a.m	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	$\Q$	$_{}$	None	None	✓				26.2.a.b	$1$	$1$	$0$	$0$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{7}-2q^{11}-q^{13}+3q^{17}+\cdots$
1872.2.a.n	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	$\Q$	$_{}$	None	None	✓				312.2.a.a	$1$	$1$	$0$	$0$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-4q^{7}+q^{13}-2q^{17}-8q^{19}+\cdots$
1872.2.a.o	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	$\Q$	$_{}$	None	None	✓				936.2.a.c	$1$	$1$	$0$	$0$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-2q^{7}-4q^{11}-q^{13}+2q^{19}+\cdots$
1872.2.a.p	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	$\Q$	$_{}$	None	None	✓				234.2.a.a	$1$	$0$	$0$	$0$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}+2q^{7}-4q^{11}-q^{13}+6q^{19}+\cdots$
1872.2.a.q	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	$\Q$	$_{}$	None	None	✓				26.2.a.a	$1$	$0$	$0$	$0$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+q^{7}+6q^{11}+q^{13}+3q^{17}+\cdots$
1872.2.a.r	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	$\Q$	$_{}$	None	None	✓				468.2.a.a	$1$	$0$	$0$	$0$	$4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}-4q^{7}+4q^{11}-q^{13}+8q^{23}+\cdots$
1872.2.a.s	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	$\Q$	$_{}$	None	None	✓				156.2.a.a	$1$	$0$	$0$	$0$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}+2q^{7}-4q^{11}+q^{13}-2q^{17}+\cdots$
1872.2.a.t	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	$\Q$	$_{}$	None	None	✓				312.2.a.d	$1$	$0$	$0$	$0$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}+4q^{7}-2q^{11}-q^{13}+6q^{17}+\cdots$
1872.2.a.u	$1872$	$2$	1872.a	1.a	$1$	$2$	$2$	$14.948$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓		✓		104.2.a.b	$1$	$1$	$0$	$0$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{5}+(1-\beta )q^{7}+(-2+2\beta )q^{11}+\cdots$
1872.2.a.v	$1872$	$2$	1872.a	1.a	$1$	$2$	$2$	$14.948$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓		✓	✓	117.2.a.b	$2$	$1$	$0$	$0$	$0$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q-2q^{7}-\beta q^{11}+q^{13}+2\beta q^{17}-2q^{19}+\cdots$
1872.2.a.w	$1872$	$2$	1872.a	1.a	$1$	$2$	$2$	$14.948$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓		✓		39.2.a.b	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{5}-\beta q^{7}-2q^{11}-q^{13}+(-2+\cdots)q^{17}+\cdots$
1872.2.a.x	$1872$	$2$	1872.a	1.a	$1$	$2$	$2$	$14.948$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				936.2.a.k	$1$	$0$	$0$	$0$	$0$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(2-\beta )q^{7}+(-2+\beta )q^{11}+\cdots$
1872.2.a.y	$1872$	$2$	1872.a	1.a	$1$	$2$	$2$	$14.948$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				936.2.a.k	$1$	$0$	$0$	$0$	$0$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(2+\beta )q^{7}+(2+\beta )q^{11}+q^{13}+\cdots$
1872.2.c.a	$1872$	$2$	1872.c	13.b	$2$	$2$	$2$	$14.948$	$\Q(\sqrt{-1}) $	$_{}$	None	None					312.2.c.b	$2$	$1$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}+\beta q^{7}-2\beta q^{11}+(\beta-3)q^{13}+\cdots$
1872.2.c.b	$1872$	$2$	1872.c	13.b	$2$	$2$	$2$	$14.948$	$\Q(\sqrt{-1}) $	$_{}$	None	None					78.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{5}-\beta q^{7}+(\beta-3)q^{13}+2 q^{17}+\cdots$
1872.2.c.c	$1872$	$2$	1872.c	13.b	$2$	$2$	$2$	$14.948$	$\Q(\sqrt{-3}) $	$_{}$	None	None					156.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{5}+\beta q^{11}+(\beta-1)q^{13}-6 q^{17}+\cdots$
1872.2.c.d	$1872$	$2$	1872.c	13.b	$2$	$2$	$2$	$14.948$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-3}) $	None					468.2.b.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{7}+(-\beta-1)q^{13}+\beta q^{19}+5 q^{25}+\cdots$
1872.2.c.e	$1872$	$2$	1872.c	13.b	$2$	$2$	$2$	$14.948$	$\Q(\sqrt{-3}) $	$_{}$	None	None					39.2.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{7}+\beta q^{11}+(-\beta-1)q^{13}+6 q^{17}+\cdots$

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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.