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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 (1-50 of 71 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	23	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4416.2.a.a	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	$\Q$	None	✓	$1$	$2$	$0$	$-1$	$-4$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{5}-2q^{7}+q^{9}-2q^{13}+\cdots$
4416.2.a.b	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$-4$	$4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{5}+4q^{7}+q^{9}+6q^{11}+\cdots$
4416.2.a.c	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-2$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+q^{9}+2q^{13}+2q^{15}+\cdots$
4416.2.a.d	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-2$	$2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+2q^{7}+q^{9}+2q^{11}+\cdots$
4416.2.a.e	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$-2$	$4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots$
4416.2.a.f	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots$
4416.2.a.g	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$-2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots$
4416.2.a.h	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}+2q^{11}+2q^{13}-6q^{17}+\cdots$
4416.2.a.i	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}+q^{9}-2q^{13}-2q^{19}+\cdots$
4416.2.a.j	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$0$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}+q^{9}-2q^{13}+8q^{17}+\cdots$
4416.2.a.k	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$2$	$-4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}-4q^{7}+q^{9}+2q^{13}+\cdots$
4416.2.a.l	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$2$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}-2q^{7}+q^{9}-2q^{11}+\cdots$
4416.2.a.m	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$2$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+2q^{7}+q^{9}-6q^{11}+\cdots$
4416.2.a.n	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$2$	$2$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+2q^{7}+q^{9}-2q^{11}+\cdots$
4416.2.a.o	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	$\Q$	None	✓	$1$	$2$	$0$	$1$	$-4$	$-4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{5}-4q^{7}+q^{9}-6q^{11}+\cdots$
4416.2.a.p	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-4$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{5}+2q^{7}+q^{9}-2q^{13}+\cdots$
4416.2.a.q	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-2$	$-4$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots$
4416.2.a.r	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-2$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-2q^{7}+q^{9}-2q^{11}+\cdots$
4416.2.a.s	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-2$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{9}+2q^{13}-2q^{15}+\cdots$
4416.2.a.t	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$-2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}+q^{9}-2q^{13}+2q^{19}+\cdots$
4416.2.a.u	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}+q^{9}-2q^{13}+8q^{17}+\cdots$
4416.2.a.v	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}-2q^{11}+2q^{13}-6q^{17}+\cdots$
4416.2.a.w	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots$
4416.2.a.x	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots$
4416.2.a.y	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$2$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}-2q^{7}+q^{9}+2q^{11}+\cdots$
4416.2.a.z	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$2$	$-2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}-2q^{7}+q^{9}+6q^{11}+\cdots$
4416.2.a.ba	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$2$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+2q^{7}+q^{9}+2q^{11}+\cdots$
4416.2.a.bb	$4416$	$2$	4416.a	1.a	$1$	$1$	$1$	$35.262$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$2$	$4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+4q^{7}+q^{9}+2q^{13}+\cdots$
4416.2.a.bc	$4416$	$2$	4416.a	1.a	$1$	$2$	$2$	$35.262$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$-2$	$-4$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-2+\beta )q^{5}-\beta q^{7}+q^{9}-4\beta q^{11}+\cdots$
4416.2.a.bd	$4416$	$2$	4416.a	1.a	$1$	$2$	$2$	$35.262$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$-2$	$-2$	$4$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta )q^{5}+2q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
4416.2.a.be	$4416$	$2$	4416.a	1.a	$1$	$2$	$2$	$35.262$	$\Q(\sqrt{10}) $	None	✓	$1$	$1$	$0$	$-2$	$0$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}+(-2-\beta )q^{7}+q^{9}-4q^{13}+\cdots$
4416.2.a.bf	$4416$	$2$	4416.a	1.a	$1$	$2$	$2$	$35.262$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$-2$	$2$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta )q^{5}+(-1+\beta )q^{7}+q^{9}+\cdots$
4416.2.a.bg	$4416$	$2$	4416.a	1.a	$1$	$2$	$2$	$35.262$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$-2$	$2$	$-2$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta )q^{5}+(-1+\beta )q^{7}+q^{9}+\cdots$
4416.2.a.bh	$4416$	$2$	4416.a	1.a	$1$	$2$	$2$	$35.262$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$0$	$-2$	$2$	$0$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta )q^{5}+2\beta q^{7}+q^{9}+(3+\cdots)q^{11}+\cdots$
4416.2.a.bi	$4416$	$2$	4416.a	1.a	$1$	$2$	$2$	$35.262$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$2$	$-4$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-2+\beta )q^{5}+\beta q^{7}+q^{9}+4\beta q^{11}+\cdots$
4416.2.a.bj	$4416$	$2$	4416.a	1.a	$1$	$2$	$2$	$35.262$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$2$	$-2$	$-4$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta )q^{5}-2q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots$
4416.2.a.bk	$4416$	$2$	4416.a	1.a	$1$	$2$	$2$	$35.262$	$\Q(\sqrt{10}) $	None	✓	$1$	$0$	$0$	$2$	$0$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}+(2+\beta )q^{7}+q^{9}-4q^{13}+\cdots$
4416.2.a.bl	$4416$	$2$	4416.a	1.a	$1$	$2$	$2$	$35.262$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$2$	$2$	$0$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta )q^{5}-2\beta q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots$
4416.2.a.bm	$4416$	$2$	4416.a	1.a	$1$	$2$	$2$	$35.262$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$2$	$2$	$2$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta )q^{5}+(1-\beta )q^{7}+q^{9}+\cdots$
4416.2.a.bn	$4416$	$2$	4416.a	1.a	$1$	$2$	$2$	$35.262$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$2$	$2$	$2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta )q^{5}+(1-\beta )q^{7}+q^{9}+\cdots$
4416.2.a.bo	$4416$	$2$	4416.a	1.a	$1$	$3$	$3$	$35.262$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$0$	$-3$	$-2$	$2$	$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta _{1})q^{5}+(1-\beta _{2})q^{7}+\cdots$
4416.2.a.bp	$4416$	$2$	4416.a	1.a	$1$	$3$	$3$	$35.262$	3.3.148.1	None	✓	$1$	$1$	$0$	$-3$	$0$	$2$	$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{2}q^{5}+(1+\beta _{1})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
4416.2.a.bq	$4416$	$2$	4416.a	1.a	$1$	$3$	$3$	$35.262$	3.3.148.1	None	✓	$1$	$0$	$0$	$-3$	$4$	$-2$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta _{1})q^{5}+(-1+\beta _{2})q^{7}+\cdots$
4416.2.a.br	$4416$	$2$	4416.a	1.a	$1$	$3$	$3$	$35.262$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$0$	$3$	$-2$	$-2$	$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta _{1})q^{5}+(-1+\beta _{2})q^{7}+\cdots$
4416.2.a.bs	$4416$	$2$	4416.a	1.a	$1$	$3$	$3$	$35.262$	3.3.148.1	None	✓	$1$	$0$	$0$	$3$	$0$	$-2$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{3}-\beta _{2}q^{5}+(-1-\beta _{1})q^{7}+q^{9}+\cdots$
4416.2.a.bt	$4416$	$2$	4416.a	1.a	$1$	$3$	$3$	$35.262$	3.3.148.1	None	✓	$1$	$0$	$0$	$3$	$4$	$2$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta _{1})q^{5}+(1-\beta _{2})q^{7}+q^{9}+\cdots$
4416.2.a.bu	$4416$	$2$	4416.a	1.a	$1$	$4$	$4$	$35.262$	4.4.19796.1	None	✓	$1$	$0$	$0$	$-4$	$2$	$0$	$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta _{1})q^{5}-\beta _{3}q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
4416.2.a.bv	$4416$	$2$	4416.a	1.a	$1$	$4$	$4$	$35.262$	4.4.19796.1	None	✓	$1$	$0$	$0$	$4$	$2$	$0$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta _{1})q^{5}+\beta _{3}q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots$
4416.2.a.bw	$4416$	$2$	4416.a	1.a	$1$	$5$	$5$	$35.262$	5.5.218524.1	None	✓	$1$	$0$	$0$	$-5$	$2$	$4$	$+$	$+$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{1}q^{5}+(1-\beta _{2})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
4416.2.a.bx	$4416$	$2$	4416.a	1.a	$1$	$5$	$5$	$35.262$	5.5.218524.1	None	✓	$1$	$0$	$0$	$5$	$2$	$-4$	$+$	$-$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{1}q^{5}+(-1+\beta _{2})q^{7}+q^{9}+\cdots$

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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.