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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 62 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	23	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8464.2.a.a	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	$\Q$	None	✓	$1$	$1$	$0$	$-3$	$-2$	$-2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-2q^{5}-2q^{7}+6q^{9}+4q^{11}+\cdots$
8464.2.a.b	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	$\Q$	None	✓	$1$	$0$	$0$	$-3$	$0$	$-2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-2q^{7}+6q^{9}-5q^{13}+6q^{17}+\cdots$
8464.2.a.c	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	$\Q$	None	✓	$1$	$1$	$0$	$-3$	$2$	$2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+2q^{5}+2q^{7}+6q^{9}-4q^{11}+\cdots$
8464.2.a.d	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	$\Q$	None	✓	$1$	$2$	$0$	$-2$	$-1$	$-2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}-2q^{7}+q^{9}-2q^{11}+\cdots$
8464.2.a.e	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	$\Q$	None	✓	$1$	$0$	$0$	$-2$	$1$	$2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+2q^{7}+q^{9}+2q^{11}+\cdots$
8464.2.a.f	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}-2q^{9}-q^{13}+6q^{17}+\cdots$
8464.2.a.g	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-4$	$-4$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}-4q^{7}-3q^{9}+2q^{11}-2q^{13}+\cdots$
8464.2.a.h	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}-3q^{9}-4q^{11}+q^{13}+\cdots$
8464.2.a.i	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$0$	$4$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{7}-3q^{9}+6q^{11}-2q^{13}-6q^{17}+\cdots$
8464.2.a.j	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$1$	$-2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}-3q^{9}+4q^{11}+q^{13}+\cdots$
8464.2.a.k	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-2$	$-2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-2q^{7}-2q^{9}-4q^{11}+\cdots$
8464.2.a.l	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-2$	$2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+2q^{7}-2q^{9}-6q^{11}+\cdots$
8464.2.a.m	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$2$	$-4$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}-4q^{7}-2q^{9}-2q^{11}+\cdots$
8464.2.a.n	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$2$	$-2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}-2q^{7}-2q^{9}+6q^{11}+\cdots$
8464.2.a.o	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$2$	$2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+2q^{7}-2q^{9}+4q^{11}+\cdots$
8464.2.a.p	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$4$	$2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{5}+2q^{7}-2q^{9}-4q^{11}+\cdots$
8464.2.a.q	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$-3$	$2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-3q^{5}+2q^{7}+q^{9}+6q^{11}+\cdots$
8464.2.a.r	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$3$	$-2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+3q^{5}-2q^{7}+q^{9}-6q^{11}+\cdots$
8464.2.a.s	$8464$	$2$	8464.a	1.a	$1$	$1$	$1$	$67.585$	$\Q$	None	✓	$1$	$1$	$0$	$3$	$2$	$-4$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+2q^{5}-4q^{7}+6q^{9}+2q^{11}+\cdots$
8464.2.a.t	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$0$	$-4$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2\beta q^{7}+q^{9}+3\beta q^{11}+6q^{13}+\cdots$
8464.2.a.u	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$0$	$-2$	$0$	$-6$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+\beta q^{5}+(-3-\beta )q^{7}+\cdots$
8464.2.a.v	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	$\Q(\sqrt{3}) $	None	✓	$2$	$1$	$0$	$-2$	$0$	$0$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}+\beta q^{7}-2q^{9}+\beta q^{11}+\cdots$
8464.2.a.w	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	$\Q(\sqrt{3}) $	None	✓	$2$	$1$	$0$	$-2$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2\beta q^{5}-2\beta q^{7}-2q^{9}+2\beta q^{11}+\cdots$
8464.2.a.x	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$0$	$-2$	$0$	$6$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}-\beta q^{5}+(3+\beta )q^{7}+(1+\cdots)q^{9}+\cdots$
8464.2.a.y	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	$\Q(\sqrt{6}) $	None	✓	$1$	$0$	$0$	$0$	$-6$	$-4$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-3q^{5}+(-2-\beta )q^{7}+3q^{9}+\cdots$
8464.2.a.z	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$0$	$-2$	$4$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-1-2\beta )q^{5}+(2-\beta )q^{7}+\cdots$
8464.2.a.ba	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$0$	$2$	$-4$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(1+2\beta )q^{5}+(-2+\beta )q^{7}+\cdots$
8464.2.a.bb	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$0$	$2$	$2$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(1+\beta )q^{5}+(1-\beta )q^{7}+2q^{9}+\cdots$
8464.2.a.bc	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	$\Q(\sqrt{6}) $	None	✓	$1$	$0$	$0$	$0$	$6$	$4$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+3q^{5}+(2+\beta )q^{7}+3q^{9}+\beta q^{11}+\cdots$
8464.2.a.bd	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$0$	$1$	$-4$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-2q^{5}+(1+\beta )q^{9}+2\beta q^{11}+\cdots$
8464.2.a.be	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$2$	$-4$	$-2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-2-\beta )q^{5}+(-1-\beta )q^{7}+\cdots$
8464.2.a.bf	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$2$	$4$	$2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(2+\beta )q^{5}+(1+\beta )q^{7}+\cdots$
8464.2.a.bg	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$4$	$-2$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{3}-q^{5}-3\beta q^{7}+(3+4\beta )q^{9}+\cdots$
8464.2.a.bh	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	$\Q(\sqrt{3}) $	None	✓	$2$	$1$	$0$	$4$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+\beta q^{5}+2\beta q^{7}+q^{9}-2\beta q^{11}+\cdots$
8464.2.a.bi	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	$\Q(\sqrt{3}) $	None	✓	$2$	$1$	$0$	$4$	$0$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+\beta q^{5}+q^{9}-2\beta q^{11}+q^{13}+\cdots$
8464.2.a.bj	$8464$	$2$	8464.a	1.a	$1$	$2$	$2$	$67.585$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$4$	$2$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(2+\beta )q^{3}+q^{5}+3\beta q^{7}+(3+4\beta )q^{9}+\cdots$
8464.2.a.bk	$8464$	$2$	8464.a	1.a	$1$	$3$	$3$	$67.585$	3.3.621.1	$\Q(\sqrt{-23}) $	✓	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$2$	$N(\mathrm{U}(1))$	$q+\beta _{2}q^{3}+(3-\beta _{1}-\beta _{2})q^{9}+(\beta _{1}-\beta _{2})q^{13}+\cdots$
8464.2.a.bl	$8464$	$2$	8464.a	1.a	$1$	$4$	$4$	$67.585$	$\Q(\zeta_{24})^+$	None	✓	$1$	$1$	$0$	$0$	$-8$	$4$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{3})q^{3}+(-2-\beta _{3})q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots$
8464.2.a.bm	$8464$	$2$	8464.a	1.a	$1$	$4$	$4$	$67.585$	$\Q(\sqrt{2}, \sqrt{5})$	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}+\beta _{1}q^{5}+(\beta _{1}+\beta _{2})q^{7}+2q^{9}+\cdots$
8464.2.a.bn	$8464$	$2$	8464.a	1.a	$1$	$4$	$4$	$67.585$	$\Q(\zeta_{24})^+$	None	✓	$1$	$1$	$0$	$0$	$8$	$-4$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}+\beta _{3})q^{3}+(2+\beta _{1})q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots$
8464.2.a.bo	$8464$	$2$	8464.a	1.a	$1$	$4$	$4$	$67.585$	4.4.9248.1	None	✓	$2$	$0$	$0$	$2$	$0$	$0$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}-\beta _{1}q^{5}-\beta _{3}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
8464.2.a.bp	$8464$	$2$	8464.a	1.a	$1$	$4$	$4$	$67.585$	$\Q(\sqrt{2}, \sqrt{13})$	None	✓	$2$	$0$	$0$	$4$	$0$	$0$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+(\beta _{1}+\beta _{2})q^{5}+\beta _{1}q^{7}-2q^{9}+\cdots$
8464.2.a.bq	$8464$	$2$	8464.a	1.a	$1$	$4$	$4$	$67.585$	$\Q(\zeta_{24})^+$	None	✓	$2$	$0$	$0$	$4$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{2})q^{3}+(\beta _{1}+2\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
8464.2.a.br	$8464$	$2$	8464.a	1.a	$1$	$4$	$4$	$67.585$	$\Q(\zeta_{24})^+$	None	✓	$2$	$0$	$0$	$4$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+\beta _{1}q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots$
8464.2.a.bs	$8464$	$2$	8464.a	1.a	$1$	$5$	$5$	$67.585$	$\Q(\zeta_{22})^+$	None	✓	$1$	$0$	$0$	$-2$	$-7$	$8$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{2}+\beta _{4})q^{3}+(-1-\beta _{1}+\beta _{2})q^{5}+\cdots$
8464.2.a.bt	$8464$	$2$	8464.a	1.a	$1$	$5$	$5$	$67.585$	$\Q(\zeta_{22})^+$	None	✓	$1$	$1$	$0$	$-2$	$7$	$-8$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{2}+\beta _{4})q^{3}+(1+\beta _{1}-\beta _{2})q^{5}+(-2+\cdots)q^{7}+\cdots$
8464.2.a.bu	$8464$	$2$	8464.a	1.a	$1$	$5$	$5$	$67.585$	$\Q(\zeta_{22})^+$	None	✓	$1$	$0$	$0$	$0$	$-2$	$9$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{2}+\beta _{3})q^{3}+(-1+\beta _{1}+\beta _{3}-\beta _{4})q^{5}+\cdots$
8464.2.a.bv	$8464$	$2$	8464.a	1.a	$1$	$5$	$5$	$67.585$	$\Q(\zeta_{22})^+$	None	✓	$1$	$1$	$0$	$0$	$2$	$-9$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{2}+\beta _{3})q^{3}+(1-\beta _{1}-\beta _{3}+\beta _{4})q^{5}+\cdots$
8464.2.a.bw	$8464$	$2$	8464.a	1.a	$1$	$5$	$5$	$67.585$	$\Q(\zeta_{22})^+$	None	✓	$1$	$1$	$0$	$2$	$-8$	$7$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}-\beta _{4})q^{3}+(-2+\beta _{1}+\beta _{3})q^{5}+\cdots$
8464.2.a.bx	$8464$	$2$	8464.a	1.a	$1$	$5$	$5$	$67.585$	$\Q(\zeta_{22})^+$	None	✓	$1$	$0$	$0$	$2$	$8$	$-7$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}-\beta _{4})q^{3}+(2-\beta _{1}-\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots$

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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.