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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 374 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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
140.1.h.a	$140$	$1$	140.h	35.c	$2$	$1$	$1$	$0.070$	$\Q$	$D_{3}$	$\Q(\sqrt{-35}) $	None	✓	$2$	$0$	$0$	$-1$	$1$	$1$	$1$		$q-q^{3}+q^{5}+q^{7}-q^{11}-q^{13}-q^{15}+\cdots$
140.1.h.b	$140$	$1$	140.h	35.c	$2$	$1$	$1$	$0.070$	$\Q$	$D_{3}$	$\Q(\sqrt{-35}) $	None	✓	$2$	$0$	$0$	$1$	$-1$	$-1$	$1$		$q+q^{3}-q^{5}-q^{7}-q^{11}+q^{13}-q^{15}+\cdots$
315.1.bg.a	$315$	$1$	315.bg	315.ag	$6$	$2$	$1$	$0.157$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$-2$	$1$	$1$	$1$		$q-q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\cdots$
315.1.bg.b	$315$	$1$	315.bg	315.ag	$6$	$2$	$1$	$0.157$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$2$	$-1$	$-1$	$1$		$q+q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots$
385.1.y.a	$385$	$1$	385.y	385.y	$10$	$4$	$1$	$0.192$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$-3$	$1$	$1$	$1$		$q+(-1+\zeta_{10})q^{3}+\zeta_{10}^{2}q^{4}-\zeta_{10}^{4}q^{5}+\cdots$
385.1.y.b	$385$	$1$	385.y	385.y	$10$	$4$	$1$	$0.192$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$3$	$-1$	$-1$	$1$		$q+(1-\zeta_{10})q^{3}+\zeta_{10}^{2}q^{4}+\zeta_{10}^{4}q^{5}+\cdots$
455.1.h.c	$455$	$1$	455.h	455.h	$2$	$2$	$2$	$0.227$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-35}) $, $\Q(\sqrt{-91}) $	$\Q(\sqrt{65}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{4}-iq^{5}-iq^{7}-q^{9}-iq^{13}+\cdots$
455.1.be.a	$455$	$1$	455.be	455.ae	$6$	$4$	$2$	$0.227$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-35}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{12}+\zeta_{12}^{3})q^{3}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{3}q^{5}+\cdots$
455.1.bp.a	$455$	$1$	455.bp	455.ap	$6$	$2$	$1$	$0.227$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$-1$	$-2$	$1$	$1$		$q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-q^{5}-\zeta_{6}^{2}q^{7}+\cdots$
455.1.bp.b	$455$	$1$	455.bp	455.ap	$6$	$2$	$1$	$0.227$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$1$	$2$	$-1$	$1$		$q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+\zeta_{6}^{2}q^{7}+\cdots$
525.1.k.a	$525$	$1$	525.k	105.k	$4$	$4$	$2$	$0.262$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-35}) $	$\Q(\sqrt{105}) $		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{9}+\cdots$
560.1.p.a	$560$	$1$	560.p	35.c	$2$	$1$	$1$	$0.279$	$\Q$	$D_{3}$	$\Q(\sqrt{-35}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$1$	$1$		$q-q^{3}-q^{5}+q^{7}+q^{11}+q^{13}+q^{15}+\cdots$
560.1.p.b	$560$	$1$	560.p	35.c	$2$	$1$	$1$	$0.279$	$\Q$	$D_{3}$	$\Q(\sqrt{-35}) $	None	✓	$2$	$0$	$0$	$1$	$1$	$-1$	$1$		$q+q^{3}+q^{5}-q^{7}+q^{11}-q^{13}+q^{15}+\cdots$
595.1.b.a	$595$	$1$	595.b	595.b	$2$	$2$	$2$	$0.297$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-35}) $, $\Q(\sqrt{-119}) $	$\Q(\sqrt{85}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}+q^{4}+iq^{5}-iq^{7}-3q^{9}+\cdots$
595.1.u.a	$595$	$1$	595.u	595.u	$4$	$4$	$2$	$0.297$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-35}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{4}-\zeta_{8}q^{5}+\zeta_{8}^{3}q^{7}-\zeta_{8}^{2}q^{9}+\cdots$
595.1.be.a	$595$	$1$	595.be	595.ae	$8$	$8$	$2$	$0.297$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-35}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{16}-\zeta_{16}^{5})q^{3}+\zeta_{16}^{4}q^{4}-\zeta_{16}^{3}q^{5}+\cdots$
700.1.d.a	$700$	$1$	700.d	7.b	$2$	$2$	$2$	$0.349$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}-iq^{7}-q^{11}-iq^{13}+iq^{17}+\cdots$
735.1.f.a	$735$	$1$	735.f	15.d	$2$	$1$	$1$	$0.367$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-35}) $	$\Q(\sqrt{21}) $	✓	$4$	$0$	$0$	$-1$	$-1$	$0$	$1$		$q-q^{3}-q^{4}-q^{5}+q^{9}+q^{12}+q^{15}+\cdots$
735.1.f.b	$735$	$1$	735.f	15.d	$2$	$1$	$1$	$0.367$	$\Q$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-35}) $	$\Q(\sqrt{21}) $	✓	$4$	$0$	$0$	$1$	$1$	$0$	$1$		$q+q^{3}-q^{4}+q^{5}+q^{9}-q^{12}+q^{15}+\cdots$
735.1.o.a	$735$	$1$	735.o	105.o	$6$	$2$	$1$	$0.367$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-35}) $	$\Q(\sqrt{21}) $		$8$	$0$	$0$	$-1$	$-1$	$0$	$1$		$q-\zeta_{6}q^{3}+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}+\cdots$
735.1.o.b	$735$	$1$	735.o	105.o	$6$	$2$	$1$	$0.367$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-35}) $	$\Q(\sqrt{21}) $		$8$	$0$	$0$	$1$	$1$	$0$	$1$		$q+\zeta_{6}q^{3}+\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}+\cdots$
875.1.c.a	$875$	$1$	875.c	35.c	$2$	$2$	$2$	$0.437$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-35}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$2$	$1$		$q+(-1+\beta )q^{3}+q^{4}+q^{7}+(1-\beta )q^{9}+\cdots$
875.1.c.b	$875$	$1$	875.c	35.c	$2$	$2$	$2$	$0.437$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-35}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$-2$	$1$		$q+(1-\beta )q^{3}+q^{4}-q^{7}+(1-\beta )q^{9}+\cdots$
875.1.d.a	$875$	$1$	875.d	7.b	$2$	$4$	$4$	$0.437$	$\Q(i, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{3}-q^{4}+\beta _{3}q^{7}+\beta _{2}q^{9}+\beta _{2}q^{11}+\cdots$
945.1.bg.a	$945$	$1$	945.bg	315.ag	$6$	$2$	$1$	$0.472$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$0$	$-1$	$1$	$1$		$q-\zeta_{6}q^{4}-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{11}+\cdots$
945.1.bg.b	$945$	$1$	945.bg	315.ag	$6$	$2$	$1$	$0.472$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$0$	$1$	$-1$	$1$		$q-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{11}+\cdots$
945.1.cw.a	$945$	$1$	945.cw	945.bw	$18$	$6$	$1$	$0.472$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$-3$	$0$	$0$	$1$		$q+\zeta_{18}^{6}q^{3}+\zeta_{18}^{4}q^{4}-\zeta_{18}q^{5}-\zeta_{18}^{5}q^{7}+\cdots$
945.1.cw.b	$945$	$1$	945.cw	945.bw	$18$	$6$	$1$	$0.472$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$3$	$0$	$0$	$1$		$q-\zeta_{18}^{6}q^{3}+\zeta_{18}^{4}q^{4}+\zeta_{18}q^{5}+\zeta_{18}^{5}q^{7}+\cdots$
980.1.n.a	$980$	$1$	980.n	35.i	$6$	$2$	$1$	$0.489$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$-1$	$1$	$0$	$1$		$q-\zeta_{6}q^{3}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{11}+q^{13}+\cdots$
980.1.n.b	$980$	$1$	980.n	35.i	$6$	$2$	$1$	$0.489$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$1$	$-1$	$0$	$1$		$q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{11}-q^{13}+\cdots$
1015.1.f.a	$1015$	$1$	1015.f	1015.f	$2$	$1$	$1$	$0.507$	$\Q$	$D_{2}$	$\Q(\sqrt{-35}) $, $\Q(\sqrt{-1015}) $	$\Q(\sqrt{29}) $	✓	$4$	$0$	$0$	$0$	$-1$	$-1$	$1$		$q-q^{4}-q^{5}-q^{7}+q^{9}+2q^{13}+q^{16}+\cdots$
1015.1.f.b	$1015$	$1$	1015.f	1015.f	$2$	$1$	$1$	$0.507$	$\Q$	$D_{2}$	$\Q(\sqrt{-35}) $, $\Q(\sqrt{-1015}) $	$\Q(\sqrt{29}) $	✓	$4$	$0$	$0$	$0$	$1$	$1$	$1$		$q-q^{4}+q^{5}+q^{7}+q^{9}-2q^{13}+q^{16}+\cdots$
1015.1.br.a	$1015$	$1$	1015.br	1015.ar	$14$	$6$	$1$	$0.507$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$0$	$-1$	$-1$	$1$		$q+(-\zeta_{14}^{2}+\zeta_{14}^{4})q^{3}-\zeta_{14}^{4}q^{4}+\cdots$
1015.1.br.b	$1015$	$1$	1015.br	1015.ar	$14$	$6$	$1$	$0.507$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$0$	$1$	$1$	$1$		$q+(\zeta_{14}^{2}-\zeta_{14}^{4})q^{3}-\zeta_{14}^{4}q^{4}-\zeta_{14}^{2}q^{5}+\cdots$
1015.1.bs.a	$1015$	$1$	1015.bs	1015.as	$14$	$6$	$1$	$0.507$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$-2$	$-1$	$-1$	$1$		$q+(-\zeta_{14}^{3}+\zeta_{14}^{6})q^{3}+\zeta_{14}^{6}q^{4}+\cdots$
1015.1.bs.b	$1015$	$1$	1015.bs	1015.as	$14$	$6$	$1$	$0.507$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$2$	$1$	$1$	$1$		$q+(\zeta_{14}^{3}-\zeta_{14}^{6})q^{3}+\zeta_{14}^{6}q^{4}+\zeta_{14}^{3}q^{5}+\cdots$
1155.1.e.a	$1155$	$1$	1155.e	1155.e	$2$	$2$	$2$	$0.576$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-35}) $, $\Q(\sqrt{-231}) $	$\Q(\sqrt{165}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}+q^{4}-iq^{5}+iq^{7}-q^{9}-q^{11}+\cdots$
1155.1.e.b	$1155$	$1$	1155.e	1155.e	$2$	$2$	$2$	$0.576$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-35}) $, $\Q(\sqrt{-231}) $	$\Q(\sqrt{165}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}+q^{4}-iq^{5}-iq^{7}-q^{9}+q^{11}+\cdots$
1155.1.ca.a	$1155$	$1$	1155.ca	1155.ba	$10$	$8$	$2$	$0.576$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-35}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{20}^{5}q^{3}+\zeta_{20}^{4}q^{4}-\zeta_{20}^{3}q^{5}+\cdots$
1155.1.ca.b	$1155$	$1$	1155.ca	1155.ba	$10$	$8$	$2$	$0.576$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-35}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{20}^{7}q^{3}+\zeta_{20}^{4}q^{4}-\zeta_{20}^{3}q^{5}+\cdots$
1225.1.g.a	$1225$	$1$	1225.g	5.c	$4$	$2$	$1$	$0.611$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-35}) $	$\Q(\sqrt{5}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{4}+iq^{9}+q^{11}-q^{16}-iq^{29}+\cdots$
1225.1.q.a	$1225$	$1$	1225.q	35.l	$12$	$4$	$1$	$0.611$	$\Q(\zeta_{12})$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-35}) $	$\Q(\sqrt{5}) $		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{12}q^{4}-\zeta_{12}^{5}q^{9}+\zeta_{12}^{4}q^{11}+\cdots$
1260.1.p.a	$1260$	$1$	1260.p	35.c	$2$	$1$	$1$	$0.629$	$\Q$	$D_{3}$	$\Q(\sqrt{-35}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$1$	$1$		$q-q^{5}+q^{7}+q^{11}-q^{13}+q^{17}+q^{25}+\cdots$
1260.1.p.b	$1260$	$1$	1260.p	35.c	$2$	$1$	$1$	$0.629$	$\Q$	$D_{3}$	$\Q(\sqrt{-35}) $	None	✓	$2$	$0$	$0$	$0$	$1$	$-1$	$1$		$q+q^{5}-q^{7}+q^{11}+q^{13}-q^{17}+q^{25}+\cdots$
1260.1.bt.a	$1260$	$1$	1260.bt	315.ag	$6$	$2$	$1$	$0.629$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$-1$	$-1$	$-1$	$1$		$q-\zeta_{6}q^{3}-\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
1260.1.bt.b	$1260$	$1$	1260.bt	315.ag	$6$	$2$	$1$	$0.629$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$-1$	$-1$	$-1$	$1$		$q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots$
1260.1.bt.c	$1260$	$1$	1260.bt	315.ag	$6$	$2$	$1$	$0.629$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$1$	$1$	$1$	$1$		$q+\zeta_{6}q^{3}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
1260.1.bt.d	$1260$	$1$	1260.bt	315.ag	$6$	$2$	$1$	$0.629$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$1$	$1$	$1$	$1$		$q-\zeta_{6}^{2}q^{3}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots$
1365.1.bg.a	$1365$	$1$	1365.bg	1365.ag	$4$	$4$	$2$	$0.681$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-35}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{3}q^{3}-\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{5}-\zeta_{8}^{3}q^{7}+\cdots$
1365.1.bg.b	$1365$	$1$	1365.bg	1365.ag	$4$	$4$	$2$	$0.681$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-35}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{3}-\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{5}+\zeta_{8}^{3}q^{7}+\cdots$

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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.