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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 98 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
79.1.b.a	$79$	$1$	79.b	79.b	$2$	$2$	$2$	$0.039$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-79}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{5}-q^{8}+\cdots$
395.1.c.a	$395$	$1$	395.c	395.c	$2$	$1$	$1$	$0.197$	$\Q$	$D_{2}$	$\Q(\sqrt{-79}) $, $\Q(\sqrt{-395}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+q^{4}+q^{5}-q^{9}-2q^{11}+q^{16}-2q^{19}+\cdots$
395.1.c.c	$395$	$1$	395.c	395.c	$2$	$4$	$4$	$0.197$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+(\zeta_{10}+\zeta_{10}^{4})q^{2}+(-1+\zeta_{10}^{2}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots$
632.1.f.a	$632$	$1$	632.f	632.f	$2$	$1$	$1$	$0.315$	$\Q$	$D_{2}$	$\Q(\sqrt{-79}) $, $\Q(\sqrt{-158}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}+q^{8}-q^{9}+q^{16}-q^{18}+\cdots$
632.1.f.c	$632$	$1$	632.f	632.f	$2$	$4$	$4$	$0.315$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+(-\zeta_{10}-\zeta_{10}^{4}+\cdots)q^{5}+\cdots$
711.1.d.a	$711$	$1$	711.d	79.b	$2$	$1$	$1$	$0.355$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-79}) $	$\Q(\sqrt{237}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{4}+2q^{13}+q^{16}+2q^{19}-q^{25}+\cdots$
711.1.d.b	$711$	$1$	711.d	79.b	$2$	$2$	$2$	$0.355$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-79}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$0$	$1$		$q+(1-\beta )q^{2}+(1-\beta )q^{4}+\beta q^{5}+q^{8}+\cdots$
711.1.d.c	$711$	$1$	711.d	79.b	$2$	$4$	$4$	$0.355$	$\Q(\zeta_{20})^+$	$D_{10}$	$\Q(\sqrt{-79}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{3}q^{5}+(-\beta _{1}+\cdots)q^{8}+\cdots$
869.1.j.a	$869$	$1$	869.j	869.j	$10$	$20$	$5$	$0.434$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{50}^{9}-\zeta_{50}^{21})q^{2}+(-\zeta_{50}^{5}+\cdots)q^{4}+\cdots$
1027.1.b.a	$1027$	$1$	1027.b	1027.b	$2$	$1$	$1$	$0.513$	$\Q$	$D_{2}$	$\Q(\sqrt{-79}) $, $\Q(\sqrt{-1027}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}+q^{9}-q^{13}+q^{16}-2q^{23}+\cdots$
1027.1.b.b	$1027$	$1$	1027.b	1027.b	$2$	$4$	$4$	$0.513$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{10}+\zeta_{10}^{4})q^{2}+(-1+\zeta_{10}^{2}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots$
1027.1.o.a	$1027$	$1$	1027.o	1027.o	$6$	$2$	$1$	$0.513$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$1$	$0$	$-2$	$0$	$1$		$q-\zeta_{6}^{2}q^{2}-q^{5}+q^{8}-\zeta_{6}q^{9}+\zeta_{6}^{2}q^{10}+\cdots$
1027.1.o.b	$1027$	$1$	1027.o	1027.o	$6$	$8$	$4$	$0.513$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$-1$	$0$	$2$	$0$	$1$		$q+(\zeta_{30}^{4}+\zeta_{30}^{6})q^{2}+(\zeta_{30}^{8}+\zeta_{30}^{10}+\cdots)q^{4}+\cdots$
1027.1.s.a	$1027$	$1$	1027.s	1027.s	$6$	$2$	$1$	$0.513$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$3$	$0$	$0$	$0$	$1$		$q+(1-\zeta_{6}^{2})q^{2}+(1-\zeta_{6}-\zeta_{6}^{2})q^{4}+\cdots$
1027.1.s.b	$1027$	$1$	1027.s	1027.s	$6$	$8$	$4$	$0.513$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$	$1$		$q+(-\zeta_{30}^{8}+\zeta_{30}^{12})q^{2}+(-\zeta_{30}+\zeta_{30}^{5}+\cdots)q^{4}+\cdots$
1264.1.e.a	$1264$	$1$	1264.e	79.b	$2$	$2$	$2$	$0.631$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-79}) $	None	✓	$2$	$0$	$0$	$0$	$-1$	$0$	$1$		$q-\beta q^{5}+q^{9}+(1-\beta )q^{11}+(-1+\beta )q^{13}+\cdots$
1264.1.l.a	$1264$	$1$	1264.l	1264.l	$4$	$2$	$1$	$0.631$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$-2$	$0$	$-2$	$0$	$1$		$q-q^{2}+q^{4}+(-1-i)q^{5}-q^{8}-iq^{9}+\cdots$
1264.1.l.b	$1264$	$1$	1264.l	1264.l	$4$	$8$	$4$	$0.631$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$2$	$0$	$2$	$0$	$1$		$q-\zeta_{20}^{8}q^{2}-\zeta_{20}^{6}q^{4}+(\zeta_{20}^{6}-\zeta_{20}^{9}+\cdots)q^{5}+\cdots$
1501.1.k.a	$1501$	$1$	1501.k	1501.k	$6$	$2$	$1$	$0.749$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$1$	$0$	$1$	$0$	$1$		$q+\zeta_{6}q^{2}+\zeta_{6}q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{10}+\cdots$
1501.1.k.b	$1501$	$1$	1501.k	1501.k	$6$	$8$	$4$	$0.749$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q+(\zeta_{30}^{8}+\zeta_{30}^{12})q^{2}+(-\zeta_{30}-\zeta_{30}^{5}+\cdots)q^{4}+\cdots$
1501.1.bc.a	$1501$	$1$	1501.bc	1501.ac	$18$	$6$	$1$	$0.749$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$-3$	$0$	$-3$	$0$	$1$		$q+(-\zeta_{18}+\zeta_{18}^{6})q^{2}+(\zeta_{18}^{2}-\zeta_{18}^{3}+\cdots)q^{4}+\cdots$
1501.1.bc.b	$1501$	$1$	1501.bc	1501.ac	$18$	$24$	$4$	$0.749$	$\Q(\zeta_{45})$	$D_{45}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$3$	$0$	$3$	$0$	$1$		$q+(-\zeta_{90}^{11}-\zeta_{90}^{39})q^{2}+(-\zeta_{90}^{5}+\cdots)q^{4}+\cdots$
1580.1.k.a	$1580$	$1$	1580.k	1580.k	$4$	$2$	$1$	$0.789$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-iq^{2}-q^{4}-q^{5}+iq^{8}-iq^{9}+iq^{10}+\cdots$
1580.1.k.b	$1580$	$1$	1580.k	1580.k	$4$	$2$	$1$	$0.789$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$2$	$0$	$-2$	$0$	$1$		$q+q^{2}+q^{4}-q^{5}+q^{8}-iq^{9}-q^{10}+\cdots$
1580.1.k.c	$1580$	$1$	1580.k	1580.k	$4$	$8$	$4$	$0.789$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$-2$	$0$	$2$	$0$	$1$		$q+\zeta_{20}^{8}q^{2}-\zeta_{20}^{6}q^{4}+\zeta_{20}^{6}q^{5}+\cdots$
1580.1.k.d	$1580$	$1$	1580.k	1580.k	$4$	$8$	$4$	$0.789$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q-\zeta_{20}q^{2}+\zeta_{20}^{2}q^{4}-\zeta_{20}^{8}q^{5}-\zeta_{20}^{3}q^{8}+\cdots$
1817.1.l.a	$1817$	$1$	1817.l	1817.l	$22$	$10$	$1$	$0.907$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$-2$	$0$	$-2$	$0$	$1$		$q+(-\zeta_{22}-\zeta_{22}^{9})q^{2}+(\zeta_{22}^{2}-\zeta_{22}^{7}+\cdots)q^{4}+\cdots$
1817.1.l.b	$1817$	$1$	1817.l	1817.l	$22$	$40$	$4$	$0.907$	$\Q(\zeta_{55})$	$D_{55}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$2$	$0$	$2$	$0$	$1$		$q+(-\zeta_{110}^{7}+\zeta_{110}^{8})q^{2}+(\zeta_{110}^{14}-\zeta_{110}^{15}+\cdots)q^{4}+\cdots$
1975.1.c.a	$1975$	$1$	1975.c	395.c	$2$	$4$	$4$	$0.986$	$\Q(i, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{3}q^{8}-q^{9}+\beta _{2}q^{11}+\cdots$
1975.1.d.a	$1975$	$1$	1975.d	79.b	$2$	$1$	$1$	$0.986$	$\Q$	$D_{2}$	$\Q(\sqrt{-79}) $, $\Q(\sqrt{-395}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{4}+q^{9}-2q^{11}+q^{16}+2q^{19}+\cdots$
1975.1.d.c	$1975$	$1$	1975.d	79.b	$2$	$2$	$2$	$0.986$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-79}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$0$	$1$		$q+(1-\beta )q^{2}+(1-\beta )q^{4}+q^{8}+q^{9}+\cdots$
1975.1.d.d	$1975$	$1$	1975.d	79.b	$2$	$4$	$4$	$0.986$	$\Q(\zeta_{20})^+$	$D_{10}$	$\Q(\sqrt{-79}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{8}+\cdots$
1975.1.l.a	$1975$	$1$	1975.l	1975.l	$10$	$20$	$5$	$0.986$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{50}^{9}-\zeta_{50}^{21})q^{2}+(-\zeta_{50}^{5}+\cdots)q^{4}+\cdots$
1975.1.m.a	$1975$	$1$	1975.m	1975.m	$10$	$20$	$5$	$0.986$	$\Q(\zeta_{50})$	$D_{50}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{50}^{18}+\zeta_{50}^{22})q^{2}+(-\zeta_{50}^{11}+\cdots)q^{4}+\cdots$
2449.1.u.a	$2449$	$1$	2449.u	2449.u	$6$	$2$	$1$	$1.222$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$-2$	$0$	$1$	$0$	$1$		$q-q^{2}+\zeta_{6}q^{5}+q^{8}-\zeta_{6}q^{9}-\zeta_{6}q^{10}+\cdots$
2449.1.u.b	$2449$	$1$	2449.u	2449.u	$6$	$8$	$4$	$1.222$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$2$	$0$	$-1$	$0$	$1$		$q+(\zeta_{30}^{4}-\zeta_{30}^{11})q^{2}+(1-\zeta_{30}^{7}+\zeta_{30}^{8}+\cdots)q^{4}+\cdots$
2449.1.x.a	$2449$	$1$	2449.x	2449.x	$10$	$20$	$5$	$1.222$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{50}^{9}-\zeta_{50}^{21})q^{2}+(-\zeta_{50}^{5}+\cdots)q^{4}+\cdots$
2449.1.bg.a	$2449$	$1$	2449.bg	2449.ag	$30$	$40$	$5$	$1.222$	$\Q(\zeta_{75})$	$D_{75}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{150}^{7}+\zeta_{150}^{8})q^{2}+(\zeta_{150}^{14}-\zeta_{150}^{15}+\cdots)q^{4}+\cdots$
2528.1.f.a	$2528$	$1$	2528.f	632.f	$2$	$1$	$1$	$1.262$	$\Q$	$D_{2}$	$\Q(\sqrt{-79}) $, $\Q(\sqrt{-158}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{9}+2q^{23}+q^{25}+2q^{31}+q^{49}+\cdots$
2528.1.f.c	$2528$	$1$	2528.f	632.f	$2$	$4$	$4$	$1.262$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{2}$		$q+(\zeta_{10}^{2}+\zeta_{10}^{3})q^{5}-q^{9}+(\zeta_{10}+\zeta_{10}^{4}+\cdots)q^{11}+\cdots$
2528.1.x.a	$2528$	$1$	2528.x	2528.x	$8$	$4$	$1$	$1.262$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}^{2}q^{2}-q^{4}+(\zeta_{8}^{2}+\zeta_{8}^{3})q^{5}-\zeta_{8}^{2}q^{8}+\cdots$
2528.1.x.b	$2528$	$1$	2528.x	2528.x	$8$	$16$	$4$	$1.262$	$\Q(\zeta_{40})$	$D_{40}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{40}^{2}q^{2}+\zeta_{40}^{4}q^{4}+(-\zeta_{40}^{11}+\cdots)q^{5}+\cdots$
2844.1.e.a	$2844$	$1$	2844.e	948.e	$2$	$4$	$4$	$1.419$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-79}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$
2844.1.e.b	$2844$	$1$	2844.e	948.e	$2$	$16$	$16$	$1.419$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-79}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{40}^{11}q^{2}-\zeta_{40}^{2}q^{4}+(-\zeta_{40}^{3}+\cdots)q^{5}+\cdots$
3160.1.g.a	$3160$	$1$	3160.g	3160.g	$2$	$1$	$1$	$1.577$	$\Q$	$D_{2}$	$\Q(\sqrt{-79}) $, $\Q(\sqrt{-790}) $	$\Q(\sqrt{10}) $	✓	$4$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{9}+q^{10}+\cdots$
3160.1.g.b	$3160$	$1$	3160.g	3160.g	$2$	$1$	$1$	$1.577$	$\Q$	$D_{2}$	$\Q(\sqrt{-79}) $, $\Q(\sqrt{-790}) $	$\Q(\sqrt{10}) $	✓	$4$	$0$	$1$	$0$	$1$	$0$	$1$		$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{9}+q^{10}+\cdots$
3160.1.g.e	$3160$	$1$	3160.g	3160.g	$2$	$4$	$4$	$1.577$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}-\zeta_{10}q^{5}+\zeta_{10}^{4}q^{8}+\cdots$
3160.1.g.f	$3160$	$1$	3160.g	3160.g	$2$	$4$	$4$	$1.577$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$1$	$0$	$1$	$0$	$1$		$q+\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+\zeta_{10}^{3}q^{5}+\zeta_{10}^{3}q^{8}+\cdots$
3160.1.v.a	$3160$	$1$	3160.v	3160.v	$4$	$2$	$1$	$1.577$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q-iq^{2}-q^{4}+q^{5}+iq^{8}+iq^{9}-iq^{10}+\cdots$
3160.1.v.b	$3160$	$1$	3160.v	3160.v	$4$	$2$	$1$	$1.577$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$2$	$0$	$-2$	$0$	$1$		$q+q^{2}+q^{4}-q^{5}+q^{8}+iq^{9}-q^{10}+\cdots$

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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.