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 71 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
3248.1.k.a	$3248$	$1$	3248.k	203.c	$2$	$1$	$1$	$1.621$	$\Q$	$D_{3}$	$\Q(\sqrt{-203}) $	None	✓				812.1.g.a	$2$	$0$	$0$	$-1$	$0$	$-1$		$1$		$q-q^{3}-q^{7}-2q^{17}-q^{19}+q^{21}+\cdots$
3248.1.k.b	$3248$	$1$	3248.k	203.c	$2$	$1$	$1$	$1.621$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-203}) $	$\Q(\sqrt{29}) $	✓				203.1.c.a	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q+q^{7}-q^{9}+2q^{23}+q^{25}-q^{29}+\cdots$
3248.1.k.c	$3248$	$1$	3248.k	203.c	$2$	$1$	$1$	$1.621$	$\Q$	$D_{3}$	$\Q(\sqrt{-203}) $	None	✓				812.1.g.a	$2$	$0$	$0$	$1$	$0$	$-1$		$1$		$q+q^{3}-q^{7}+2q^{17}+q^{19}-q^{21}+\cdots$
3248.1.k.d	$3248$	$1$	3248.k	203.c	$2$	$2$	$2$	$1.621$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-203}) $	None	✓		✓		812.1.g.c	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-\beta q^{3}+q^{7}+2q^{9}+\beta q^{19}-\beta q^{21}+\cdots$
3248.1.s.a	$3248$	$1$	3248.s	3248.s	$4$	$2$	$1$	$1.621$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None		✓			3248.1.s.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q-i q^{2}-q^{4}+q^{7}+i q^{8}+q^{9}+\cdots$
3248.1.s.b	$3248$	$1$	3248.s	3248.s	$4$	$2$	$1$	$1.621$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None		✓			3248.1.s.b	$4$	$0$	$2$	$0$	$0$	$-2$		$1$		$q+q^{2}+q^{4}-q^{7}+q^{8}+q^{9}+2 i q^{11}+\cdots$
3248.1.bb.a	$3248$	$1$	3248.bb	3248.ab	$4$	$2$	$1$	$1.621$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None		✓			3248.1.bb.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-i q^{2}-q^{4}+i q^{7}+i q^{8}-i q^{9}+\cdots$
3248.1.bb.b	$3248$	$1$	3248.bb	3248.ab	$4$	$2$	$1$	$1.621$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None		✓			3248.1.bb.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+i q^{2}-q^{4}+i q^{7}-i q^{8}-i q^{9}+\cdots$
3248.1.bo.a	$3248$	$1$	3248.bo	3248.ao	$4$	$2$	$1$	$1.621$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None		✓			3248.1.s.a	$4$	$0$	$-2$	$0$	$0$	$2$		$1$		$q-q^{2}+q^{4}+q^{7}-q^{8}-q^{9}-q^{14}+\cdots$
3248.1.bo.b	$3248$	$1$	3248.bo	3248.ao	$4$	$2$	$1$	$1.621$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None		✓			3248.1.s.b	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+i q^{2}-q^{4}-q^{7}-i q^{8}-q^{9}+\cdots$
3248.1.bp.a	$3248$	$1$	3248.bp	812.n	$6$	$2$	$1$	$1.621$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{29}) $		✓			3248.1.bp.a	$4$	$0$	$0$	$0$	$1$	$-1$		$1$		$q+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}+\zeta_{6}q^{9}+q^{13}+\cdots$
3248.1.bp.b	$3248$	$1$	3248.bp	812.n	$6$	$2$	$1$	$1.621$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{29}) $		✓			3248.1.bp.a	$4$	$0$	$0$	$0$	$1$	$1$		$1$		$q+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+\zeta_{6}q^{9}+q^{13}+\cdots$
3248.1.bu.a	$3248$	$1$	3248.bu	203.i	$6$	$2$	$1$	$1.621$	$\Q(\sqrt{-3}) $	$D_{6}$	None	$\Q(\sqrt{29}) $			✓	✓	812.1.o.a	$4$	$0$	$0$	$0$	$-3$	$-1$		$1$		$q+(-1-\zeta_{6})q^{5}-\zeta_{6}q^{7}-\zeta_{6}^{2}q^{9}+\cdots$
3248.1.cw.a	$3248$	$1$	3248.cw	203.m	$12$	$4$	$1$	$1.621$	$\Q(\zeta_{12})$	$S_{4}$	None	None					1624.1.bu.a	$4$	$0$	$0$	$2$	$0$	$-2$		$1$		$q+(\zeta_{12}^{2}-\zeta_{12}^{5})q^{3}-\zeta_{12}q^{5}-\zeta_{12}^{2}q^{7}+\cdots$
3248.1.cw.b	$3248$	$1$	3248.cw	203.m	$12$	$4$	$1$	$1.621$	$\Q(\zeta_{12})$	$S_{4}$	None	None					812.1.x.a	$4$	$0$	$0$	$2$	$0$	$-2$		$1$		$q+(\zeta_{12}^{2}-\zeta_{12}^{5})q^{3}+\zeta_{12}q^{5}-\zeta_{12}^{2}q^{7}+\cdots$
3248.1.dj.a	$3248$	$1$	3248.dj	203.o	$14$	$6$	$1$	$1.621$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-7}) $	None			✓	✓	203.1.o.a	$4$	$0$	$0$	$0$	$0$	$-1$		$1$		$q+\zeta_{14}^{4}q^{7}+\zeta_{14}q^{9}+(1+\zeta_{14}^{5})q^{11}+\cdots$
3248.1.do.a	$3248$	$1$	3248.do	203.n	$14$	$6$	$1$	$1.621$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-7}) $	None			✓	✓	203.1.n.a	$4$	$0$	$0$	$0$	$0$	$1$		$1$		$q-\zeta_{14}^{4}q^{7}-\zeta_{14}q^{9}+(-1+\zeta_{14}^{5}+\cdots)q^{11}+\cdots$
3248.1.dt.a	$3248$	$1$	3248.dt	3248.ct	$28$	$12$	$1$	$1.621$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-7}) $	None		✓			3248.1.dt.a	$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+\zeta_{28}^{3}q^{2}+\zeta_{28}^{6}q^{4}-\zeta_{28}^{12}q^{7}+\cdots$
3248.1.dt.b	$3248$	$1$	3248.dt	3248.ct	$28$	$12$	$1$	$1.621$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-7}) $	None		✓			3248.1.dt.b	$4$	$0$	$2$	$0$	$0$	$-2$		$1$		$q+\zeta_{28}^{6}q^{2}+\zeta_{28}^{12}q^{4}+\zeta_{28}^{12}q^{7}+\cdots$
3248.1.ec.a	$3248$	$1$	3248.ec	3248.dc	$28$	$12$	$1$	$1.621$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-7}) $	None		✓			3248.1.ec.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{28}^{9}q^{2}-\zeta_{28}^{4}q^{4}+\zeta_{28}^{11}q^{7}+\cdots$
3248.1.ec.b	$3248$	$1$	3248.ec	3248.dc	$28$	$12$	$1$	$1.621$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-7}) $	None		✓			3248.1.ec.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{28}q^{2}+\zeta_{28}^{2}q^{4}+\zeta_{28}^{11}q^{7}+\cdots$
3248.1.ei.a	$3248$	$1$	3248.ei	3248.di	$28$	$12$	$1$	$1.621$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-7}) $	None		✓			3248.1.ei.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{28}^{5}q^{2}+\zeta_{28}^{10}q^{4}-\zeta_{28}^{13}q^{7}+\cdots$
3248.1.ei.b	$3248$	$1$	3248.ei	3248.di	$28$	$12$	$1$	$1.621$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-7}) $	None		✓			3248.1.ei.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{28}^{3}q^{2}+\zeta_{28}^{6}q^{4}-\zeta_{28}^{13}q^{7}+\cdots$
3248.1.ep.a	$3248$	$1$	3248.ep	3248.dp	$28$	$12$	$1$	$1.621$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-7}) $	None		✓			3248.1.dt.a	$4$	$0$	$-2$	$0$	$0$	$2$		$1$		$q+\zeta_{28}^{12}q^{2}-\zeta_{28}^{10}q^{4}+\zeta_{28}^{10}q^{7}+\cdots$
3248.1.ep.b	$3248$	$1$	3248.ep	3248.dp	$28$	$12$	$1$	$1.621$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-7}) $	None		✓			3248.1.dt.b	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-\zeta_{28}^{13}q^{2}-\zeta_{28}^{12}q^{4}-\zeta_{28}^{10}q^{7}+\cdots$
3248.2.a.a	$3248$	$2$	3248.a	1.a	$1$	$1$	$1$	$25.935$	$\Q$	$_{}$	None	None	✓				812.2.a.b	$1$	$1$	$0$	$-3$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+q^{7}+6q^{9}-2q^{11}+2q^{17}+\cdots$
3248.2.a.b	$3248$	$2$	3248.a	1.a	$1$	$1$	$1$	$25.935$	$\Q$	$_{}$	None	None	✓				1624.2.a.d	$1$	$1$	$0$	$-2$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{7}+q^{9}+4q^{13}+2q^{17}+\cdots$
3248.2.a.c	$3248$	$2$	3248.a	1.a	$1$	$1$	$1$	$25.935$	$\Q$	$_{}$	None	None	✓				406.2.a.c	$1$	$0$	$0$	$-2$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{5}-q^{7}+q^{9}-4q^{11}+\cdots$
3248.2.a.d	$3248$	$2$	3248.a	1.a	$1$	$1$	$1$	$25.935$	$\Q$	$_{}$	None	None	✓				203.2.a.c	$1$	$0$	$0$	$-2$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}+\cdots$
3248.2.a.e	$3248$	$2$	3248.a	1.a	$1$	$1$	$1$	$25.935$	$\Q$	$_{}$	None	None	✓				1624.2.a.e	$1$	$0$	$0$	$-2$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{5}+q^{7}+q^{9}+6q^{13}+\cdots$
3248.2.a.f	$3248$	$2$	3248.a	1.a	$1$	$1$	$1$	$25.935$	$\Q$	$_{}$	None	None	✓				406.2.a.b	$1$	$1$	$0$	$-1$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}-q^{7}-2q^{9}+3q^{11}+\cdots$
3248.2.a.g	$3248$	$2$	3248.a	1.a	$1$	$1$	$1$	$25.935$	$\Q$	$_{}$	None	None	✓				1624.2.a.c	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}-2q^{9}+6q^{11}+4q^{13}+\cdots$
3248.2.a.h	$3248$	$2$	3248.a	1.a	$1$	$1$	$1$	$25.935$	$\Q$	$_{}$	None	None	✓				1624.2.a.b	$1$	$0$	$0$	$0$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-q^{7}-3q^{9}+4q^{11}-2q^{13}+\cdots$
3248.2.a.i	$3248$	$2$	3248.a	1.a	$1$	$1$	$1$	$25.935$	$\Q$	$_{}$	None	None	✓				406.2.a.a	$1$	$1$	$0$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{7}-3q^{9}+4q^{11}-4q^{17}-4q^{19}+\cdots$
3248.2.a.j	$3248$	$2$	3248.a	1.a	$1$	$1$	$1$	$25.935$	$\Q$	$_{}$	None	None	✓				203.2.a.a	$1$	$0$	$0$	$1$	$-4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{5}-q^{7}-2q^{9}-2q^{11}+\cdots$
3248.2.a.k	$3248$	$2$	3248.a	1.a	$1$	$1$	$1$	$25.935$	$\Q$	$_{}$	None	None	✓				406.2.a.d	$1$	$0$	$0$	$1$	$-3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}+q^{7}-2q^{9}+q^{11}-q^{13}+\cdots$
3248.2.a.l	$3248$	$2$	3248.a	1.a	$1$	$1$	$1$	$25.935$	$\Q$	$_{}$	None	None	✓				812.2.a.a	$1$	$0$	$0$	$1$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-q^{7}-2q^{9}-q^{11}+q^{13}+\cdots$
3248.2.a.m	$3248$	$2$	3248.a	1.a	$1$	$1$	$1$	$25.935$	$\Q$	$_{}$	None	None	✓				203.2.a.b	$1$	$1$	$0$	$1$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-q^{7}-2q^{9}+5q^{11}-5q^{13}+\cdots$
3248.2.a.n	$3248$	$2$	3248.a	1.a	$1$	$1$	$1$	$25.935$	$\Q$	$_{}$	None	None	✓				1624.2.a.a	$1$	$1$	$0$	$2$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{5}-q^{7}+q^{9}+2q^{13}+\cdots$
3248.2.a.o	$3248$	$2$	3248.a	1.a	$1$	$2$	$2$	$25.935$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				406.2.a.e	$1$	$1$	$0$	$-4$	$2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+(1+\beta )q^{5}+q^{7}+q^{9}+2\beta q^{11}+\cdots$
3248.2.a.p	$3248$	$2$	3248.a	1.a	$1$	$2$	$2$	$25.935$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓				203.2.a.e	$1$	$0$	$0$	$-2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+2\beta q^{5}+q^{7}-2\beta q^{9}+\cdots$
3248.2.a.q	$3248$	$2$	3248.a	1.a	$1$	$2$	$2$	$25.935$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓				1624.2.a.f	$1$	$1$	$0$	$0$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}+q^{7}+(-2-\beta )q^{11}+\cdots$
3248.2.a.r	$3248$	$2$	3248.a	1.a	$1$	$2$	$2$	$25.935$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓				203.2.a.d	$1$	$0$	$0$	$1$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(2-\beta )q^{5}+q^{7}+(1+\beta )q^{9}+\cdots$
3248.2.a.s	$3248$	$2$	3248.a	1.a	$1$	$2$	$2$	$25.935$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓				812.2.a.c	$1$	$1$	$0$	$2$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1+\beta )q^{5}+q^{7}-2q^{9}+(-1+\cdots)q^{11}+\cdots$
3248.2.a.t	$3248$	$2$	3248.a	1.a	$1$	$3$	$3$	$25.935$	3.3.148.1	$_{}$	None	None	✓				1624.2.a.g	$1$	$1$	$0$	$-1$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}-q^{7}+(-1+\cdots)q^{9}+\cdots$
3248.2.a.u	$3248$	$2$	3248.a	1.a	$1$	$3$	$3$	$25.935$	3.3.568.1	$_{}$	None	None	✓				406.2.a.f	$1$	$0$	$0$	$-1$	$5$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(2-\beta _{1})q^{5}+q^{7}+(3-2\beta _{1}+\cdots)q^{9}+\cdots$
3248.2.a.v	$3248$	$2$	3248.a	1.a	$1$	$3$	$3$	$25.935$	3.3.148.1	$_{}$	None	None	✓		✓		203.2.a.f	$1$	$1$	$0$	$3$	$-5$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+(-2+\beta _{1}+\beta _{2})q^{5}+\cdots$
3248.2.a.w	$3248$	$2$	3248.a	1.a	$1$	$4$	$4$	$25.935$	4.4.7232.1	$_{}$	None	None	✓		✓		1624.2.a.j	$1$	$1$	$0$	$-2$	$2$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{5}+q^{7}+(\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots$
3248.2.a.x	$3248$	$2$	3248.a	1.a	$1$	$4$	$4$	$25.935$	4.4.11348.1	$_{}$	None	None	✓				406.2.a.g	$1$	$1$	$0$	$-1$	$-1$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+\beta _{1}q^{5}-q^{7}+(2-\beta _{1}+\beta _{3})q^{9}+\cdots$
3248.2.a.y	$3248$	$2$	3248.a	1.a	$1$	$4$	$4$	$25.935$	4.4.20308.1	$_{}$	None	None	✓		✓		1624.2.a.i	$1$	$1$	$0$	$1$	$3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}+(1-\beta _{1})q^{5}-q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots$

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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.