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 128 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
1400.1.c.a	$1400$	$1$	1400.c	280.c	$2$	$2$	$2$	$0.699$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-14}) $	$\Q(\sqrt{2}) $					56.1.h.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{2}-q^{4}-i q^{7}+i q^{8}+q^{9}+\cdots$
1400.1.c.b	$1400$	$1$	1400.c	280.c	$2$	$4$	$4$	$0.699$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-7}) $	None		✓	✓		1400.1.m.c	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{7}-\zeta_{12}^{3}q^{8}+\cdots$
1400.1.m.a	$1400$	$1$	1400.m	56.h	$2$	$1$	$1$	$0.699$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-14}) $	$\Q(\sqrt{2}) $	✓				56.1.h.a	$4$	$0$	$1$	$0$	$0$	$1$		$1$		$q+q^{2}+q^{4}+q^{7}+q^{8}-q^{9}+q^{14}+\cdots$
1400.1.m.b	$1400$	$1$	1400.m	56.h	$2$	$2$	$2$	$0.699$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-14}) $	None	✓				280.1.c.a	$4$	$0$	$-2$	$0$	$0$	$2$		$1$		$q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}+q^{7}-q^{8}+\cdots$
1400.1.m.c	$1400$	$1$	1400.m	56.h	$2$	$2$	$2$	$0.699$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-7}) $	None		✓			1400.1.m.c	$4$	$0$	$-1$	$0$	$0$	$2$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{7}+q^{8}-q^{9}+\cdots$
1400.1.m.d	$1400$	$1$	1400.m	56.h	$2$	$2$	$2$	$0.699$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-7}) $	None		✓			1400.1.m.c	$4$	$0$	$1$	$0$	$0$	$-2$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{7}-q^{8}-q^{9}+\cdots$
1400.1.m.e	$1400$	$1$	1400.m	56.h	$2$	$2$	$2$	$0.699$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-14}) $	None	✓				280.1.c.a	$4$	$0$	$2$	$0$	$0$	$-2$		$1$		$q+q^{2}-\beta q^{3}+q^{4}-\beta q^{6}-q^{7}+q^{8}+\cdots$
1400.1.y.a	$1400$	$1$	1400.y	280.y	$4$	$4$	$2$	$0.699$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-10}) $	$\Q(\sqrt{70}) $		✓			1400.1.y.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}-\zeta_{8}q^{8}+\cdots$
1400.1.y.b	$1400$	$1$	1400.y	280.y	$4$	$8$	$4$	$0.699$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-7}) $	None		✓	✓		1400.1.y.b	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{3}q^{7}+\cdots$
1400.1.ba.a	$1400$	$1$	1400.ba	56.k	$6$	$4$	$2$	$0.699$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-10}) $	None			✓	✓	280.1.bi.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{3}q^{7}+\cdots$
1400.1.bf.a	$1400$	$1$	1400.bf	56.j	$6$	$2$	$1$	$0.699$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{2}) $		✓			1400.1.bf.a	$4$	$0$	$-1$	$0$	$0$	$-1$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{7}+q^{8}+\cdots$
1400.1.bf.b	$1400$	$1$	1400.bf	56.j	$6$	$2$	$1$	$0.699$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{2}) $		✓			1400.1.bf.a	$4$	$0$	$1$	$0$	$0$	$1$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{7}-q^{8}+\cdots$
1400.1.bl.a	$1400$	$1$	1400.bl	280.ak	$6$	$4$	$2$	$0.699$	$\Q(\zeta_{12})$	$D_{6}$	None	$\Q(\sqrt{2}) $		✓	✓	✓	1400.1.bf.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{5}q^{7}+\cdots$
1400.1.bs.a	$1400$	$1$	1400.bs	1400.as	$10$	$4$	$1$	$0.699$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-14}) $	None		✓			1400.1.bs.a	$4$	$0$	$-1$	$-3$	$1$	$4$		$1$		$q+\zeta_{10}^{4}q^{2}+(-1+\zeta_{10})q^{3}-\zeta_{10}^{3}q^{4}+\cdots$
1400.1.bs.b	$1400$	$1$	1400.bs	1400.as	$10$	$4$	$1$	$0.699$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-14}) $	None		✓			1400.1.bs.a	$4$	$0$	$-1$	$3$	$-1$	$4$		$1$		$q+\zeta_{10}^{4}q^{2}+(1-\zeta_{10})q^{3}-\zeta_{10}^{3}q^{4}+\cdots$
1400.1.bs.c	$1400$	$1$	1400.bs	1400.as	$10$	$8$	$2$	$0.699$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-14}) $	None		✓	✓		1400.1.bs.c	$8$	$0$	$2$	$0$	$0$	$-8$		$1$		$q-\zeta_{20}^{8}q^{2}+(\zeta_{20}^{5}+\zeta_{20}^{7})q^{3}-\zeta_{20}^{6}q^{4}+\cdots$
1400.1.cc.a	$1400$	$1$	1400.cc	1400.bc	$10$	$16$	$4$	$0.699$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-14}) $	None		✓	✓	✓	1400.1.cc.a	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{40}^{6}q^{2}+(\zeta_{40}^{9}-\zeta_{40}^{15})q^{3}+\zeta_{40}^{12}q^{4}+\cdots$
1400.1.cf.a	$1400$	$1$	1400.cf	280.ap	$12$	$8$	$2$	$0.699$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-10}) $	None		✓	✓	✓	1400.1.cf.a	$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{11}q^{2}-\zeta_{24}^{10}q^{4}-\zeta_{24}^{3}q^{7}+\cdots$
1400.2.a.a	$1400$	$2$	1400.a	1.a	$1$	$1$	$1$	$11.179$	$\Q$	$_{}$	None	None	✓				56.2.a.b	$1$	$0$	$0$	$-2$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{7}+q^{9}+2q^{17}-2q^{19}+\cdots$
1400.2.a.b	$1400$	$2$	1400.a	1.a	$1$	$1$	$1$	$11.179$	$\Q$	$_{}$	None	None	✓	✓			1400.2.a.b	$1$	$1$	$0$	$-2$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{7}+q^{9}+5q^{11}-8q^{17}+\cdots$
1400.2.a.c	$1400$	$2$	1400.a	1.a	$1$	$1$	$1$	$11.179$	$\Q$	$_{}$	None	None	✓	✓			1400.2.a.c	$1$	$1$	$0$	$-2$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{7}+q^{9}+q^{11}-4q^{13}+\cdots$
1400.2.a.d	$1400$	$2$	1400.a	1.a	$1$	$1$	$1$	$11.179$	$\Q$	$_{}$	None	None	✓				280.2.g.a	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}-2q^{9}-q^{11}+q^{13}+3q^{17}+\cdots$
1400.2.a.e	$1400$	$2$	1400.a	1.a	$1$	$1$	$1$	$11.179$	$\Q$	$_{}$	None	None	✓	✓			1400.2.a.e	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}-2q^{9}-q^{11}+6q^{13}+\cdots$
1400.2.a.f	$1400$	$2$	1400.a	1.a	$1$	$1$	$1$	$11.179$	$\Q$	$_{}$	None	None	✓	✓			1400.2.a.f	$1$	$0$	$0$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{7}-3q^{9}+q^{11}+2q^{13}+4q^{17}+\cdots$
1400.2.a.g	$1400$	$2$	1400.a	1.a	$1$	$1$	$1$	$11.179$	$\Q$	$_{}$	None	None	✓				56.2.a.a	$1$	$0$	$0$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-3q^{9}-4q^{11}-2q^{13}+6q^{17}+\cdots$
1400.2.a.h	$1400$	$2$	1400.a	1.a	$1$	$1$	$1$	$11.179$	$\Q$	$_{}$	None	None	✓	✓			1400.2.a.f	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-3q^{9}+q^{11}-2q^{13}-4q^{17}+\cdots$
1400.2.a.i	$1400$	$2$	1400.a	1.a	$1$	$1$	$1$	$11.179$	$\Q$	$_{}$	None	None	✓	✓			1400.2.a.e	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}-2q^{9}-q^{11}-6q^{13}+\cdots$
1400.2.a.j	$1400$	$2$	1400.a	1.a	$1$	$1$	$1$	$11.179$	$\Q$	$_{}$	None	None	✓				280.2.g.a	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}-2q^{9}-q^{11}-q^{13}-3q^{17}+\cdots$
1400.2.a.k	$1400$	$2$	1400.a	1.a	$1$	$1$	$1$	$11.179$	$\Q$	$_{}$	None	None	✓				280.2.a.b	$1$	$1$	$0$	$1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}-2q^{9}-5q^{11}-q^{13}+\cdots$
1400.2.a.l	$1400$	$2$	1400.a	1.a	$1$	$1$	$1$	$11.179$	$\Q$	$_{}$	None	None	✓	✓			1400.2.a.c	$1$	$0$	$0$	$2$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{7}+q^{9}+q^{11}+4q^{13}+\cdots$
1400.2.a.m	$1400$	$2$	1400.a	1.a	$1$	$1$	$1$	$11.179$	$\Q$	$_{}$	None	None	✓	✓			1400.2.a.b	$1$	$0$	$0$	$2$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{7}+q^{9}+5q^{11}+8q^{17}+\cdots$
1400.2.a.n	$1400$	$2$	1400.a	1.a	$1$	$1$	$1$	$11.179$	$\Q$	$_{}$	None	None	✓				280.2.a.a	$1$	$0$	$0$	$3$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-q^{7}+6q^{9}-5q^{11}+5q^{13}+\cdots$
1400.2.a.o	$1400$	$2$	1400.a	1.a	$1$	$2$	$2$	$11.179$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓			1400.2.a.o	$1$	$1$	$0$	$-1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}-q^{7}+(1+\beta )q^{9}+(-3+2\beta )q^{11}+\cdots$
1400.2.a.p	$1400$	$2$	1400.a	1.a	$1$	$2$	$2$	$11.179$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				280.2.a.d	$1$	$1$	$0$	$-1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}-q^{7}+(1+\beta )q^{9}-\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
1400.2.a.q	$1400$	$2$	1400.a	1.a	$1$	$2$	$2$	$11.179$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	✓			1400.2.a.o	$1$	$0$	$0$	$1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+q^{7}+(1+\beta )q^{9}+(-3+2\beta )q^{11}+\cdots$
1400.2.a.r	$1400$	$2$	1400.a	1.a	$1$	$2$	$2$	$11.179$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓		✓		280.2.a.c	$1$	$0$	$0$	$1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+q^{7}+(5+\beta )q^{9}+(4-\beta )q^{11}+\cdots$
1400.2.a.s	$1400$	$2$	1400.a	1.a	$1$	$3$	$3$	$11.179$	3.3.568.1	$_{}$	None	None	✓		✓		280.2.g.b	$1$	$0$	$0$	$-1$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+q^{7}+(1+2\beta _{1}+\beta _{2})q^{9}+\cdots$
1400.2.a.t	$1400$	$2$	1400.a	1.a	$1$	$3$	$3$	$11.179$	3.3.568.1	$_{}$	None	None	✓		✓		280.2.g.b	$1$	$0$	$0$	$1$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-q^{7}+(1+2\beta _{1}+\beta _{2})q^{9}+\cdots$
1400.2.g.a	$1400$	$2$	1400.g	5.b	$2$	$2$	$2$	$11.179$	$\Q(\sqrt{-1}) $	$_{}$	None	None					280.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3 i q^{3}+i q^{7}-6 q^{9}-5 q^{11}+\cdots$
1400.2.g.b	$1400$	$2$	1400.g	5.b	$2$	$2$	$2$	$11.179$	$\Q(\sqrt{-1}) $	$_{}$	None	None					56.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{3}-i q^{7}-q^{9}+2 i q^{17}+\cdots$
1400.2.g.c	$1400$	$2$	1400.g	5.b	$2$	$2$	$2$	$11.179$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1400.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{3}+i q^{7}-q^{9}+q^{11}+4 i q^{13}+\cdots$
1400.2.g.d	$1400$	$2$	1400.g	5.b	$2$	$2$	$2$	$11.179$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1400.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2 i q^{3}-i q^{7}-q^{9}+5 q^{11}-8 i q^{17}+\cdots$
1400.2.g.e	$1400$	$2$	1400.g	5.b	$2$	$2$	$2$	$11.179$	$\Q(\sqrt{-1}) $	$_{}$	None	None					280.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}-i q^{7}+2 q^{9}-5 q^{11}-i q^{13}+\cdots$
1400.2.g.f	$1400$	$2$	1400.g	5.b	$2$	$2$	$2$	$11.179$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1400.2.a.e	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+i q^{7}+2 q^{9}-q^{11}-6 i q^{13}+\cdots$
1400.2.g.g	$1400$	$2$	1400.g	5.b	$2$	$2$	$2$	$11.179$	$\Q(\sqrt{-1}) $	$_{}$	None	None					56.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{7}+3 q^{9}-4 q^{11}+2 i q^{13}+\cdots$
1400.2.g.h	$1400$	$2$	1400.g	5.b	$2$	$2$	$2$	$11.179$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1400.2.a.f	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{7}+3 q^{9}+q^{11}-2 i q^{13}+4 i q^{17}+\cdots$
1400.2.g.i	$1400$	$2$	1400.g	5.b	$2$	$4$	$4$	$11.179$	$\Q(i, \sqrt{33})$	$_{}$	None	None					280.2.a.c	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{2}q^{7}+(-6+\beta _{3})q^{9}+(3+\cdots)q^{11}+\cdots$
1400.2.g.j	$1400$	$2$	1400.g	5.b	$2$	$4$	$4$	$11.179$	$\Q(i, \sqrt{17})$	$_{}$	None	None		✓			1400.2.a.o	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{2}q^{7}+(-2+\beta _{3})q^{9}+(-1+\cdots)q^{11}+\cdots$
1400.2.g.k	$1400$	$2$	1400.g	5.b	$2$	$4$	$4$	$11.179$	$\Q(i, \sqrt{17})$	$_{}$	None	None					280.2.a.d	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{2}q^{7}+(-2+\beta _{3})q^{9}+(-1+\cdots)q^{11}+\cdots$
1400.2.q.a	$1400$	$2$	1400.q	7.c	$3$	$2$	$1$	$11.179$	$\Q(\sqrt{-3}) $	$_{}$	None	None					280.2.q.c	$2$	$0$	$0$	$-2$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{3}+(-3+2\zeta_{6})q^{7}+\cdots$

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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.