LMFDB - Newform search results

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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (50 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	3	17	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
5202.2.a.a	$5202$	$2$	5202.a	1.a	$1$	$1$	$1$	$41.538$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-4$	$3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-4q^{5}+3q^{7}-q^{8}+4q^{10}+\cdots$
5202.2.a.b	$5202$	$2$	5202.a	1.a	$1$	$1$	$1$	$41.538$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$-3$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-3q^{5}+4q^{7}-q^{8}+3q^{10}+\cdots$
5202.2.a.c	$5202$	$2$	5202.a	1.a	$1$	$1$	$1$	$41.538$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$-2$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}-4q^{11}+\cdots$
5202.2.a.d	$5202$	$2$	5202.a	1.a	$1$	$1$	$1$	$41.538$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{7}-q^{8}+6q^{11}+2q^{13}+\cdots$
5202.2.a.e	$5202$	$2$	5202.a	1.a	$1$	$1$	$1$	$41.538$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$3$	$-4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3q^{5}-4q^{7}-q^{8}-3q^{10}+\cdots$
5202.2.a.f	$5202$	$2$	5202.a	1.a	$1$	$1$	$1$	$41.538$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$4$	$-3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{5}-3q^{7}-q^{8}-4q^{10}+\cdots$
5202.2.a.g	$5202$	$2$	5202.a	1.a	$1$	$1$	$1$	$41.538$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-4$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-4q^{5}+2q^{7}+q^{8}-4q^{10}+\cdots$
5202.2.a.h	$5202$	$2$	5202.a	1.a	$1$	$1$	$1$	$41.538$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-2$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}+2q^{7}+q^{8}-2q^{10}+\cdots$
5202.2.a.i	$5202$	$2$	5202.a	1.a	$1$	$1$	$1$	$41.538$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-1$	$-4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots$
5202.2.a.j	$5202$	$2$	5202.a	1.a	$1$	$1$	$1$	$41.538$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{7}+q^{8}+2q^{13}-2q^{14}+\cdots$
5202.2.a.k	$5202$	$2$	5202.a	1.a	$1$	$1$	$1$	$41.538$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$-1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{7}+q^{8}-q^{13}-q^{14}+\cdots$
5202.2.a.l	$5202$	$2$	5202.a	1.a	$1$	$1$	$1$	$41.538$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{7}+q^{8}-q^{13}+q^{14}+\cdots$
5202.2.a.m	$5202$	$2$	5202.a	1.a	$1$	$1$	$1$	$41.538$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$1$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+4q^{7}+q^{8}+q^{10}+\cdots$
5202.2.a.n	$5202$	$2$	5202.a	1.a	$1$	$1$	$1$	$41.538$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$2$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}-2q^{7}+q^{8}+2q^{10}+\cdots$
5202.2.a.o	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$-2$	$0$	$-4$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-2+\beta )q^{5}+(2+2\beta )q^{7}+\cdots$
5202.2.a.p	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{33}) $	None	✓	$1$	$1$	$-2$	$0$	$-3$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1-\beta )q^{5}-\beta q^{7}-q^{8}+\cdots$
5202.2.a.q	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{6}) $	None	✓	$1$	$1$	$-2$	$0$	$0$	$-4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}+(-2+\beta )q^{7}-q^{8}+\cdots$
5202.2.a.r	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$-2$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2\beta q^{5}-\beta q^{7}-q^{8}-2\beta q^{10}+\cdots$
5202.2.a.s	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$-2$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2\beta q^{5}-3\beta q^{7}-q^{8}+\cdots$
5202.2.a.t	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$-2$	$0$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}-3\beta q^{7}-q^{8}-\beta q^{10}+\cdots$
5202.2.a.u	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$-2$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}-\beta q^{11}+\cdots$
5202.2.a.v	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$-2$	$0$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2\beta q^{5}+2\beta q^{7}-q^{8}+\cdots$
5202.2.a.w	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{33}) $	None	✓	$1$	$0$	$-2$	$0$	$3$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta )q^{5}+\beta q^{7}-q^{8}+\cdots$
5202.2.a.x	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$-2$	$0$	$4$	$-4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(2+\beta )q^{5}+(-2+2\beta )q^{7}+\cdots$
5202.2.a.y	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{33}) $	None	✓	$1$	$1$	$2$	$0$	$-3$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta )q^{5}+\beta q^{7}+q^{8}+\cdots$
5202.2.a.z	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{6}) $	None	✓	$1$	$0$	$2$	$0$	$0$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{5}+(-2-\beta )q^{7}+q^{8}+\cdots$
5202.2.a.ba	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$2$	$0$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2\beta q^{5}+\beta q^{7}+q^{8}+2\beta q^{10}+\cdots$
5202.2.a.bb	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$2$	$0$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}-4\beta q^{11}+\cdots$
5202.2.a.bc	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$2$	$0$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2\beta q^{5}+3\beta q^{7}+q^{8}+\cdots$
5202.2.a.bd	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$2$	$0$	$0$	$0$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{5}+3\beta q^{7}+q^{8}+\beta q^{10}+\cdots$
5202.2.a.be	$5202$	$2$	5202.a	1.a	$1$	$2$	$2$	$41.538$	$\Q(\sqrt{33}) $	None	✓	$1$	$0$	$2$	$0$	$3$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1+\beta )q^{5}-\beta q^{7}+q^{8}+\cdots$
5202.2.a.bf	$5202$	$2$	5202.a	1.a	$1$	$3$	$3$	$41.538$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$-3$	$0$	$-6$	$-3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-2+\beta _{1})q^{5}+(-1+2\beta _{1}+\cdots)q^{7}+\cdots$
5202.2.a.bg	$5202$	$2$	5202.a	1.a	$1$	$3$	$3$	$41.538$	$\Q(\zeta_{18})^+$	None	✓	$1$	$0$	$-3$	$0$	$-6$	$3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-2-\beta _{1})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots$
5202.2.a.bh	$5202$	$2$	5202.a	1.a	$1$	$3$	$3$	$41.538$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$-3$	$0$	$-6$	$3$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-2-\beta _{1})q^{5}+q^{7}-q^{8}+\cdots$
5202.2.a.bi	$5202$	$2$	5202.a	1.a	$1$	$3$	$3$	$41.538$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$-3$	$0$	$6$	$-3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(2+\beta _{1})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
5202.2.a.bj	$5202$	$2$	5202.a	1.a	$1$	$3$	$3$	$41.538$	$\Q(\zeta_{18})^+$	None	✓	$1$	$0$	$-3$	$0$	$6$	$-3$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(2+\beta _{1})q^{5}-q^{7}-q^{8}+\cdots$
5202.2.a.bk	$5202$	$2$	5202.a	1.a	$1$	$3$	$3$	$41.538$	$\Q(\zeta_{18})^+$	None	✓	$1$	$0$	$-3$	$0$	$6$	$3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(2-\beta _{1})q^{5}+(1-2\beta _{1}+\cdots)q^{7}+\cdots$
5202.2.a.bl	$5202$	$2$	5202.a	1.a	$1$	$3$	$3$	$41.538$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$3$	$0$	$-6$	$-3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-2-\beta _{1})q^{5}-q^{7}+q^{8}+\cdots$
5202.2.a.bm	$5202$	$2$	5202.a	1.a	$1$	$3$	$3$	$41.538$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$3$	$0$	$-6$	$3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-2+\beta _{1})q^{5}+(1+2\beta _{1}+\cdots)q^{7}+\cdots$
5202.2.a.bn	$5202$	$2$	5202.a	1.a	$1$	$3$	$3$	$41.538$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$3$	$0$	$0$	$-9$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+(-3+\cdots)q^{7}+\cdots$
5202.2.a.bo	$5202$	$2$	5202.a	1.a	$1$	$3$	$3$	$41.538$	$\Q(\zeta_{18})^+$	None	✓	$1$	$0$	$3$	$0$	$0$	$9$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-2\beta _{1}+\beta _{2})q^{5}+(3+\beta _{2})q^{7}+\cdots$
5202.2.a.bp	$5202$	$2$	5202.a	1.a	$1$	$3$	$3$	$41.538$	$\Q(\zeta_{18})^+$	None	✓	$1$	$0$	$3$	$0$	$6$	$-3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(2-\beta _{1})q^{5}+(-1-2\beta _{1}+\cdots)q^{7}+\cdots$
5202.2.a.bq	$5202$	$2$	5202.a	1.a	$1$	$3$	$3$	$41.538$	$\Q(\zeta_{18})^+$	None	✓	$1$	$0$	$3$	$0$	$6$	$3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(2+\beta _{1})q^{5}+q^{7}+q^{8}+\cdots$
5202.2.a.br	$5202$	$2$	5202.a	1.a	$1$	$4$	$4$	$41.538$	$\Q(\zeta_{16})^+$	None	✓	$1$	$1$	$-4$	$0$	$0$	$-8$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(\beta _{2}+\beta _{3})q^{5}+(-2+\beta _{2}+\cdots)q^{7}+\cdots$
5202.2.a.bs	$5202$	$2$	5202.a	1.a	$1$	$4$	$4$	$41.538$	$\Q(\zeta_{16})^+$	None	✓	$2$	$0$	$-4$	$0$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta _{1}q^{5}+2\beta _{3}q^{7}-q^{8}+\cdots$
5202.2.a.bt	$5202$	$2$	5202.a	1.a	$1$	$4$	$4$	$41.538$	$\Q(\zeta_{16})^+$	None	✓	$1$	$1$	$-4$	$0$	$0$	$8$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-\beta _{2}+\beta _{3})q^{5}+(2-\beta _{2}+\cdots)q^{7}+\cdots$
5202.2.a.bu	$5202$	$2$	5202.a	1.a	$1$	$4$	$4$	$41.538$	$\Q(\zeta_{16})^+$	None	✓	$1$	$0$	$4$	$0$	$-8$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-2-\beta _{2}+\beta _{3})q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots$
5202.2.a.bv	$5202$	$2$	5202.a	1.a	$1$	$4$	$4$	$41.538$	$\Q(\zeta_{16})^+$	None	✓	$2$	$1$	$4$	$0$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta _{1}q^{5}-2\beta _{3}q^{7}+q^{8}+\cdots$
5202.2.a.bw	$5202$	$2$	5202.a	1.a	$1$	$4$	$4$	$41.538$	$\Q(\zeta_{16})^+$	None	✓	$2$	$0$	$4$	$0$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2\beta _{1}q^{5}+2\beta _{3}q^{7}+q^{8}+\cdots$
5202.2.a.bx	$5202$	$2$	5202.a	1.a	$1$	$4$	$4$	$41.538$	$\Q(\zeta_{16})^+$	None	✓	$1$	$0$	$4$	$0$	$8$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(2+\beta _{2}+\beta _{3})q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots$

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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.