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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 82 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
1785.1.ba.a	$1785$	$1$	1785.ba	1785.aa	$4$	$2$	$1$	$0.891$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{21}) $		$4$	$0$	$0$	$-2$	$0$	$-2$		$1$		$q-q^{3}+iq^{4}-iq^{5}-q^{7}+q^{9}-iq^{12}+\cdots$
1785.1.ba.b	$1785$	$1$	1785.ba	1785.aa	$4$	$2$	$1$	$0.891$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{21}) $		$4$	$0$	$0$	$2$	$0$	$-2$		$1$		$q+q^{3}+iq^{4}+iq^{5}-q^{7}+q^{9}+iq^{12}+\cdots$
1785.1.bb.a	$1785$	$1$	1785.bb	1785.ab	$4$	$2$	$1$	$0.891$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{21}) $		$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-iq^{3}-iq^{4}-q^{5}-iq^{7}-q^{9}-q^{12}+\cdots$
1785.1.bb.b	$1785$	$1$	1785.bb	1785.ab	$4$	$2$	$1$	$0.891$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{21}) $		$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+iq^{3}-iq^{4}+q^{5}-iq^{7}-q^{9}+q^{12}+\cdots$
1785.1.bk.a	$1785$	$1$	1785.bk	1785.ak	$4$	$4$	$2$	$0.891$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-119}) $	None		$8$	$0$	$-4$	$0$	$0$	$0$		$1$		$q+(-1-\zeta_{8}^{2})q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}+\cdots$
1785.1.bk.b	$1785$	$1$	1785.bk	1785.ak	$4$	$4$	$2$	$0.891$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-119}) $	None		$8$	$0$	$4$	$0$	$0$	$0$		$1$		$q+(1+\zeta_{8}^{2})q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}+\cdots$
1785.1.bk.c	$1785$	$1$	1785.bk	1785.ak	$4$	$16$	$8$	$0.891$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-119}) $	None		$8$	$0$	$-4$	$0$	$0$	$0$		$1$		$q+(-\zeta_{40}^{14}+\zeta_{40}^{16})q^{2}-\zeta_{40}^{11}q^{3}+\cdots$
1785.1.bk.d	$1785$	$1$	1785.bk	1785.ak	$4$	$16$	$8$	$0.891$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-119}) $	None		$8$	$0$	$4$	$0$	$0$	$0$		$1$		$q+(\zeta_{40}^{4}+\zeta_{40}^{6})q^{2}-\zeta_{40}^{11}q^{3}+(\zeta_{40}^{8}+\cdots)q^{4}+\cdots$
1785.1.bp.a	$1785$	$1$	1785.bp	1785.ap	$6$	$6$	$3$	$0.891$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-255}) $	None		$4$	$0$	$0$	$-3$	$-3$	$0$		$1$		$q+(-\zeta_{18}-\zeta_{18}^{5})q^{2}+\zeta_{18}^{6}q^{3}+(-\zeta_{18}+\cdots)q^{4}+\cdots$
1785.1.bp.b	$1785$	$1$	1785.bp	1785.ap	$6$	$6$	$3$	$0.891$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-255}) $	None		$4$	$0$	$0$	$-3$	$3$	$0$		$1$		$q+(\zeta_{18}+\zeta_{18}^{5})q^{2}+\zeta_{18}^{6}q^{3}+(-\zeta_{18}+\cdots)q^{4}+\cdots$
1785.1.bp.c	$1785$	$1$	1785.bp	1785.ap	$6$	$6$	$3$	$0.891$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-255}) $	None		$4$	$0$	$0$	$3$	$-3$	$0$		$1$		$q+(\zeta_{18}^{7}-\zeta_{18}^{8})q^{2}-\zeta_{18}^{6}q^{3}+(-\zeta_{18}^{5}+\cdots)q^{4}+\cdots$
1785.1.bp.d	$1785$	$1$	1785.bp	1785.ap	$6$	$6$	$3$	$0.891$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-255}) $	None		$4$	$0$	$0$	$3$	$3$	$0$		$1$		$q+(\zeta_{18}^{2}+\zeta_{18}^{4})q^{2}-\zeta_{18}^{6}q^{3}+(\zeta_{18}^{4}+\cdots)q^{4}+\cdots$
1785.1.ec.a	$1785$	$1$	1785.ec	1785.dc	$16$	$16$	$2$	$0.891$	$\Q(\zeta_{32})$	$D_{16}$	$\Q(\sqrt{-35}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{32}^{3}q^{3}-\zeta_{32}^{12}q^{4}-\zeta_{32}q^{5}+\cdots$
1785.1.ec.b	$1785$	$1$	1785.ec	1785.dc	$16$	$16$	$2$	$0.891$	$\Q(\zeta_{32})$	$D_{16}$	$\Q(\sqrt{-35}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{32}^{7}q^{3}-\zeta_{32}^{12}q^{4}+\zeta_{32}q^{5}+\cdots$
1785.2.a.a	$1785$	$2$	1785.a	1.a	$1$	$1$	$1$	$14.253$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$-1$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}+q^{7}+\cdots$
1785.2.a.b	$1785$	$2$	1785.a	1.a	$1$	$1$	$1$	$14.253$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$-1$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
1785.2.a.c	$1785$	$2$	1785.a	1.a	$1$	$1$	$1$	$14.253$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}+q^{7}+\cdots$
1785.2.a.d	$1785$	$2$	1785.a	1.a	$1$	$1$	$1$	$14.253$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$1$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
1785.2.a.e	$1785$	$2$	1785.a	1.a	$1$	$1$	$1$	$14.253$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$1$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
1785.2.a.f	$1785$	$2$	1785.a	1.a	$1$	$1$	$1$	$14.253$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}-q^{5}+q^{7}+q^{9}+2q^{11}+\cdots$
1785.2.a.g	$1785$	$2$	1785.a	1.a	$1$	$1$	$1$	$14.253$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{4}+q^{5}-q^{7}+q^{9}-2q^{11}+\cdots$
1785.2.a.h	$1785$	$2$	1785.a	1.a	$1$	$1$	$1$	$14.253$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{4}-q^{5}+q^{7}+q^{9}-6q^{11}+\cdots$
1785.2.a.i	$1785$	$2$	1785.a	1.a	$1$	$1$	$1$	$14.253$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$-1$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}-q^{7}+\cdots$
1785.2.a.j	$1785$	$2$	1785.a	1.a	$1$	$1$	$1$	$14.253$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$-1$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}+q^{7}+\cdots$
1785.2.a.k	$1785$	$2$	1785.a	1.a	$1$	$1$	$1$	$14.253$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$-1$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
1785.2.a.l	$1785$	$2$	1785.a	1.a	$1$	$1$	$1$	$14.253$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$-1$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
1785.2.a.m	$1785$	$2$	1785.a	1.a	$1$	$1$	$1$	$14.253$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$1$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
1785.2.a.n	$1785$	$2$	1785.a	1.a	$1$	$1$	$1$	$14.253$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}+q^{7}+\cdots$
1785.2.a.o	$1785$	$2$	1785.a	1.a	$1$	$1$	$1$	$14.253$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$1$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
1785.2.a.p	$1785$	$2$	1785.a	1.a	$1$	$2$	$2$	$14.253$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$-2$	$2$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}-q^{5}+\cdots$
1785.2.a.q	$1785$	$2$	1785.a	1.a	$1$	$2$	$2$	$14.253$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-q^{3}+q^{4}+q^{5}-\beta q^{6}-q^{7}+\cdots$
1785.2.a.r	$1785$	$2$	1785.a	1.a	$1$	$2$	$2$	$14.253$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+3q^{4}+q^{5}+\beta q^{6}+q^{7}+\cdots$
1785.2.a.s	$1785$	$2$	1785.a	1.a	$1$	$2$	$2$	$14.253$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$1$	$2$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(2+\beta )q^{4}-q^{5}+\beta q^{6}+\cdots$
1785.2.a.t	$1785$	$2$	1785.a	1.a	$1$	$2$	$2$	$14.253$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$1$	$2$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{3}+(2+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots$
1785.2.a.u	$1785$	$2$	1785.a	1.a	$1$	$3$	$3$	$14.253$	3.3.148.1	$_{}$	None	None	✓	$1$	$1$	$-3$	$-3$	$-3$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
1785.2.a.v	$1785$	$2$	1785.a	1.a	$1$	$3$	$3$	$14.253$	3.3.148.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$3$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots$
1785.2.a.w	$1785$	$2$	1785.a	1.a	$1$	$3$	$3$	$14.253$	3.3.148.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$3$	$3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots$
1785.2.a.x	$1785$	$2$	1785.a	1.a	$1$	$3$	$3$	$14.253$	3.3.564.1	$_{}$	None	None	✓	$1$	$0$	$-1$	$3$	$3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
1785.2.a.y	$1785$	$2$	1785.a	1.a	$1$	$4$	$4$	$14.253$	4.4.8468.1	$_{}$	None	None	✓	$1$	$0$	$-2$	$-4$	$4$	$-4$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}-q^{3}+(2-\beta _{1})q^{4}+q^{5}-\beta _{2}q^{6}+\cdots$
1785.2.a.z	$1785$	$2$	1785.a	1.a	$1$	$4$	$4$	$14.253$	4.4.8468.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$-4$	$4$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
1785.2.a.ba	$1785$	$2$	1785.a	1.a	$1$	$4$	$4$	$14.253$	4.4.11348.1	$_{}$	None	None	✓	$1$	$0$	$2$	$-4$	$-4$	$-4$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}-q^{3}+(2+\beta _{2}-\beta _{3})q^{4}+\cdots$
1785.2.a.bb	$1785$	$2$	1785.a	1.a	$1$	$5$	$5$	$14.253$	5.5.246832.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$-5$	$-5$	$-5$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{4})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
1785.2.a.bc	$1785$	$2$	1785.a	1.a	$1$	$5$	$5$	$14.253$	5.5.674848.1	$_{}$	None	None	✓	$1$	$0$	$-1$	$5$	$-5$	$5$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
1785.2.a.bd	$1785$	$2$	1785.a	1.a	$1$	$6$	$6$	$14.253$	6.6.17749184.1	$_{}$	None	None	✓	$1$	$0$	$3$	$6$	$6$	$-6$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+q^{3}+(2+\beta _{4})q^{4}+q^{5}+\cdots$
1785.2.g.a	$1785$	$2$	1785.g	5.b	$2$	$2$	$2$	$14.253$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{2}+iq^{3}-2q^{4}+(1-2i)q^{5}+\cdots$
1785.2.g.b	$1785$	$2$	1785.g	5.b	$2$	$4$	$4$	$14.253$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$8$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{12}^{2}q^{2}+\zeta_{12}q^{3}-q^{4}+(2+\zeta_{12}+\cdots)q^{5}+\cdots$
1785.2.g.c	$1785$	$2$	1785.g	5.b	$2$	$8$	$8$	$14.253$	8.0.386672896.3	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{2}-\beta _{6})q^{2}+\beta _{2}q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots$
1785.2.g.d	$1785$	$2$	1785.g	5.b	$2$	$12$	$12$	$14.253$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{10}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
1785.2.g.e	$1785$	$2$	1785.g	5.b	$2$	$14$	$14$	$14.253$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-10$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(\beta _{7}+\beta _{8})q^{4}+(\beta _{4}+\cdots)q^{5}+\cdots$
1785.2.g.f	$1785$	$2$	1785.g	5.b	$2$	$28$	$28$	$14.253$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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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.