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 96 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
1664.1.h.a	$1664$	$1$	1664.h	104.h	$2$	$1$	$1$	$0.830$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-26}) $	$\Q(\sqrt{26}) $	✓	✓			1664.1.h.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-2q^{5}-q^{9}+q^{13}+2q^{17}+3q^{25}+\cdots$
1664.1.h.b	$1664$	$1$	1664.h	104.h	$2$	$1$	$1$	$0.830$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-26}) $	$\Q(\sqrt{26}) $	✓	✓			1664.1.h.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+2q^{5}-q^{9}-q^{13}+2q^{17}+3q^{25}+\cdots$
1664.1.h.c	$1664$	$1$	1664.h	104.h	$2$	$2$	$2$	$0.830$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-26}) $	None	✓	✓			1664.1.h.c	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\beta q^{3}-q^{5}-\beta q^{7}+2q^{9}-q^{13}+\cdots$
1664.1.h.d	$1664$	$1$	1664.h	104.h	$2$	$2$	$2$	$0.830$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-26}) $	None	✓	✓			1664.1.h.c	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\beta q^{3}+q^{5}+\beta q^{7}+2q^{9}+q^{13}+\cdots$
1664.1.h.e	$1664$	$1$	1664.h	104.h	$2$	$4$	$4$	$0.830$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-13}) $	None		✓	✓		1664.1.h.e	$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q+(-\zeta_{8}+\zeta_{8}^{3})q^{7}-q^{9}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{11}+\cdots$
1664.1.j.a	$1664$	$1$	1664.j	104.j	$4$	$2$	$1$	$0.830$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓			1664.1.j.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+(i-1)q^{5}+q^{9}-i q^{13}+2 i q^{17}+\cdots$
1664.1.j.b	$1664$	$1$	1664.j	104.j	$4$	$2$	$1$	$0.830$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		✓			1664.1.j.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+(-i+1)q^{5}+q^{9}+i q^{13}+2 i q^{17}+\cdots$
1664.1.j.c	$1664$	$1$	1664.j	104.j	$4$	$4$	$2$	$0.830$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓			1664.1.j.c	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{2}q^{3}-\zeta_{8}q^{5}-\zeta_{8}q^{7}+(-1+\zeta_{8}^{2}+\cdots)q^{11}+\cdots$
1664.1.j.d	$1664$	$1$	1664.j	104.j	$4$	$4$	$2$	$0.830$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓			1664.1.j.c	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{2}q^{3}-\zeta_{8}q^{5}+\zeta_{8}q^{7}+(1-\zeta_{8}^{2}+\cdots)q^{11}+\cdots$
1664.1.v.a	$1664$	$1$	1664.v	104.n	$6$	$2$	$1$	$0.830$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None		✓			1664.1.v.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{5}+\zeta_{6}q^{9}+\zeta_{6}^{2}q^{13}+\cdots$
1664.1.v.b	$1664$	$1$	1664.v	104.n	$6$	$2$	$1$	$0.830$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None		✓			1664.1.v.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{6}-\zeta_{6}^{2})q^{5}+\zeta_{6}q^{9}-\zeta_{6}^{2}q^{13}+\cdots$
1664.1.v.c	$1664$	$1$	1664.v	104.n	$6$	$8$	$4$	$0.830$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓	✓		1664.1.v.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$		$q+(\zeta_{24}^{5}+\zeta_{24}^{11})q^{3}-\zeta_{24}^{6}q^{5}-\zeta_{24}^{4}q^{9}+\cdots$
1664.1.x.a	$1664$	$1$	1664.x	104.p	$6$	$2$	$1$	$0.830$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None		✓			1664.1.x.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-q^{5}-\zeta_{6}^{2}q^{9}+\zeta_{6}q^{13}-\zeta_{6}^{2}q^{17}+\cdots$
1664.1.x.b	$1664$	$1$	1664.x	104.p	$6$	$2$	$1$	$0.830$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None		✓			1664.1.x.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+q^{5}-\zeta_{6}^{2}q^{9}-\zeta_{6}q^{13}-\zeta_{6}^{2}q^{17}+\cdots$
1664.1.bv.a	$1664$	$1$	1664.bv	104.x	$12$	$4$	$1$	$0.830$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		✓			1664.1.bv.a	$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+(\zeta_{12}^{4}+\zeta_{12}^{5})q^{5}-\zeta_{12}^{2}q^{9}-\zeta_{12}q^{13}+\cdots$
1664.1.bv.b	$1664$	$1$	1664.bv	104.x	$12$	$4$	$1$	$0.830$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		✓			1664.1.bv.a	$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+(-\zeta_{12}^{4}-\zeta_{12}^{5})q^{5}-\zeta_{12}^{2}q^{9}+\cdots$
1664.2.a.a	$1664$	$2$	1664.a	1.a	$1$	$1$	$1$	$13.287$	$\Q$	$_{}$	None	None	✓	✓			1664.2.a.a	$1$	$2$	$0$	$-3$	$-3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-3q^{5}-q^{7}+6q^{9}-4q^{11}+\cdots$
1664.2.a.b	$1664$	$2$	1664.a	1.a	$1$	$1$	$1$	$13.287$	$\Q$	$_{}$	None	None	✓	✓			1664.2.a.a	$1$	$1$	$0$	$-3$	$3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+3q^{5}+q^{7}+6q^{9}-4q^{11}+\cdots$
1664.2.a.c	$1664$	$2$	1664.a	1.a	$1$	$1$	$1$	$13.287$	$\Q$	$_{}$	None	None	✓	✓			1664.2.a.c	$1$	$1$	$0$	$-2$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{5}+2q^{7}+q^{9}-q^{13}+\cdots$
1664.2.a.d	$1664$	$2$	1664.a	1.a	$1$	$1$	$1$	$13.287$	$\Q$	$_{}$	None	None	✓	✓			1664.2.a.d	$1$	$0$	$0$	$-2$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{5}+4q^{7}+q^{9}-6q^{11}+\cdots$
1664.2.a.e	$1664$	$2$	1664.a	1.a	$1$	$1$	$1$	$13.287$	$\Q$	$_{}$	None	None	✓	✓			1664.2.a.d	$1$	$0$	$0$	$-2$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{5}-4q^{7}+q^{9}-6q^{11}+\cdots$
1664.2.a.f	$1664$	$2$	1664.a	1.a	$1$	$1$	$1$	$13.287$	$\Q$	$_{}$	None	None	✓	✓			1664.2.a.c	$1$	$1$	$0$	$-2$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{5}-2q^{7}+q^{9}+q^{13}+\cdots$
1664.2.a.g	$1664$	$2$	1664.a	1.a	$1$	$1$	$1$	$13.287$	$\Q$	$_{}$	None	None	✓	✓			1664.2.a.g	$1$	$0$	$0$	$-1$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-q^{7}-2q^{9}+q^{13}+q^{15}+\cdots$
1664.2.a.h	$1664$	$2$	1664.a	1.a	$1$	$1$	$1$	$13.287$	$\Q$	$_{}$	None	None	✓	✓			1664.2.a.h	$1$	$1$	$0$	$-1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-q^{7}-2q^{9}+4q^{11}+q^{13}+\cdots$
1664.2.a.i	$1664$	$2$	1664.a	1.a	$1$	$1$	$1$	$13.287$	$\Q$	$_{}$	None	None	✓	✓			1664.2.a.g	$1$	$1$	$0$	$-1$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{7}-2q^{9}-q^{13}-q^{15}+\cdots$
1664.2.a.j	$1664$	$2$	1664.a	1.a	$1$	$1$	$1$	$13.287$	$\Q$	$_{}$	None	None	✓	✓			1664.2.a.h	$1$	$0$	$0$	$-1$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{7}-2q^{9}+4q^{11}-q^{13}+\cdots$
1664.2.a.k	$1664$	$2$	1664.a	1.a	$1$	$1$	$1$	$13.287$	$\Q$	$_{}$	None	None	✓	✓			1664.2.a.h	$1$	$1$	$0$	$1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{7}-2q^{9}-4q^{11}+q^{13}+\cdots$
1664.2.a.l	$1664$	$2$	1664.a	1.a	$1$	$1$	$1$	$13.287$	$\Q$	$_{}$	None	None	✓	✓			1664.2.a.g	$1$	$1$	$0$	$1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{7}-2q^{9}+q^{13}-q^{15}+\cdots$
1664.2.a.m	$1664$	$2$	1664.a	1.a	$1$	$1$	$1$	$13.287$	$\Q$	$_{}$	None	None	✓	✓			1664.2.a.h	$1$	$1$	$0$	$1$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-q^{7}-2q^{9}-4q^{11}-q^{13}+\cdots$
1664.2.a.n	$1664$	$2$	1664.a	1.a	$1$	$1$	$1$	$13.287$	$\Q$	$_{}$	None	None	✓	✓			1664.2.a.g	$1$	$1$	$0$	$1$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-q^{7}-2q^{9}-q^{13}+q^{15}+\cdots$
1664.2.a.o	$1664$	$2$	1664.a	1.a	$1$	$1$	$1$	$13.287$	$\Q$	$_{}$	None	None	✓	✓			1664.2.a.d	$1$	$1$	$0$	$2$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{5}-4q^{7}+q^{9}+6q^{11}+\cdots$
1664.2.a.p	$1664$	$2$	1664.a	1.a	$1$	$1$	$1$	$13.287$	$\Q$	$_{}$	None	None	✓	✓			1664.2.a.c	$1$	$1$	$0$	$2$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{5}-2q^{7}+q^{9}-q^{13}+\cdots$
1664.2.a.q	$1664$	$2$	1664.a	1.a	$1$	$1$	$1$	$13.287$	$\Q$	$_{}$	None	None	✓	✓			1664.2.a.c	$1$	$0$	$0$	$2$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+2q^{5}+2q^{7}+q^{9}+q^{13}+\cdots$
1664.2.a.r	$1664$	$2$	1664.a	1.a	$1$	$1$	$1$	$13.287$	$\Q$	$_{}$	None	None	✓	✓			1664.2.a.d	$1$	$0$	$0$	$2$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+2q^{5}+4q^{7}+q^{9}+6q^{11}+\cdots$
1664.2.a.s	$1664$	$2$	1664.a	1.a	$1$	$1$	$1$	$13.287$	$\Q$	$_{}$	None	None	✓	✓			1664.2.a.a	$1$	$0$	$0$	$3$	$-3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-3q^{5}+q^{7}+6q^{9}+4q^{11}+\cdots$
1664.2.a.t	$1664$	$2$	1664.a	1.a	$1$	$1$	$1$	$13.287$	$\Q$	$_{}$	None	None	✓	✓			1664.2.a.a	$1$	$0$	$0$	$3$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+3q^{5}-q^{7}+6q^{9}+4q^{11}+\cdots$
1664.2.a.u	$1664$	$2$	1664.a	1.a	$1$	$2$	$2$	$13.287$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓	✓		1664.2.a.u	$1$	$1$	$0$	$-2$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+(-1+2\beta )q^{5}+(-1+\cdots)q^{7}+\cdots$
1664.2.a.v	$1664$	$2$	1664.a	1.a	$1$	$2$	$2$	$13.287$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1664.2.a.u	$1$	$0$	$0$	$-2$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+(1-2\beta )q^{5}+(1+\beta )q^{7}+\cdots$
1664.2.a.w	$1664$	$2$	1664.a	1.a	$1$	$2$	$2$	$13.287$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1664.2.a.u	$1$	$0$	$0$	$2$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-1-2\beta )q^{5}+(1-\beta )q^{7}+\cdots$
1664.2.a.x	$1664$	$2$	1664.a	1.a	$1$	$2$	$2$	$13.287$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓			1664.2.a.u	$1$	$0$	$0$	$2$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(1+2\beta )q^{5}+(-1+\beta )q^{7}+\cdots$
1664.2.a.y	$1664$	$2$	1664.a	1.a	$1$	$5$	$5$	$13.287$	5.5.592456.1	$_{}$	None	None	✓	✓	✓		1664.2.a.y	$1$	$1$	$0$	$-1$	$-1$	$-5$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}-\beta _{3}q^{5}+(-1-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$
1664.2.a.z	$1664$	$2$	1664.a	1.a	$1$	$5$	$5$	$13.287$	5.5.592456.1	$_{}$	None	None	✓	✓			1664.2.a.y	$1$	$0$	$0$	$-1$	$1$	$5$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+\beta _{3}q^{5}+(1+\beta _{2}-\beta _{3}-\beta _{4})q^{7}+\cdots$
1664.2.a.ba	$1664$	$2$	1664.a	1.a	$1$	$5$	$5$	$13.287$	5.5.592456.1	$_{}$	None	None	✓	✓	✓		1664.2.a.y	$1$	$0$	$0$	$1$	$-1$	$5$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}-\beta _{3}q^{5}+(1+\beta _{2}-\beta _{3}-\beta _{4})q^{7}+\cdots$
1664.2.a.bb	$1664$	$2$	1664.a	1.a	$1$	$5$	$5$	$13.287$	5.5.592456.1	$_{}$	None	None	✓	✓			1664.2.a.y	$1$	$0$	$0$	$1$	$1$	$-5$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+\beta _{3}q^{5}+(-1-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$
1664.2.b.a	$1664$	$2$	1664.b	8.b	$2$	$2$	$2$	$13.287$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1664.2.b.a	$2$	$0$	$0$	$0$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3 i q^{3}+i q^{5}-3 q^{7}-6 q^{9}-6 i q^{11}+\cdots$
1664.2.b.b	$1664$	$2$	1664.b	8.b	$2$	$2$	$2$	$13.287$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1664.2.b.b	$2$	$0$	$0$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+i q^{5}-q^{7}+2 q^{9}-2 i q^{11}+\cdots$
1664.2.b.c	$1664$	$2$	1664.b	8.b	$2$	$2$	$2$	$13.287$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1664.2.b.b	$2$	$0$	$0$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}-i q^{5}+q^{7}+2 q^{9}-2 i q^{11}+\cdots$
1664.2.b.d	$1664$	$2$	1664.b	8.b	$2$	$2$	$2$	$13.287$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1664.2.b.a	$2$	$0$	$0$	$0$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3 i q^{3}-i q^{5}+3 q^{7}-6 q^{9}-6 i q^{11}+\cdots$
1664.2.b.e	$1664$	$2$	1664.b	8.b	$2$	$4$	$4$	$13.287$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1664.2.b.e	$2$	$0$	$0$	$0$	$0$	$-4$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_1 q^{3}+(-\beta_{2}-\beta_1)q^{5}+(-\beta_{3}-1)q^{7}+\cdots$
1664.2.b.f	$1664$	$2$	1664.b	8.b	$2$	$4$	$4$	$13.287$	$\Q(\zeta_{8})$	$_{}$	None	None		✓			1664.2.b.f	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta_{2} q^{3}+2\beta_1 q^{5}+3\beta_{3} q^{7}+\cdots$

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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.