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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 61 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	5	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
7840.2.a.a	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	$\Q$	None	✓	$1$	$1$	$0$	$-3$	$-1$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{5}+6q^{9}+3q^{11}-q^{13}+\cdots$
7840.2.a.b	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	$\Q$	None	✓	$1$	$1$	$0$	$-3$	$1$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+q^{5}+6q^{9}+q^{11}+q^{13}+\cdots$
7840.2.a.c	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	$\Q$	None	✓	$1$	$0$	$0$	$-2$	$-1$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}+q^{9}+3q^{11}+q^{13}+\cdots$
7840.2.a.d	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	$\Q$	None	✓	$1$	$1$	$0$	$-2$	$1$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+q^{9}-3q^{11}-q^{13}+\cdots$
7840.2.a.e	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	$\Q$	None	✓	$1$	$0$	$0$	$-2$	$1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots$
7840.2.a.f	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-1$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{9}-3q^{11}+7q^{13}+\cdots$
7840.2.a.g	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-1$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{9}-2q^{11}+2q^{13}+\cdots$
7840.2.a.h	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$-1$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{9}+5q^{11}-5q^{13}+\cdots$
7840.2.a.i	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$1$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{9}-q^{11}-3q^{13}+\cdots$
7840.2.a.j	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$1$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{9}-q^{11}+q^{13}-q^{15}+\cdots$
7840.2.a.k	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$1$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{9}+2q^{11}-2q^{13}+\cdots$
7840.2.a.l	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{9}+2q^{13}-2q^{17}-8q^{19}+\cdots$
7840.2.a.m	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$-1$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{9}+2q^{13}-2q^{17}+8q^{19}+\cdots$
7840.2.a.n	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	$\Q$	None	✓	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-3q^{9}-4q^{11}-2q^{13}-6q^{17}+\cdots$
7840.2.a.o	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	$\Q$	None	✓	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-3q^{9}+4q^{11}-2q^{13}-6q^{17}+\cdots$
7840.2.a.p	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-1$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{9}-5q^{11}-5q^{13}+\cdots$
7840.2.a.q	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-1$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{9}+2q^{11}+2q^{13}+\cdots$
7840.2.a.r	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-1$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{9}+3q^{11}+7q^{13}+\cdots$
7840.2.a.s	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$1$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{9}-2q^{11}-2q^{13}+\cdots$
7840.2.a.t	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{9}+q^{11}-3q^{13}+\cdots$
7840.2.a.u	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$1$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{9}+q^{11}+q^{13}+q^{15}+\cdots$
7840.2.a.v	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$-1$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-q^{5}+q^{9}-3q^{11}+q^{13}+\cdots$
7840.2.a.w	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	$\Q$	None	✓	$1$	$1$	$0$	$2$	$1$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}+q^{9}-4q^{11}+6q^{13}+\cdots$
7840.2.a.x	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	$\Q$	None	✓	$1$	$0$	$0$	$2$	$1$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}+q^{9}+3q^{11}-q^{13}+\cdots$
7840.2.a.y	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	$\Q$	None	✓	$1$	$1$	$0$	$3$	$-1$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-q^{5}+6q^{9}-3q^{11}-q^{13}+\cdots$
7840.2.a.z	$7840$	$2$	7840.a	1.a	$1$	$1$	$1$	$62.603$	$\Q$	None	✓	$1$	$0$	$0$	$3$	$1$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+q^{5}+6q^{9}-q^{11}+q^{13}+\cdots$
7840.2.a.ba	$7840$	$2$	7840.a	1.a	$1$	$2$	$2$	$62.603$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$-2$	$-2$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}-q^{5}-2\beta q^{9}+(-2+\cdots)q^{11}+\cdots$
7840.2.a.bb	$7840$	$2$	7840.a	1.a	$1$	$2$	$2$	$62.603$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$-2$	$2$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+q^{5}-2\beta q^{9}+(2-2\beta )q^{11}+\cdots$
7840.2.a.bc	$7840$	$2$	7840.a	1.a	$1$	$2$	$2$	$62.603$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$0$	$-1$	$-2$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}-q^{5}+(1+\beta )q^{9}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
7840.2.a.bd	$7840$	$2$	7840.a	1.a	$1$	$2$	$2$	$62.603$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$0$	$-1$	$2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+q^{5}+(1+\beta )q^{9}+(4-\beta )q^{11}+\cdots$
7840.2.a.be	$7840$	$2$	7840.a	1.a	$1$	$2$	$2$	$62.603$	$\Q(\sqrt{5}) $	None	✓	$2$	$0$	$0$	$0$	$-2$	$0$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{3}-q^{5}+2q^{9}-\beta q^{11}+q^{13}+\cdots$
7840.2.a.bf	$7840$	$2$	7840.a	1.a	$1$	$2$	$2$	$62.603$	$\Q(\sqrt{2}) $	None	✓	$2$	$0$	$0$	$0$	$-2$	$0$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}+5q^{9}+2\beta q^{11}+2q^{13}+\cdots$
7840.2.a.bg	$7840$	$2$	7840.a	1.a	$1$	$2$	$2$	$62.603$	$\Q(\sqrt{5}) $	None	✓	$2$	$1$	$0$	$0$	$2$	$0$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{3}+q^{5}+2q^{9}+\beta q^{11}-q^{13}+\cdots$
7840.2.a.bh	$7840$	$2$	7840.a	1.a	$1$	$2$	$2$	$62.603$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$0$	$1$	$-2$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}+(1+\beta )q^{9}-\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
7840.2.a.bi	$7840$	$2$	7840.a	1.a	$1$	$2$	$2$	$62.603$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$0$	$1$	$2$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+q^{5}+(1+\beta )q^{9}+(-4+\beta )q^{11}+\cdots$
7840.2.a.bj	$7840$	$2$	7840.a	1.a	$1$	$2$	$2$	$62.603$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$2$	$-2$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-q^{5}+2\beta q^{9}+(2+2\beta )q^{11}+\cdots$
7840.2.a.bk	$7840$	$2$	7840.a	1.a	$1$	$2$	$2$	$62.603$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$2$	$2$	$0$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+q^{5}+2\beta q^{9}+(-2-2\beta )q^{11}+\cdots$
7840.2.a.bl	$7840$	$2$	7840.a	1.a	$1$	$3$	$3$	$62.603$	3.3.229.1	None	✓	$1$	$1$	$0$	$-2$	$-3$	$0$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}-q^{5}+(2-\beta _{1}+2\beta _{2})q^{9}+\cdots$
7840.2.a.bm	$7840$	$2$	7840.a	1.a	$1$	$3$	$3$	$62.603$	3.3.229.1	None	✓	$1$	$1$	$0$	$-2$	$3$	$0$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{3}+q^{5}+(2-\beta _{1}+2\beta _{2})q^{9}+\cdots$
7840.2.a.bn	$7840$	$2$	7840.a	1.a	$1$	$3$	$3$	$62.603$	3.3.229.1	None	✓	$1$	$0$	$0$	$2$	$-3$	$0$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}-q^{5}+(2-\beta _{1}+2\beta _{2})q^{9}+\cdots$
7840.2.a.bo	$7840$	$2$	7840.a	1.a	$1$	$3$	$3$	$62.603$	3.3.229.1	None	✓	$1$	$0$	$0$	$2$	$3$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+q^{5}+(2-\beta _{1}+2\beta _{2})q^{9}+\cdots$
7840.2.a.bp	$7840$	$2$	7840.a	1.a	$1$	$4$	$4$	$62.603$	$\Q(\sqrt{3}, \sqrt{7})$	None	✓	$2$	$1$	$0$	$0$	$-4$	$0$	$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-q^{5}+2\beta _{1}q^{11}+(-1-\beta _{3})q^{13}+\cdots$
7840.2.a.bq	$7840$	$2$	7840.a	1.a	$1$	$4$	$4$	$62.603$	$\Q(\zeta_{24})^+$	None	✓	$2$	$0$	$0$	$0$	$-4$	$0$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{5}+(\beta _{1}+\beta _{3})q^{11}+(3-\beta _{2}+\cdots)q^{13}+\cdots$
7840.2.a.br	$7840$	$2$	7840.a	1.a	$1$	$4$	$4$	$62.603$	$\Q(\sqrt{5}, \sqrt{13})$	None	✓	$2$	$1$	$0$	$0$	$-4$	$0$	$-$	$+$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-q^{5}+(2+\beta _{2})q^{9}+\beta _{3}q^{11}+\cdots$
7840.2.a.bs	$7840$	$2$	7840.a	1.a	$1$	$4$	$4$	$62.603$	$\Q(\sqrt{5}, \sqrt{13})$	None	✓	$2$	$0$	$0$	$0$	$-4$	$0$	$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-q^{5}+(2+\beta _{2})q^{9}-\beta _{3}q^{11}+\cdots$
7840.2.a.bt	$7840$	$2$	7840.a	1.a	$1$	$4$	$4$	$62.603$	$\Q(\zeta_{24})^+$	None	✓	$2$	$1$	$0$	$0$	$4$	$0$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{5}+(\beta _{1}-\beta _{3})q^{11}+(-3+\cdots)q^{13}+\cdots$
7840.2.a.bu	$7840$	$2$	7840.a	1.a	$1$	$4$	$4$	$62.603$	$\Q(\sqrt{3}, \sqrt{7})$	None	✓	$2$	$1$	$0$	$0$	$4$	$0$	$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{5}-2\beta _{1}q^{11}+(1-\beta _{3})q^{13}+\cdots$
7840.2.a.bv	$7840$	$2$	7840.a	1.a	$1$	$4$	$4$	$62.603$	$\Q(\sqrt{5}, \sqrt{13})$	None	✓	$2$	$0$	$0$	$0$	$4$	$0$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{5}+(2+\beta _{2})q^{9}+\beta _{3}q^{11}+\cdots$
7840.2.a.bw	$7840$	$2$	7840.a	1.a	$1$	$4$	$4$	$62.603$	$\Q(\sqrt{5}, \sqrt{13})$	None	✓	$2$	$0$	$0$	$0$	$4$	$0$	$-$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{5}+(2+\beta _{2})q^{9}-\beta _{3}q^{11}+\cdots$
7840.2.a.bx	$7840$	$2$	7840.a	1.a	$1$	$5$	$5$	$62.603$	5.5.1686096.1	None	✓	$1$	$1$	$0$	$0$	$-5$	$0$	$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{5}+(2+\beta _{2})q^{9}+(-1-\beta _{4})q^{11}+\cdots$

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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.