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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 83 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
3700.1.b.a	$3700$	$1$	3700.b	148.b	$2$	$1$	$1$	$1.847$	$\Q$	$D_{3}$	$\Q(\sqrt{-37}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{18}+\cdots$
3700.1.b.b	$3700$	$1$	3700.b	148.b	$2$	$1$	$1$	$1.847$	$\Q$	$D_{3}$	$\Q(\sqrt{-37}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{18}+\cdots$
3700.1.b.c	$3700$	$1$	3700.b	148.b	$2$	$1$	$1$	$1.847$	$\Q$	$D_{3}$	$\Q(\sqrt{-37}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+q^{8}+q^{9}+q^{16}+q^{18}+\cdots$
3700.1.b.d	$3700$	$1$	3700.b	148.b	$2$	$1$	$1$	$1.847$	$\Q$	$D_{3}$	$\Q(\sqrt{-37}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+q^{8}+q^{9}+q^{16}+q^{18}+\cdots$
3700.1.b.e	$3700$	$1$	3700.b	148.b	$2$	$2$	$2$	$1.847$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-185}) $	$\Q(\sqrt{185}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{2}-q^{4}+iq^{8}+q^{9}-iq^{13}+\cdots$
3700.1.b.f	$3700$	$1$	3700.b	148.b	$2$	$4$	$4$	$1.847$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-185}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q+\zeta_{8}^{2}q^{2}+(-\zeta_{8}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots$
3700.1.g.a	$3700$	$1$	3700.g	740.g	$2$	$2$	$2$	$1.847$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-37}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{2}-q^{4}+iq^{8}-q^{9}+q^{16}+iq^{18}+\cdots$
3700.1.g.b	$3700$	$1$	3700.g	740.g	$2$	$2$	$2$	$1.847$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-37}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{2}-q^{4}+iq^{8}-q^{9}+q^{16}+iq^{18}+\cdots$
3700.1.j.a	$3700$	$1$	3700.j	37.d	$4$	$2$	$1$	$1.847$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-iq^{3}-q^{7}-iq^{11}+iq^{21}-iq^{27}+\cdots$
3700.1.j.b	$3700$	$1$	3700.j	37.d	$4$	$2$	$1$	$1.847$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$0$	$2$		$1$		$q+iq^{3}+q^{7}-iq^{11}+iq^{21}+iq^{27}+\cdots$
3700.1.j.c	$3700$	$1$	3700.j	37.d	$4$	$2$	$1$	$1.847$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$0$	$2$		$1$		$q-iq^{3}+q^{7}-iq^{11}+(1+i)q^{17}+\cdots$
3700.1.p.a	$3700$	$1$	3700.p	740.p	$4$	$2$	$1$	$1.847$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+iq^{2}-q^{4}-iq^{8}+iq^{9}+q^{16}+\cdots$
3700.1.s.a	$3700$	$1$	3700.s	740.s	$4$	$2$	$1$	$1.847$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+q^{8}-iq^{9}+q^{16}+iq^{17}+\cdots$
3700.1.t.a	$3700$	$1$	3700.t	185.j	$4$	$2$	$1$	$1.847$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-q^{3}+iq^{7}-iq^{11}+(-1+i)q^{17}+\cdots$
3700.1.t.b	$3700$	$1$	3700.t	185.j	$4$	$2$	$1$	$1.847$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$0$	$2$	$0$	$0$		$1$		$q+q^{3}-iq^{7}-iq^{11}+(1-i)q^{17}+\cdots$
3700.1.x.a	$3700$	$1$	3700.x	740.w	$6$	$4$	$2$	$1.847$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{3}q^{8}+\cdots$
3700.1.z.a	$3700$	$1$	3700.z	148.i	$6$	$2$	$1$	$1.847$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
3700.1.ba.a	$3700$	$1$	3700.ba	148.j	$6$	$4$	$2$	$1.847$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{3}q^{8}+\cdots$
3700.1.bf.a	$3700$	$1$	3700.bf	3700.af	$10$	$4$	$1$	$1.847$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-1$	$0$		$1$		$q+\zeta_{10}^{2}q^{2}+\zeta_{10}^{4}q^{4}-\zeta_{10}q^{5}-\zeta_{10}q^{8}+\cdots$
3700.1.bf.b	$3700$	$1$	3700.bf	3700.af	$10$	$4$	$1$	$1.847$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$1$	$0$		$1$		$q-\zeta_{10}^{2}q^{2}+\zeta_{10}^{4}q^{4}+\zeta_{10}q^{5}+\zeta_{10}q^{8}+\cdots$
3700.1.br.a	$3700$	$1$	3700.br	740.aj	$12$	$4$	$1$	$1.847$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{4}q^{2}-\zeta_{12}^{2}q^{4}+q^{8}-\zeta_{12}q^{9}+\cdots$
3700.1.bu.a	$3700$	$1$	3700.bu	740.am	$12$	$4$	$1$	$1.847$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{3}q^{8}+\cdots$
3700.1.cb.a	$3700$	$1$	3700.cb	740.as	$18$	$12$	$2$	$1.847$	$\Q(\zeta_{36})$	$D_{9}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{36}^{17}q^{2}-\zeta_{36}^{16}q^{4}-\zeta_{36}^{15}q^{8}+\cdots$
3700.1.cc.a	$3700$	$1$	3700.cc	148.o	$18$	$12$	$2$	$1.847$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{36}^{11}q^{2}-\zeta_{36}^{4}q^{4}-\zeta_{36}^{15}q^{8}+\cdots$
3700.1.ce.a	$3700$	$1$	3700.ce	148.p	$18$	$6$	$1$	$1.847$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+\zeta_{18}^{3}q^{8}+\cdots$
3700.1.ch.a	$3700$	$1$	3700.ch	3700.bh	$20$	$8$	$1$	$1.847$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$2$	$0$	$2$	$0$		$1$		$q+\zeta_{20}^{2}q^{2}+\zeta_{20}^{4}q^{4}+\zeta_{20}^{6}q^{5}+\cdots$
3700.1.ck.a	$3700$	$1$	3700.ck	3700.bk	$20$	$8$	$1$	$1.847$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{20}^{3}q^{2}+\zeta_{20}^{6}q^{4}-\zeta_{20}^{9}q^{5}+\cdots$
3700.1.cu.a	$3700$	$1$	3700.cu	3700.bu	$30$	$8$	$1$	$1.847$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$-2$	$0$		$1$		$q+\zeta_{30}^{14}q^{2}-\zeta_{30}^{13}q^{4}+\zeta_{30}^{12}q^{5}+\cdots$
3700.1.cu.b	$3700$	$1$	3700.cu	3700.bu	$30$	$8$	$1$	$1.847$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$1$	$0$		$1$		$q+\zeta_{30}^{14}q^{2}-\zeta_{30}^{13}q^{4}+\zeta_{30}^{2}q^{5}+\cdots$
3700.1.cx.a	$3700$	$1$	3700.cx	3700.bx	$30$	$8$	$1$	$1.847$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$2$	$0$		$1$		$q+\zeta_{30}^{11}q^{2}-\zeta_{30}^{7}q^{4}+\zeta_{30}^{3}q^{5}+\cdots$
3700.1.cx.b	$3700$	$1$	3700.cx	3700.bx	$30$	$8$	$1$	$1.847$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$1$	$0$		$1$		$q-\zeta_{30}^{11}q^{2}-\zeta_{30}^{7}q^{4}+\zeta_{30}^{8}q^{5}+\cdots$
3700.1.cy.a	$3700$	$1$	3700.cy	740.aw	$36$	$12$	$1$	$1.847$	$\Q(\zeta_{36})$	$D_{36}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{36}^{11}q^{2}-\zeta_{36}^{4}q^{4}-\zeta_{36}^{15}q^{8}+\cdots$
3700.1.dd.a	$3700$	$1$	3700.dd	740.bb	$36$	$12$	$1$	$1.847$	$\Q(\zeta_{36})$	$D_{36}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{36}^{16}q^{2}-\zeta_{36}^{14}q^{4}+\zeta_{36}^{12}q^{8}+\cdots$
3700.1.dn.a	$3700$	$1$	3700.dn	3700.cn	$60$	$16$	$1$	$1.847$	$\Q(\zeta_{60})$	$D_{60}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{60}^{13}q^{2}+\zeta_{60}^{26}q^{4}+\zeta_{60}^{9}q^{5}+\cdots$
3700.1.dq.a	$3700$	$1$	3700.dq	3700.cq	$60$	$16$	$1$	$1.847$	$\Q(\zeta_{60})$	$D_{60}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$-2$	$0$		$1$		$q+\zeta_{60}^{26}q^{2}-\zeta_{60}^{22}q^{4}-\zeta_{60}^{8}q^{5}+\cdots$
3700.1.dx.a	$3700$	$1$	3700.dx	3700.cx	$90$	$24$	$1$	$1.847$	$\Q(\zeta_{45})$	$D_{45}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{90}^{19}q^{2}+\zeta_{90}^{38}q^{4}+\zeta_{90}^{22}q^{5}+\cdots$
3700.1.dx.b	$3700$	$1$	3700.dx	3700.cx	$90$	$24$	$1$	$1.847$	$\Q(\zeta_{45})$	$D_{45}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$3$	$0$		$1$		$q-\zeta_{90}^{19}q^{2}+\zeta_{90}^{38}q^{4}+\zeta_{90}^{42}q^{5}+\cdots$
3700.1.dy.a	$3700$	$1$	3700.dy	3700.cy	$90$	$24$	$1$	$1.847$	$\Q(\zeta_{45})$	$D_{90}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-3$	$0$		$1$		$q-\zeta_{90}^{2}q^{2}+\zeta_{90}^{4}q^{4}+\zeta_{90}^{21}q^{5}+\cdots$
3700.1.dy.b	$3700$	$1$	3700.dy	3700.cy	$90$	$24$	$1$	$1.847$	$\Q(\zeta_{45})$	$D_{90}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{90}^{2}q^{2}+\zeta_{90}^{4}q^{4}+\zeta_{90}^{26}q^{5}+\cdots$
3700.1.ek.a	$3700$	$1$	3700.ek	3700.dk	$180$	$48$	$1$	$1.847$	$\Q(\zeta_{180})$	$D_{180}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{180}^{52}q^{2}-\zeta_{180}^{14}q^{4}+\zeta_{180}^{46}q^{5}+\cdots$
3700.1.ep.a	$3700$	$1$	3700.ep	3700.dp	$180$	$48$	$1$	$1.847$	$\Q(\zeta_{180})$	$D_{180}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{180}^{89}q^{2}-\zeta_{180}^{88}q^{4}+\zeta_{180}^{57}q^{5}+\cdots$
3700.2.a.a	$3700$	$2$	3700.a	1.a	$1$	$1$	$1$	$29.545$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$0$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+3q^{7}+6q^{9}+5q^{11}-2q^{13}+\cdots$
3700.2.a.b	$3700$	$2$	3700.a	1.a	$1$	$1$	$1$	$29.545$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+2q^{7}+q^{9}+6q^{11}-4q^{13}+\cdots$
3700.2.a.c	$3700$	$2$	3700.a	1.a	$1$	$1$	$1$	$29.545$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}-2q^{9}-3q^{11}+4q^{13}+\cdots$
3700.2.a.d	$3700$	$2$	3700.a	1.a	$1$	$1$	$1$	$29.545$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}-2q^{9}-3q^{11}+6q^{13}+\cdots$
3700.2.a.e	$3700$	$2$	3700.a	1.a	$1$	$1$	$1$	$29.545$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{7}-2q^{9}+5q^{11}+6q^{17}+\cdots$
3700.2.a.f	$3700$	$2$	3700.a	1.a	$1$	$1$	$1$	$29.545$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{7}+q^{9}+6q^{11}+4q^{13}+\cdots$
3700.2.a.g	$3700$	$2$	3700.a	1.a	$1$	$2$	$2$	$29.545$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-\beta q^{7}+(1+\beta )q^{9}+\beta q^{11}+\cdots$
3700.2.a.h	$3700$	$2$	3700.a	1.a	$1$	$2$	$2$	$29.545$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-3+\beta )q^{7}+(1+2\beta )q^{9}+\cdots$
3700.2.a.i	$3700$	$2$	3700.a	1.a	$1$	$3$	$3$	$29.545$	3.3.148.1	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(-2\beta _{1}+\beta _{2})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots$

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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.