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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 52 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	17	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
9248.2.a.a	$9248$	$2$	9248.a	1.a	$1$	$1$	$1$	$73.846$	$\Q$	None	✓	$1$	$0$	$0$	$-2$	$-4$	$4$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-4q^{5}+4q^{7}+q^{9}-2q^{11}+\cdots$
9248.2.a.b	$9248$	$2$	9248.a	1.a	$1$	$1$	$1$	$73.846$	$\Q$	None	✓	$1$	$1$	$0$	$-2$	$-2$	$-2$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{5}-2q^{7}+q^{9}+2q^{11}+\cdots$
9248.2.a.c	$9248$	$2$	9248.a	1.a	$1$	$1$	$1$	$73.846$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$2$	$0$	$0$	$-4$	$0$	$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	$q-4q^{5}-3q^{9}-6q^{13}+11q^{25}-4q^{29}+\cdots$
9248.2.a.d	$9248$	$2$	9248.a	1.a	$1$	$1$	$1$	$73.846$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$0$	$-2$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{7}-3q^{9}-4q^{11}+2q^{13}+4q^{19}+\cdots$
9248.2.a.e	$9248$	$2$	9248.a	1.a	$1$	$1$	$1$	$73.846$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{7}-3q^{9}+4q^{11}+2q^{13}-4q^{19}+\cdots$
9248.2.a.f	$9248$	$2$	9248.a	1.a	$1$	$1$	$1$	$73.846$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$0$	$0$	$0$	$2$	$0$	$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	$q+2q^{5}-3q^{9}+6q^{13}-q^{25}+10q^{29}+\cdots$
9248.2.a.g	$9248$	$2$	9248.a	1.a	$1$	$1$	$1$	$73.846$	$\Q$	$\Q(\sqrt{-1}) $	✓	$2$	$0$	$0$	$0$	$4$	$0$	$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	$q+4q^{5}-3q^{9}-6q^{13}+11q^{25}+4q^{29}+\cdots$
9248.2.a.h	$9248$	$2$	9248.a	1.a	$1$	$1$	$1$	$73.846$	$\Q$	None	✓	$1$	$0$	$0$	$2$	$-4$	$-4$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-4q^{5}-4q^{7}+q^{9}+2q^{11}+\cdots$
9248.2.a.i	$9248$	$2$	9248.a	1.a	$1$	$1$	$1$	$73.846$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$-2$	$2$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{5}+2q^{7}+q^{9}-2q^{11}+\cdots$
9248.2.a.j	$9248$	$2$	9248.a	1.a	$1$	$2$	$2$	$73.846$	$\Q(\sqrt{2}) $	$\Q(\sqrt{-1}) $	✓	$4$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	$q-3\beta q^{5}-3q^{9}-4q^{13}+13q^{25}+\cdots$
9248.2.a.k	$9248$	$2$	9248.a	1.a	$1$	$2$	$2$	$73.846$	$\Q(\sqrt{2}) $	$\Q(\sqrt{-1}) $	✓	$4$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	$q-\beta q^{5}-3q^{9}+4q^{13}-3q^{25}-3\beta q^{29}+\cdots$
9248.2.a.l	$9248$	$2$	9248.a	1.a	$1$	$2$	$2$	$73.846$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-2\beta q^{5}-q^{9}+3\beta q^{11}+2q^{13}+\cdots$
9248.2.a.m	$9248$	$2$	9248.a	1.a	$1$	$2$	$2$	$73.846$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+2\beta q^{5}-q^{9}+3\beta q^{11}+2q^{13}+\cdots$
9248.2.a.n	$9248$	$2$	9248.a	1.a	$1$	$2$	$2$	$73.846$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{3}-\beta q^{5}-2\beta q^{7}+5q^{9}+2\beta q^{11}+\cdots$
9248.2.a.o	$9248$	$2$	9248.a	1.a	$1$	$2$	$2$	$73.846$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{3}+\beta q^{5}-2\beta q^{7}+5q^{9}+2\beta q^{11}+\cdots$
9248.2.a.p	$9248$	$2$	9248.a	1.a	$1$	$2$	$2$	$73.846$	$\Q(\sqrt{2}) $	None	✓	$2$	$1$	$0$	$0$	$4$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+2q^{5}-3\beta q^{7}-q^{9}+\beta q^{11}+\cdots$
9248.2.a.q	$9248$	$2$	9248.a	1.a	$1$	$2$	$2$	$73.846$	$\Q(\sqrt{10}) $	None	✓	$2$	$0$	$0$	$0$	$4$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+2q^{5}+\beta q^{7}+7q^{9}+\beta q^{11}+\cdots$
9248.2.a.r	$9248$	$2$	9248.a	1.a	$1$	$3$	$3$	$73.846$	$\Q(\zeta_{18})^+$	None	✓	$1$	$0$	$0$	$-3$	$0$	$9$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(3+\cdots)q^{7}+\cdots$
9248.2.a.s	$9248$	$2$	9248.a	1.a	$1$	$3$	$3$	$73.846$	$\Q(\zeta_{18})^+$	None	✓	$1$	$0$	$0$	$-3$	$0$	$9$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(3-\beta _{1}+\cdots)q^{7}+\cdots$
9248.2.a.t	$9248$	$2$	9248.a	1.a	$1$	$3$	$3$	$73.846$	3.3.148.1	None	✓	$1$	$1$	$0$	$-2$	$2$	$-2$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots$
9248.2.a.u	$9248$	$2$	9248.a	1.a	$1$	$3$	$3$	$73.846$	3.3.148.1	None	✓	$1$	$0$	$0$	$2$	$2$	$2$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(1-\beta _{2})q^{7}+\cdots$
9248.2.a.v	$9248$	$2$	9248.a	1.a	$1$	$3$	$3$	$73.846$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$0$	$3$	$0$	$-9$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-3+\beta _{1}+\cdots)q^{7}+\cdots$
9248.2.a.w	$9248$	$2$	9248.a	1.a	$1$	$3$	$3$	$73.846$	$\Q(\zeta_{18})^+$	None	✓	$1$	$1$	$0$	$3$	$0$	$-9$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(-3+\cdots)q^{7}+\cdots$
9248.2.a.x	$9248$	$2$	9248.a	1.a	$1$	$4$	$4$	$73.846$	4.4.14272.1	None	✓	$1$	$1$	$0$	$-2$	$-2$	$-6$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}+(-1+\beta _{2}-\beta _{3})q^{5}+(-2+\cdots)q^{7}+\cdots$
9248.2.a.y	$9248$	$2$	9248.a	1.a	$1$	$4$	$4$	$73.846$	4.4.14272.1	None	✓	$1$	$1$	$0$	$-2$	$2$	$-6$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}+(1-\beta _{2}+\beta _{3})q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots$
9248.2.a.z	$9248$	$2$	9248.a	1.a	$1$	$4$	$4$	$73.846$	4.4.45968.1	None	✓	$2$	$1$	$0$	$0$	$-6$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-1+\beta _{2})q^{5}-\beta _{3}q^{7}+(2+\cdots)q^{9}+\cdots$
9248.2.a.ba	$9248$	$2$	9248.a	1.a	$1$	$4$	$4$	$73.846$	$\Q(\sqrt{3}, \sqrt{7})$	None	✓	$2$	$1$	$0$	$0$	$-2$	$0$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}+\beta _{2}q^{5}-\beta _{1}q^{7}+(-1-\beta _{2}+\cdots)q^{9}+\cdots$
9248.2.a.bb	$9248$	$2$	9248.a	1.a	$1$	$4$	$4$	$73.846$	$\Q(\zeta_{16})^+$	$\Q(\sqrt{-1}) $	✓	$4$	$1$	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	$q+(\beta _{1}+2\beta _{3})q^{5}-3q^{9}-\beta _{2}q^{13}+(5+\cdots)q^{25}+\cdots$
9248.2.a.bc	$9248$	$2$	9248.a	1.a	$1$	$4$	$4$	$73.846$	$\Q(\zeta_{16})^+$	$\Q(\sqrt{-1}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	$q+(2\beta _{1}+\beta _{3})q^{5}-3q^{9}+5\beta _{2}q^{13}+\cdots$
9248.2.a.bd	$9248$	$2$	9248.a	1.a	$1$	$4$	$4$	$73.846$	$\Q(\zeta_{16})^+$	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{2}q^{7}+\cdots$
9248.2.a.be	$9248$	$2$	9248.a	1.a	$1$	$4$	$4$	$73.846$	$\Q(\zeta_{16})^+$	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{5}+\beta _{2}q^{7}+(1+\cdots)q^{9}+\cdots$
9248.2.a.bf	$9248$	$2$	9248.a	1.a	$1$	$4$	$4$	$73.846$	4.4.9248.1	$\Q(\sqrt{-17}) $	✓	$4$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$2^{3}$	$N(\mathrm{U}(1))$	$q+\beta _{1}q^{3}+\beta _{1}q^{7}+(2-\beta _{3})q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots$
9248.2.a.bg	$9248$	$2$	9248.a	1.a	$1$	$4$	$4$	$73.846$	4.4.9248.1	$\Q(\sqrt{-17}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$2^{3}$	$N(\mathrm{U}(1))$	$q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{7}+(4+\beta _{3})q^{9}+\cdots$
9248.2.a.bh	$9248$	$2$	9248.a	1.a	$1$	$4$	$4$	$73.846$	$\Q(\sqrt{3}, \sqrt{7})$	None	✓	$2$	$0$	$0$	$0$	$2$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}+(-1-\beta _{2}+\cdots)q^{9}+\cdots$
9248.2.a.bi	$9248$	$2$	9248.a	1.a	$1$	$4$	$4$	$73.846$	4.4.45968.1	None	✓	$2$	$0$	$0$	$0$	$6$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1-\beta _{2})q^{5}-\beta _{3}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
9248.2.a.bj	$9248$	$2$	9248.a	1.a	$1$	$4$	$4$	$73.846$	4.4.14272.1	None	✓	$1$	$0$	$0$	$2$	$-2$	$6$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}+(-1+\beta _{2}-\beta _{3})q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots$
9248.2.a.bk	$9248$	$2$	9248.a	1.a	$1$	$4$	$4$	$73.846$	4.4.14272.1	None	✓	$1$	$0$	$0$	$2$	$2$	$6$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{3}+(1-\beta _{2}+\beta _{3})q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots$
9248.2.a.bl	$9248$	$2$	9248.a	1.a	$1$	$6$	$6$	$73.846$	6.6.3359232.1	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{2}q^{5}-\beta _{5}q^{7}+(1+\beta _{3}+\cdots)q^{9}+\cdots$
9248.2.a.bm	$9248$	$2$	9248.a	1.a	$1$	$6$	$6$	$73.846$	6.6.3359232.1	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{2}q^{5}-\beta _{5}q^{7}+(1+\beta _{3}+\cdots)q^{9}+\cdots$
9248.2.a.bn	$9248$	$2$	9248.a	1.a	$1$	$8$	$8$	$73.846$	8.8.3288334336.1	None	✓	$4$	$1$	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{2}q^{5}+(\beta _{1}-\beta _{7})q^{7}+(1+\cdots)q^{9}+\cdots$
9248.2.a.bo	$9248$	$2$	9248.a	1.a	$1$	$9$	$9$	$73.846$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$0$	$-9$	$-6$	$-3$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-1+\beta _{1}+\beta _{5}-\beta _{6}+\cdots)q^{5}+\cdots$
9248.2.a.bp	$9248$	$2$	9248.a	1.a	$1$	$9$	$9$	$73.846$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$0$	$-9$	$6$	$-3$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(1-\beta _{1}-\beta _{5}+\beta _{6}+\cdots)q^{5}+\cdots$
9248.2.a.bq	$9248$	$2$	9248.a	1.a	$1$	$9$	$9$	$73.846$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$0$	$9$	$-6$	$3$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(-1+\beta _{1}+\beta _{5}-\beta _{6}+\cdots)q^{5}+\cdots$
9248.2.a.br	$9248$	$2$	9248.a	1.a	$1$	$9$	$9$	$73.846$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$0$	$0$	$9$	$6$	$3$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{3}+(1-\beta _{1}-\beta _{5}+\beta _{6})q^{5}+\cdots$
9248.2.a.bs	$9248$	$2$	9248.a	1.a	$1$	$12$	$12$	$73.846$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$2$	$1$	$0$	$0$	$-12$	$0$	$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1+\beta _{2}+\beta _{5})q^{5}+\beta _{8}q^{7}+\cdots$
9248.2.a.bt	$9248$	$2$	9248.a	1.a	$1$	$12$	$12$	$73.846$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-\beta _{2}q^{5}+(-\beta _{1}-\beta _{11})q^{7}+\cdots$
9248.2.a.bu	$9248$	$2$	9248.a	1.a	$1$	$12$	$12$	$73.846$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+\beta _{2}q^{5}+(-\beta _{1}-\beta _{11})q^{7}+\cdots$
9248.2.a.bv	$9248$	$2$	9248.a	1.a	$1$	$12$	$12$	$73.846$	12.12.$\cdots$.1	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$2^{14}$	$\mathrm{SU}(2)$	$q-\beta _{6}q^{3}-\beta _{4}q^{5}+(-\beta _{6}+\beta _{11})q^{7}+\cdots$
9248.2.a.bw	$9248$	$2$	9248.a	1.a	$1$	$12$	$12$	$73.846$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$2$	$0$	$0$	$0$	$12$	$0$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(1-\beta _{2}-\beta _{5})q^{5}+\beta _{8}q^{7}+\cdots$
9248.2.a.bx	$9248$	$2$	9248.a	1.a	$1$	$16$	$16$	$73.846$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$+$	$-$	$-$	$2^{9}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(\beta _{6}-\beta _{12})q^{5}+(\beta _{1}-\beta _{9}+\cdots)q^{7}+\cdots$

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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.