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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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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
497.1.ba.a	$497$	$1$	497.ba	497.aa	$70$	$24$	$1$	$0.248$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-3$	$0$	$0$	$1$	$1$		$q+(\zeta_{70}^{12}+\zeta_{70}^{20})q^{2}+(-\zeta_{70}^{5}+\zeta_{70}^{24}+\cdots)q^{4}+\cdots$
633.1.z.a	$633$	$1$	633.z	633.z	$70$	$24$	$1$	$0.316$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-3$	$1$		$q-\zeta_{70}^{9}q^{3}-\zeta_{70}^{11}q^{4}+(-\zeta_{70}^{5}+\cdots)q^{7}+\cdots$
781.1.bp.a	$781$	$1$	781.bp	781.ap	$70$	$24$	$1$	$0.390$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-5$	$2$	$0$	$1$		$q+(\zeta_{70}^{8}+\zeta_{70}^{14})q^{3}+\zeta_{70}^{32}q^{4}+\cdots$
1031.1.b.c	$1031$	$1$	1031.b	1031.b	$2$	$12$	$12$	$0.515$	$\Q(\zeta_{35})^+$	$D_{35}$	$\Q(\sqrt{-1031}) $	None	✓	$2$	$0$	$1$	$-4$	$1$	$0$	$1$		$q+\beta _{9}q^{2}+\beta _{5}q^{3}+(-\beta _{3}-\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots$
1124.1.ba.a	$1124$	$1$	1124.ba	1124.aa	$70$	$24$	$1$	$0.561$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$2$	$0$	$1$		$q-\zeta_{70}^{19}q^{2}-\zeta_{70}^{3}q^{4}+(\zeta_{70}^{4}+\zeta_{70}^{8}+\cdots)q^{5}+\cdots$
1223.1.b.c	$1223$	$1$	1223.b	1223.b	$2$	$12$	$12$	$0.610$	$\Q(\zeta_{35})^+$	$D_{35}$	$\Q(\sqrt{-1223}) $	None	✓	$2$	$0$	$1$	$1$	$0$	$1$	$1$		$q+\beta _{9}q^{2}+\beta _{2}q^{3}+(-\beta _{3}-\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots$
1263.1.bj.a	$1263$	$1$	1263.bj	1263.aj	$70$	$24$	$1$	$0.630$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$2$	$1$		$q+\zeta_{70}^{6}q^{3}+\zeta_{70}^{8}q^{4}+(\zeta_{70}^{26}+\zeta_{70}^{32}+\cdots)q^{7}+\cdots$
1477.1.cl.a	$1477$	$1$	1477.cl	1477.bl	$70$	$24$	$1$	$0.737$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-5$	$0$	$0$	$1$	$1$		$q+(\zeta_{70}^{14}-\zeta_{70}^{23})q^{2}+(\zeta_{70}^{2}-\zeta_{70}^{11}+\cdots)q^{4}+\cdots$
1633.1.t.a	$1633$	$1$	1633.t	1633.t	$70$	$24$	$1$	$0.815$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$2$	$-3$	$0$	$0$	$1$		$q+(\zeta_{70}^{2}+\zeta_{70}^{16})q^{2}+(-\zeta_{70}^{13}+\zeta_{70}^{30}+\cdots)q^{3}+\cdots$
1661.1.t.b	$1661$	$1$	1661.t	1661.t	$10$	$24$	$6$	$0.829$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-151}) $	None		$4$	$0$	$-3$	$0$	$2$	$0$	$1$		$q+(-\zeta_{70}+\zeta_{70}^{20})q^{2}+(\zeta_{70}^{2}-\zeta_{70}^{5}+\cdots)q^{4}+\cdots$
1684.1.bj.a	$1684$	$1$	1684.bj	1684.aj	$70$	$24$	$1$	$0.840$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$2$	$0$	$1$		$q-\zeta_{70}^{23}q^{2}-\zeta_{70}^{11}q^{4}+(\zeta_{70}^{16}+\cdots)q^{5}+\cdots$
1688.1.cc.a	$1688$	$1$	1688.cc	1688.bc	$70$	$24$	$1$	$0.842$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$-3$	$0$	$0$	$1$		$q-\zeta_{70}^{19}q^{2}+(-\zeta_{70}^{25}+\zeta_{70}^{34}+\cdots)q^{3}+\cdots$
1775.1.p.b	$1775$	$1$	1775.p	1775.p	$10$	$24$	$6$	$0.886$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-71}) $	None		$4$	$0$	$-3$	$2$	$1$	$0$	$1$		$q+(-\zeta_{70}+\zeta_{70}^{20})q^{2}+(\zeta_{70}^{18}+\zeta_{70}^{24}+\cdots)q^{3}+\cdots$
1893.1.bh.a	$1893$	$1$	1893.bh	1893.ah	$70$	$24$	$1$	$0.945$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-3$	$1$		$q+\zeta_{70}^{8}q^{3}+\zeta_{70}^{28}q^{4}+(-\zeta_{70}^{15}+\cdots)q^{7}+\cdots$
1967.1.br.a	$1967$	$1$	1967.br	1967.ar	$70$	$24$	$1$	$0.982$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-3$	$0$	$0$	$-6$	$1$		$q+(-\zeta_{70}^{13}-\zeta_{70}^{25})q^{2}+(-\zeta_{70}^{3}+\cdots)q^{4}+\cdots$
2087.1.b.c	$2087$	$1$	2087.b	2087.b	$2$	$12$	$12$	$1.042$	$\Q(\zeta_{35})^+$	$D_{35}$	$\Q(\sqrt{-2087}) $	None	✓	$2$	$0$	$1$	$-4$	$0$	$0$	$1$		$q+\beta _{9}q^{2}+(-1-\beta _{5}-\beta _{10})q^{3}+(-\beta _{3}+\cdots)q^{4}+\cdots$
2201.1.da.a	$2201$	$1$	2201.da	2201.ca	$70$	$24$	$1$	$1.098$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$-3$	$0$	$-3$	$-5$	$1$		$q+(\zeta_{70}^{8}+\zeta_{70}^{10})q^{2}+(\zeta_{70}^{16}+\zeta_{70}^{18}+\cdots)q^{4}+\cdots$
2233.1.cv.a	$2233$	$1$	2233.cv	2233.bv	$70$	$24$	$1$	$1.114$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$1$	$1$		$q+(-\zeta_{70}^{17}-\zeta_{70}^{19})q^{2}+(-\zeta_{70}+\cdots)q^{4}+\cdots$
2233.1.cv.b	$2233$	$1$	2233.cv	2233.bv	$70$	$24$	$1$	$1.114$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$1$	$1$		$q+(\zeta_{70}^{12}+\zeta_{70}^{24})q^{2}+(-\zeta_{70}-\zeta_{70}^{13}+\cdots)q^{4}+\cdots$
2239.1.b.c	$2239$	$1$	2239.b	2239.b	$2$	$12$	$12$	$1.117$	$\Q(\zeta_{35})^+$	$D_{35}$	$\Q(\sqrt{-2239}) $	None	✓	$2$	$0$	$1$	$0$	$-4$	$1$	$1$		$q+\beta _{9}q^{2}+(-\beta _{3}-\beta _{5}+\beta _{6}-\beta _{7}-\beta _{10}+\cdots)q^{4}+\cdots$
2248.1.cc.a	$2248$	$1$	2248.cc	2248.bc	$70$	$24$	$1$	$1.122$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$-3$	$0$	$0$	$1$		$q+\zeta_{70}^{4}q^{2}+(-\zeta_{70}^{27}+\zeta_{70}^{30})q^{3}+\cdots$
2303.1.j.b	$2303$	$1$	2303.j	2303.j	$14$	$24$	$4$	$1.149$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-47}) $	None		$4$	$0$	$2$	$2$	$0$	$1$	$1$		$q+(-\zeta_{70}^{13}-\zeta_{70}^{27})q^{2}+(\zeta_{70}^{6}-\zeta_{70}^{9}+\cdots)q^{3}+\cdots$
2365.1.w.c	$2365$	$1$	2365.w	2365.w	$10$	$24$	$6$	$1.180$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-215}) $	None		$4$	$0$	$-2$	$3$	$6$	$3$	$1$		$q+(-\zeta_{70}^{2}+\zeta_{70}^{19})q^{2}+(\zeta_{70}^{3}+\zeta_{70}^{25}+\cdots)q^{3}+\cdots$
2365.1.w.d	$2365$	$1$	2365.w	2365.w	$10$	$24$	$6$	$1.180$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-215}) $	None		$4$	$0$	$2$	$-3$	$-6$	$-3$	$1$		$q+(\zeta_{70}^{2}-\zeta_{70}^{19})q^{2}+(-\zeta_{70}^{3}-\zeta_{70}^{25}+\cdots)q^{3}+\cdots$
2485.1.cu.a	$2485$	$1$	2485.cu	2485.bu	$70$	$24$	$1$	$1.240$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$-3$	$-6$	$1$	$1$		$q+(\zeta_{70}^{10}+\zeta_{70}^{12})q^{3}+\zeta_{70}^{32}q^{4}+\cdots$
2485.1.cu.b	$2485$	$1$	2485.cu	2485.bu	$70$	$24$	$1$	$1.240$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$3$	$6$	$-1$	$1$		$q+(-\zeta_{70}^{10}-\zeta_{70}^{12})q^{3}+\zeta_{70}^{32}q^{4}+\cdots$
2543.1.b.c	$2543$	$1$	2543.b	2543.b	$2$	$12$	$12$	$1.269$	$\Q(\zeta_{35})^+$	$D_{35}$	$\Q(\sqrt{-2543}) $	None	✓	$2$	$0$	$1$	$1$	$0$	$0$	$1$		$q+\beta _{9}q^{2}+\beta _{2}q^{3}+(-\beta _{3}-\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots$
2769.1.cw.a	$2769$	$1$	2769.cw	2769.bw	$70$	$24$	$1$	$1.382$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-39}) $	None		$4$	$0$	$-5$	$1$	$-3$	$0$	$1$		$q+(-\zeta_{70}^{21}-\zeta_{70}^{31})q^{2}-\zeta_{70}^{31}q^{3}+\cdots$
2769.1.cw.b	$2769$	$1$	2769.cw	2769.bw	$70$	$24$	$1$	$1.382$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-39}) $	None		$4$	$0$	$5$	$1$	$3$	$0$	$1$		$q+(\zeta_{70}^{21}+\zeta_{70}^{31})q^{2}-\zeta_{70}^{31}q^{3}+\cdots$
2804.1.x.a	$2804$	$1$	2804.x	2804.x	$70$	$24$	$1$	$1.399$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$2$	$0$	$1$		$q+\zeta_{70}^{26}q^{2}-\zeta_{70}^{17}q^{4}+(\zeta_{70}^{2}-\zeta_{70}^{29}+\cdots)q^{5}+\cdots$
2900.1.cl.a	$2900$	$1$	2900.cl	2900.bl	$70$	$24$	$1$	$1.447$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$1$	$0$	$1$		$q+\zeta_{70}^{8}q^{2}+\zeta_{70}^{16}q^{4}+\zeta_{70}^{4}q^{5}+\cdots$
2900.1.cl.b	$2900$	$1$	2900.cl	2900.bl	$70$	$24$	$1$	$1.447$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$1$	$0$	$1$		$q+\zeta_{70}^{8}q^{2}+\zeta_{70}^{16}q^{4}-\zeta_{70}^{19}q^{5}+\cdots$
2947.1.dh.a	$2947$	$1$	2947.dh	2947.ch	$70$	$24$	$1$	$1.471$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-3$	$0$	$0$	$1$	$1$		$q+(\zeta_{70}^{6}+\zeta_{70}^{30})q^{2}+(-\zeta_{70}+\zeta_{70}^{12}+\cdots)q^{4}+\cdots$
2987.1.n.b	$2987$	$1$	2987.n	2987.n	$14$	$24$	$4$	$1.491$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$-5$	$0$	$0$	$2$	$1$		$q+(-\zeta_{70}^{3}-\zeta_{70}^{7})q^{2}+(\zeta_{70}^{6}+\zeta_{70}^{10}+\cdots)q^{4}+\cdots$
3153.1.bd.a	$3153$	$1$	3153.bd	3153.ad	$70$	$24$	$1$	$1.574$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-4$	$0$	$2$	$1$		$q-\zeta_{70}^{25}q^{3}+\zeta_{70}^{22}q^{4}+(\zeta_{70}^{2}+\zeta_{70}^{4}+\cdots)q^{7}+\cdots$
3165.1.cv.a	$3165$	$1$	3165.cv	3165.bv	$70$	$24$	$1$	$1.580$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-2$	$-1$	$-1$	$0$	$1$		$q+(-\zeta_{70}^{18}+\zeta_{70}^{29})q^{2}+\zeta_{70}^{13}q^{3}+\cdots$
3165.1.cv.b	$3165$	$1$	3165.cv	3165.bv	$70$	$24$	$1$	$1.580$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$2$	$1$	$1$	$0$	$1$		$q+(\zeta_{70}^{18}-\zeta_{70}^{29})q^{2}-\zeta_{70}^{13}q^{3}+\cdots$
3239.1.d.e	$3239$	$1$	3239.d	3239.d	$2$	$12$	$12$	$1.616$	$\Q(\zeta_{35})^+$	$D_{35}$	$\Q(\sqrt{-3239}) $	None	✓	$2$	$0$	$1$	$-6$	$1$	$1$	$1$		$q+\beta _{9}q^{2}+(-1-\beta _{7})q^{3}+(-\beta _{3}-\beta _{5}+\cdots)q^{4}+\cdots$
3239.1.d.f	$3239$	$1$	3239.d	3239.d	$2$	$12$	$12$	$1.616$	$\Q(\zeta_{35})^+$	$D_{35}$	$\Q(\sqrt{-3239}) $	None	✓	$2$	$0$	$1$	$6$	$1$	$-1$	$1$		$q+(-1-\beta _{3}-\beta _{5}+\beta _{6}-\beta _{7}-\beta _{10}+\cdots)q^{2}+\cdots$
3311.1.ev.a	$3311$	$1$	3311.ev	3311.dv	$70$	$24$	$1$	$1.652$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$-6$	$1$		$q+(\zeta_{70}^{16}-\zeta_{70}^{17})q^{2}+(\zeta_{70}^{32}-\zeta_{70}^{33}+\cdots)q^{4}+\cdots$
3311.1.ev.b	$3311$	$1$	3311.ev	3311.dv	$70$	$24$	$1$	$1.652$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$-6$	$1$		$q+(\zeta_{70}^{2}-\zeta_{70}^{31})q^{2}+(\zeta_{70}^{4}-\zeta_{70}^{27}+\cdots)q^{4}+\cdots$
3337.1.j.b	$3337$	$1$	3337.j	3337.j	$14$	$24$	$4$	$1.665$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-47}) $	None		$4$	$0$	$2$	$2$	$0$	$-5$	$1$		$q+(-\zeta_{70}^{23}+\zeta_{70}^{32})q^{2}+(\zeta_{70}^{6}+\zeta_{70}^{34}+\cdots)q^{3}+\cdots$
3437.1.bc.a	$3437$	$1$	3437.bc	3437.ac	$70$	$24$	$1$	$1.715$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-5$	$0$	$0$	$1$	$1$		$q+(-\zeta_{70}^{3}+\zeta_{70}^{28})q^{2}+(\zeta_{70}^{6}-\zeta_{70}^{21}+\cdots)q^{4}+\cdots$
3479.1.ey.a	$3479$	$1$	3479.ey	497.ae	$210$	$48$	$1$	$1.736$	$\Q(\zeta_{210})$	$D_{35}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$3$	$0$	$0$	$0$	$1$		$q+(-\zeta_{210}^{11}-\zeta_{210}^{65})q^{2}+(\zeta_{210}^{22}+\cdots)q^{4}+\cdots$
3621.1.cb.a	$3621$	$1$	3621.cb	3621.bb	$70$	$24$	$1$	$1.807$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-51}) $	None		$4$	$0$	$0$	$-1$	$-2$	$0$	$1$		$q+\zeta_{70}^{9}q^{3}-\zeta_{70}^{23}q^{4}+(-\zeta_{70}^{16}+\cdots)q^{5}+\cdots$
3621.1.cb.b	$3621$	$1$	3621.cb	3621.bb	$70$	$24$	$1$	$1.807$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-51}) $	None		$4$	$0$	$0$	$1$	$2$	$0$	$1$		$q-\zeta_{70}^{9}q^{3}-\zeta_{70}^{23}q^{4}+(\zeta_{70}^{16}-\zeta_{70}^{33}+\cdots)q^{5}+\cdots$
3692.1.cu.a	$3692$	$1$	3692.cu	3692.bu	$70$	$24$	$1$	$1.843$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$-1$	$0$	$0$	$-2$	$1$		$q-\zeta_{70}^{6}q^{2}+\zeta_{70}^{12}q^{4}+(\zeta_{70}^{13}-\zeta_{70}^{24}+\cdots)q^{7}+\cdots$
3692.1.cu.b	$3692$	$1$	3692.cu	3692.bu	$70$	$24$	$1$	$1.843$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$1$	$0$	$0$	$2$	$1$		$q+\zeta_{70}^{6}q^{2}+\zeta_{70}^{12}q^{4}+(-\zeta_{70}^{13}+\cdots)q^{7}+\cdots$
3773.1.k.a	$3773$	$1$	3773.k	77.j	$10$	$24$	$6$	$1.883$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+(\zeta_{70}^{2}-\zeta_{70}^{19})q^{2}+(-\zeta_{70}^{3}+\zeta_{70}^{4}+\cdots)q^{4}+\cdots$
3773.1.u.a	$3773$	$1$	3773.u	77.p	$30$	$48$	$6$	$1.883$	$\Q(\zeta_{210})$	$D_{35}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$-2$	$0$	$0$	$0$	$1$		$q+(-\zeta_{210}^{19}-\zeta_{210}^{37})q^{2}+(\zeta_{210}^{38}+\cdots)q^{4}+\cdots$

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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.