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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

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Results (1-50 of 112 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
3520.1.i.a	$3520$	$1$	3520.i	55.d	$2$	$1$	$1$	$1.757$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q+q^{5}+q^{9}-q^{11}+q^{25}+2q^{31}+\cdots$
3520.1.i.b	$3520$	$1$	3520.i	55.d	$2$	$1$	$1$	$1.757$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q+q^{5}+q^{9}+q^{11}+q^{25}-2q^{31}+\cdots$
3520.1.i.c	$3520$	$1$	3520.i	55.d	$2$	$2$	$2$	$1.757$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{3}+\zeta_{6}^{2}q^{5}+(-1-\zeta_{6}+\cdots)q^{9}+\cdots$
3520.1.i.d	$3520$	$1$	3520.i	55.d	$2$	$2$	$2$	$1.757$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$		$1$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{3}-\zeta_{6}q^{5}+(-1-\zeta_{6}+\cdots)q^{9}+\cdots$
3520.1.i.e	$3520$	$1$	3520.i	55.d	$2$	$4$	$4$	$1.757$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{55}) $		$8$	$0$	$0$	$0$	$-4$	$0$		$2$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{3}-q^{5}-q^{9}+\zeta_{8}^{2}q^{11}+\cdots$
3520.1.o.a	$3520$	$1$	3520.o	440.o	$2$	$2$	$2$	$1.757$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-10}) $	$\Q(\sqrt{110}) $		$8$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-q^{5}-q^{9}-iq^{11}+iq^{23}+q^{25}+\cdots$
3520.1.o.b	$3520$	$1$	3520.o	440.o	$2$	$2$	$2$	$1.757$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-10}) $	$\Q(\sqrt{110}) $		$8$	$0$	$0$	$0$	$2$	$0$		$1$		$q+q^{5}-q^{9}-iq^{11}-iq^{23}+q^{25}+\cdots$
3520.1.o.c	$3520$	$1$	3520.o	440.o	$2$	$4$	$4$	$1.757$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-11}) $	None		$8$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+(\zeta_{12}-\zeta_{12}^{5})q^{3}+\zeta_{12}^{4}q^{5}+(1+\zeta_{12}^{2}+\cdots)q^{9}+\cdots$
3520.1.o.d	$3520$	$1$	3520.o	440.o	$2$	$4$	$4$	$1.757$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-11}) $	None		$8$	$0$	$0$	$0$	$2$	$0$		$1$		$q+(\zeta_{12}-\zeta_{12}^{5})q^{3}-\zeta_{12}^{4}q^{5}+(1+\zeta_{12}^{2}+\cdots)q^{9}+\cdots$
3520.1.x.a	$3520$	$1$	3520.x	880.x	$4$	$8$	$4$	$1.757$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q-\zeta_{16}^{2}q^{5}+(\zeta_{16}^{3}+\zeta_{16}^{5})q^{7}-\zeta_{16}^{4}q^{9}+\cdots$
3520.1.y.a	$3520$	$1$	3520.y	220.i	$4$	$2$	$1$	$1.757$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+(-1-i)q^{3}+iq^{5}+iq^{9}-iq^{11}+\cdots$
3520.1.y.b	$3520$	$1$	3520.y	220.i	$4$	$2$	$1$	$1.757$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+(1+i)q^{3}+iq^{5}+iq^{9}+iq^{11}+\cdots$
3520.1.y.c	$3520$	$1$	3520.y	220.i	$4$	$4$	$2$	$1.757$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+(\zeta_{12}^{4}-\zeta_{12}^{5})q^{3}-\zeta_{12}q^{5}+(-\zeta_{12}^{2}+\cdots)q^{9}+\cdots$
3520.1.y.d	$3520$	$1$	3520.y	220.i	$4$	$4$	$2$	$1.757$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+(-\zeta_{12}^{4}+\zeta_{12}^{5})q^{3}-\zeta_{12}q^{5}+(-\zeta_{12}^{2}+\cdots)q^{9}+\cdots$
3520.1.be.a	$3520$	$1$	3520.be	440.w	$4$	$2$	$1$	$1.757$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+(-1+i)q^{3}+iq^{5}-iq^{9}-q^{11}+\cdots$
3520.1.be.b	$3520$	$1$	3520.be	440.w	$4$	$2$	$1$	$1.757$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+(-1+i)q^{3}-iq^{5}-iq^{9}-q^{11}+\cdots$
3520.1.be.c	$3520$	$1$	3520.be	440.w	$4$	$2$	$1$	$1.757$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+(1-i)q^{3}-iq^{5}-iq^{9}+q^{11}+(-1+\cdots)q^{15}+\cdots$
3520.1.be.d	$3520$	$1$	3520.be	440.w	$4$	$2$	$1$	$1.757$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+(1-i)q^{3}+iq^{5}-iq^{9}+q^{11}+(1+\cdots)q^{15}+\cdots$
3520.1.be.e	$3520$	$1$	3520.be	440.w	$4$	$4$	$2$	$1.757$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+(\zeta_{12}-\zeta_{12}^{2})q^{3}-\zeta_{12}q^{5}+(\zeta_{12}^{2}+\cdots)q^{9}+\cdots$
3520.1.be.f	$3520$	$1$	3520.be	440.w	$4$	$4$	$2$	$1.757$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+(\zeta_{12}^{4}+\zeta_{12}^{5})q^{3}+\zeta_{12}^{5}q^{5}+(-\zeta_{12}^{2}+\cdots)q^{9}+\cdots$
3520.1.be.g	$3520$	$1$	3520.be	440.w	$4$	$4$	$2$	$1.757$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+(-\zeta_{12}^{4}-\zeta_{12}^{5})q^{3}+\zeta_{12}^{5}q^{5}+\cdots$
3520.1.be.h	$3520$	$1$	3520.be	440.w	$4$	$4$	$2$	$1.757$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+(-\zeta_{12}+\zeta_{12}^{2})q^{3}-\zeta_{12}q^{5}+(\zeta_{12}^{2}+\cdots)q^{9}+\cdots$
3520.1.cg.a	$3520$	$1$	3520.cg	440.aa	$10$	$8$	$2$	$1.757$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-10}) $	None		$8$	$0$	$0$	$0$	$-2$	$0$		$1$		$q+\zeta_{20}^{8}q^{5}+(\zeta_{20}^{3}+\zeta_{20}^{5})q^{7}+\zeta_{20}^{2}q^{9}+\cdots$
3520.1.cg.b	$3520$	$1$	3520.cg	440.aa	$10$	$8$	$2$	$1.757$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-10}) $	None		$8$	$0$	$0$	$0$	$2$	$0$		$1$		$q-\zeta_{20}^{8}q^{5}+(\zeta_{20}^{3}+\zeta_{20}^{5})q^{7}+\zeta_{20}^{2}q^{9}+\cdots$
3520.1.db.a	$3520$	$1$	3520.db	3520.cb	$16$	$32$	$4$	$1.757$	$\Q(\zeta_{64})$	$D_{32}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{64}^{27}q^{2}-\zeta_{64}^{22}q^{4}+\zeta_{64}^{26}q^{5}+\cdots$
3520.2.a.a	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{5}+q^{7}+6q^{9}+q^{11}+6q^{13}+\cdots$
3520.2.a.b	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}+q^{9}-q^{11}-4q^{13}+\cdots$
3520.2.a.c	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}+q^{9}-q^{11}+2q^{15}+\cdots$
3520.2.a.d	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}+4q^{7}+q^{9}-q^{11}+4q^{13}+\cdots$
3520.2.a.e	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-1$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}+4q^{7}+q^{9}+q^{11}-4q^{13}+\cdots$
3520.2.a.f	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}-2q^{7}+q^{9}+q^{11}+2q^{13}+\cdots$
3520.2.a.g	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-3q^{7}-2q^{9}+q^{11}+2q^{13}+\cdots$
3520.2.a.h	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-3q^{7}-2q^{9}+q^{11}+6q^{13}+\cdots$
3520.2.a.i	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-q^{7}-2q^{9}-q^{11}+2q^{13}+\cdots$
3520.2.a.j	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-3q^{7}-2q^{9}-q^{11}+2q^{13}+\cdots$
3520.2.a.k	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-q^{7}-2q^{9}+q^{11}-2q^{13}+\cdots$
3520.2.a.l	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$1$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+5q^{7}-2q^{9}-q^{11}-2q^{13}+\cdots$
3520.2.a.m	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-4q^{7}-3q^{9}-q^{11}-6q^{13}+\cdots$
3520.2.a.n	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{9}-q^{11}-2q^{13}+6q^{17}+\cdots$
3520.2.a.o	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{9}-q^{11}+2q^{13}-2q^{17}+\cdots$
3520.2.a.p	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{9}+q^{11}-2q^{13}+6q^{17}+\cdots$
3520.2.a.q	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{9}+q^{11}+2q^{13}-2q^{17}+\cdots$
3520.2.a.r	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{7}-3q^{9}+q^{11}-6q^{13}+\cdots$
3520.2.a.s	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}-3q^{9}-q^{11}+4q^{13}+\cdots$
3520.2.a.t	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}-3q^{9}+q^{11}+8q^{19}+\cdots$
3520.2.a.u	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}-3q^{9}-q^{11}-8q^{19}+\cdots$
3520.2.a.v	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}-3q^{9}+q^{11}+4q^{13}+\cdots$
3520.2.a.w	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{7}-2q^{9}+q^{11}+2q^{13}+\cdots$
3520.2.a.x	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+3q^{7}-2q^{9}-q^{11}+2q^{13}+\cdots$
3520.2.a.y	$3520$	$2$	3520.a	1.a	$1$	$1$	$1$	$28.107$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+3q^{7}-2q^{9}-q^{11}+6q^{13}+\cdots$

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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.