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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 78 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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	7	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8281.2.a.a	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$1$	$-2$	$-2$	$-1$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-2q^{3}+2q^{4}-q^{5}+4q^{6}+\cdots$
8281.2.a.b	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$1$	$-2$	$2$	$1$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{3}+2q^{4}+q^{5}-4q^{6}+\cdots$
8281.2.a.c	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$1$	$-1$	$-3$	$-3$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-3q^{3}-q^{4}-3q^{5}+3q^{6}+3q^{8}+\cdots$
8281.2.a.d	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	$\Q(\sqrt{-7}) $	✓	$2$	$0$	$-1$	$0$	$0$	$0$	$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	$q-q^{2}-q^{4}+3q^{8}-3q^{9}-4q^{11}+\cdots$
8281.2.a.e	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+3q^{8}-3q^{9}+3q^{11}+\cdots$
8281.2.a.f	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+3q^{8}-3q^{9}+3q^{11}+\cdots$
8281.2.a.g	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$0$	$-1$	$3$	$3$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}-q^{4}+3q^{5}-3q^{6}+3q^{8}+\cdots$
8281.2.a.h	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$0$	$0$	$2$	$-3$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{4}-3q^{5}+q^{9}-4q^{12}+\cdots$
8281.2.a.i	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$1$	$1$	$-3$	$3$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}-q^{4}+3q^{5}-3q^{6}-3q^{8}+\cdots$
8281.2.a.j	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$0$	$1$	$3$	$-3$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}-q^{4}-3q^{5}+3q^{6}-3q^{8}+\cdots$
8281.2.a.k	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$1$	$2$	$-2$	$1$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-2q^{3}+2q^{4}+q^{5}-4q^{6}+\cdots$
8281.2.a.l	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$0$	$2$	$0$	$-3$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-3q^{5}-3q^{9}-6q^{10}+\cdots$
8281.2.a.m	$8281$	$2$	8281.a	1.a	$1$	$1$	$1$	$66.124$	$\Q$	None	✓	$1$	$1$	$2$	$2$	$-1$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{3}+2q^{4}-q^{5}+4q^{6}+\cdots$
8281.2.a.n	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-3$	$3$	$3$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+(1+\beta )q^{3}+3\beta q^{4}+\cdots$
8281.2.a.o	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$-2$	$0$	$-2$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}-\beta q^{3}+(1-2\beta )q^{4}+\cdots$
8281.2.a.p	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$-2$	$0$	$2$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+\beta q^{3}+(1-2\beta )q^{4}+\cdots$
8281.2.a.q	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{3}) $	None	✓	$2$	$1$	$0$	$-4$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-2q^{3}+q^{4}+\beta q^{5}-2\beta q^{6}+\cdots$
8281.2.a.r	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$-2$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1-\beta )q^{3}+q^{4}-\beta q^{5}+\cdots$
8281.2.a.s	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{3}) $	None	✓	$2$	$0$	$0$	$-2$	$0$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+q^{4}-\beta q^{5}-\beta q^{6}-\beta q^{8}+\cdots$
8281.2.a.t	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$-2$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{3}+q^{4}-\beta q^{5}+\cdots$
8281.2.a.u	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{13}) $	$\Q(\sqrt{-91}) $	✓	$4$	$1$	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$2$	$N(\mathrm{U}(1))$	$q-2q^{4}-\beta q^{5}-3q^{9}+4q^{16}-\beta q^{19}+\cdots$
8281.2.a.v	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$0$	$6$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-\beta q^{3}+(3-\beta )q^{5}-2q^{6}-2\beta q^{8}+\cdots$
8281.2.a.w	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{3}) $	None	✓	$2$	$1$	$0$	$2$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+q^{4}+\beta q^{5}+\beta q^{6}-\beta q^{8}+\cdots$
8281.2.a.x	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$2$	$0$	$-2$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-\beta q^{3}+(1+2\beta )q^{4}+(-1+\cdots)q^{5}+\cdots$
8281.2.a.y	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$2$	$0$	$2$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+\beta q^{3}+(1+2\beta )q^{4}+(1+\cdots)q^{5}+\cdots$
8281.2.a.z	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$3$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1-2\beta )q^{3}+3\beta q^{4}+(1+\cdots)q^{5}+\cdots$
8281.2.a.ba	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$3$	$0$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(-1+2\beta )q^{3}+3\beta q^{4}+\cdots$
8281.2.a.bb	$8281$	$2$	8281.a	1.a	$1$	$2$	$2$	$66.124$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$3$	$3$	$-3$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(1+\beta )q^{3}+3\beta q^{4}+(-1+\cdots)q^{5}+\cdots$
8281.2.a.bc	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	$\Q(\zeta_{14})^+$	$\Q(\sqrt{-7}) $	✓	$2$	$1$	$-4$	$0$	$0$	$0$	$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	$q+(-1-\beta _{1})q^{2}+(1+2\beta _{1}+\beta _{2})q^{4}+\cdots$
8281.2.a.bd	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	$\Q(\zeta_{14})^+$	$\Q(\sqrt{-7}) $	✓	$2$	$0$	$-3$	$0$	$0$	$0$	$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	$q+(-1+\beta _{1}+\beta _{2})q^{2}+(4-\beta _{1})q^{4}+\cdots$
8281.2.a.be	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	3.3.148.1	None	✓	$1$	$1$	$-2$	$0$	$3$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
8281.2.a.bf	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	$\Q(\zeta_{14})^+$	None	✓	$1$	$0$	$-2$	$2$	$4$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+(\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$
8281.2.a.bg	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	3.3.316.1	None	✓	$1$	$0$	$-1$	$2$	$2$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots$
8281.2.a.bh	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	3.3.404.1	None	✓	$1$	$0$	$2$	$-4$	$5$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(-1-\beta _{2})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots$
8281.2.a.bi	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	3.3.148.1	None	✓	$1$	$1$	$2$	$0$	$-3$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
8281.2.a.bj	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	$\Q(\zeta_{14})^+$	None	✓	$1$	$1$	$2$	$2$	$-4$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1+\beta _{2})q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots$
8281.2.a.bk	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	3.3.404.1	None	✓	$1$	$0$	$2$	$4$	$-5$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1+\beta _{2})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots$
8281.2.a.bl	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	$\Q(\zeta_{14})^+$	$\Q(\sqrt{-7}) $	✓	$2$	$1$	$3$	$0$	$0$	$0$	$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	$q+(1-\beta _{1}-\beta _{2})q^{2}+(4-\beta _{1})q^{4}+(5+\cdots)q^{8}+\cdots$
8281.2.a.bm	$8281$	$2$	8281.a	1.a	$1$	$3$	$3$	$66.124$	$\Q(\zeta_{14})^+$	$\Q(\sqrt{-7}) $	✓	$2$	$0$	$4$	$0$	$0$	$0$	$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	$q+(1+\beta _{1})q^{2}+(1+2\beta _{1}+\beta _{2})q^{4}+(4+\cdots)q^{8}+\cdots$
8281.2.a.bn	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	$\Q(\sqrt{2}, \sqrt{23})$	None	✓	$2$	$1$	$-4$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{2}q^{3}-q^{4}-\beta _{1}q^{5}-\beta _{2}q^{6}+\cdots$
8281.2.a.bo	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	4.4.105456.1	None	✓	$2$	$0$	$-2$	$0$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+\beta _{1}q^{3}+(1-\beta _{2})q^{4}-\beta _{1}q^{5}+\cdots$
8281.2.a.bp	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	4.4.27004.1	None	✓	$1$	$0$	$-1$	$-1$	$7$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots$
8281.2.a.bq	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	$\Q(\sqrt{3}, \sqrt{7})$	None	✓	$2$	$1$	$0$	$-2$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+(-1-\beta _{2})q^{3}-\beta _{2}q^{4}-\beta _{3}q^{5}+\cdots$
8281.2.a.br	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	$\Q(\sqrt{3}, \sqrt{13})$	None	✓	$4$	$1$	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+q^{4}+\beta _{3}q^{5}+\beta _{2}q^{8}-3q^{9}+\cdots$
8281.2.a.bs	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	$\Q(\sqrt{3}, \sqrt{7})$	None	✓	$2$	$1$	$0$	$2$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}+(1+\beta _{2})q^{3}-\beta _{2}q^{4}+\beta _{3}q^{5}+\cdots$
8281.2.a.bt	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	4.4.27004.1	None	✓	$1$	$0$	$1$	$-1$	$-7$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots$
8281.2.a.bu	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	4.4.105456.1	None	✓	$2$	$0$	$2$	$0$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+\beta _{1}q^{3}+(1-\beta _{2})q^{4}+\beta _{1}q^{5}+\cdots$
8281.2.a.bv	$8281$	$2$	8281.a	1.a	$1$	$4$	$4$	$66.124$	$\Q(\sqrt{2}, \sqrt{23})$	None	✓	$2$	$1$	$4$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{2}q^{3}-q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots$
8281.2.a.bw	$8281$	$2$	8281.a	1.a	$1$	$5$	$5$	$66.124$	5.5.746052.1	None	✓	$1$	$1$	$-4$	$0$	$-2$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-\beta _{4}q^{3}+(2-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$
8281.2.a.bx	$8281$	$2$	8281.a	1.a	$1$	$5$	$5$	$66.124$	5.5.746052.1	None	✓	$1$	$0$	$-4$	$0$	$2$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+\beta _{4}q^{3}+(2-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$

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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.