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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 211 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
55.1.d.a	$55$	$1$	55.d	55.d	$2$	$1$	$1$	$0.027$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q-q^{4}-q^{5}+q^{9}-q^{11}+q^{16}+q^{20}+\cdots$
275.1.c.a	$275$	$1$	275.c	11.b	$2$	$1$	$1$	$0.137$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{4}-q^{9}-q^{11}+q^{16}-2q^{31}+\cdots$
385.1.q.a	$385$	$1$	385.q	385.q	$6$	$2$	$1$	$0.192$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-55}) $	None		$4$	$0$	$-1$	$0$	$-1$	$-2$	$1$		$q-\zeta_{6}q^{2}-\zeta_{6}q^{5}-q^{7}-q^{8}-\zeta_{6}q^{9}+\cdots$
385.1.q.b	$385$	$1$	385.q	385.q	$6$	$2$	$1$	$0.192$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-55}) $	None		$4$	$0$	$1$	$0$	$-1$	$2$	$1$		$q+\zeta_{6}q^{2}-\zeta_{6}q^{5}+q^{7}+q^{8}-\zeta_{6}q^{9}+\cdots$
385.1.q.c	$385$	$1$	385.q	385.q	$6$	$4$	$2$	$0.192$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$2$	$0$	$1$		$q+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{2}+(-1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots$
440.1.o.e	$440$	$1$	440.o	440.o	$2$	$4$	$4$	$0.220$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{2}q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots$
495.1.h.a	$495$	$1$	495.h	55.d	$2$	$1$	$1$	$0.247$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q-q^{4}+q^{5}+q^{11}+q^{16}-q^{20}+q^{25}+\cdots$
495.1.h.b	$495$	$1$	495.h	55.d	$2$	$2$	$2$	$0.247$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-55}) $	None	✓	$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-\beta q^{2}+q^{4}-q^{5}-\beta q^{7}+\beta q^{10}+\cdots$
495.1.h.c	$495$	$1$	495.h	55.d	$2$	$2$	$2$	$0.247$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-55}) $	None	✓	$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q-\beta q^{2}+q^{4}+q^{5}+\beta q^{7}-\beta q^{10}+\cdots$
605.1.h.a	$605$	$1$	605.h	55.h	$10$	$4$	$1$	$0.302$	$\Q(\zeta_{10})$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{5}) $		$16$	$0$	$0$	$0$	$1$	$0$	$1$		$q+\zeta_{10}^{3}q^{4}+\zeta_{10}q^{5}+\zeta_{10}^{4}q^{9}-\zeta_{10}q^{16}+\cdots$
715.1.c.a	$715$	$1$	715.c	715.c	$2$	$4$	$4$	$0.357$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}-q^{4}+\zeta_{8}^{2}q^{5}+\cdots$
715.1.x.a	$715$	$1$	715.x	715.x	$6$	$2$	$1$	$0.357$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-55}) $	None		$4$	$0$	$-1$	$0$	$2$	$2$	$1$		$q-\zeta_{6}q^{2}+q^{5}-\zeta_{6}^{2}q^{7}-q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
715.1.x.b	$715$	$1$	715.x	715.x	$6$	$2$	$1$	$0.357$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-55}) $	None		$4$	$0$	$1$	$0$	$2$	$-2$	$1$		$q+\zeta_{6}q^{2}+q^{5}+\zeta_{6}^{2}q^{7}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
715.1.x.c	$715$	$1$	715.x	715.x	$6$	$4$	$2$	$0.357$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$-4$	$0$	$1$		$q+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{2}+(-1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots$
715.1.bb.a	$715$	$1$	715.bb	715.ab	$6$	$8$	$4$	$0.357$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{24}^{7}-\zeta_{24}^{9})q^{2}+(-\zeta_{24}^{2}+\zeta_{24}^{4}+\cdots)q^{4}+\cdots$
880.1.i.a	$880$	$1$	880.i	55.d	$2$	$1$	$1$	$0.439$	$\Q$	$D_{2}$	$\Q(\sqrt{-11}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q-q^{5}+q^{9}+q^{11}+q^{25}+2q^{31}+\cdots$
880.1.x.a	$880$	$1$	880.x	880.x	$4$	$8$	$4$	$0.439$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}+\zeta_{16}^{6}q^{5}+\cdots$
935.1.h.e	$935$	$1$	935.h	935.h	$2$	$4$	$4$	$0.467$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+q^{4}+\zeta_{8}^{2}q^{5}+(\zeta_{8}+\cdots)q^{7}+\cdots$
935.1.j.a	$935$	$1$	935.j	935.j	$4$	$8$	$4$	$0.467$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{16}-\zeta_{16}^{7})q^{2}+(-1+\zeta_{16}^{2}+\cdots)q^{4}+\cdots$
935.1.y.a	$935$	$1$	935.y	935.y	$8$	$16$	$4$	$0.467$	$\Q(\zeta_{32})$	$D_{16}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{32}^{11}-\zeta_{32}^{13})q^{2}+(-\zeta_{32}^{6}+\zeta_{32}^{8}+\cdots)q^{4}+\cdots$
1100.1.i.a	$1100$	$1$	1100.i	220.i	$4$	$2$	$1$	$0.549$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-55}) $	None		$4$	$0$	$-2$	$0$	$0$	$2$	$1$		$q-q^{2}+q^{4}+(1-i)q^{7}-q^{8}+iq^{9}+\cdots$
1100.1.i.b	$1100$	$1$	1100.i	220.i	$4$	$2$	$1$	$0.549$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-55}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-iq^{2}-q^{4}+(-1+i)q^{7}+iq^{8}+\cdots$
1100.1.i.c	$1100$	$1$	1100.i	220.i	$4$	$2$	$1$	$0.549$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-55}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+iq^{2}-q^{4}+(1-i)q^{7}-iq^{8}+iq^{9}+\cdots$
1100.1.i.d	$1100$	$1$	1100.i	220.i	$4$	$2$	$1$	$0.549$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-55}) $	None		$4$	$0$	$2$	$0$	$0$	$-2$	$1$		$q+q^{2}+q^{4}+(-1+i)q^{7}+q^{8}+iq^{9}+\cdots$
1375.1.c.a	$1375$	$1$	1375.c	11.b	$2$	$4$	$4$	$0.686$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-55}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{2}$		$q+(\zeta_{10}+\zeta_{10}^{4})q^{2}+(-1+\zeta_{10}^{2}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots$
1375.1.c.b	$1375$	$1$	1375.c	11.b	$2$	$4$	$4$	$0.686$	$\Q(i, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-55}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{7}-\beta _{3}q^{8}+\cdots$
1375.1.d.a	$1375$	$1$	1375.d	55.d	$2$	$2$	$2$	$0.686$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-55}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{7}-q^{8}+\cdots$
1375.1.d.b	$1375$	$1$	1375.d	55.d	$2$	$2$	$2$	$0.686$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-55}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$1$	$1$		$q+(1-\beta )q^{2}+(1-\beta )q^{4}+\beta q^{7}+q^{8}+\cdots$
1375.1.d.c	$1375$	$1$	1375.d	55.d	$2$	$4$	$4$	$0.686$	$\Q(\zeta_{20})^+$	$D_{10}$	$\Q(\sqrt{-55}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{3}q^{7}+(-\beta _{1}+\cdots)q^{8}+\cdots$
1540.1.b.a	$1540$	$1$	1540.b	1540.b	$2$	$4$	$4$	$0.769$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{2}q^{5}-\zeta_{8}^{3}q^{7}+\cdots$
1540.1.b.b	$1540$	$1$	1540.b	1540.b	$2$	$4$	$4$	$0.769$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}^{2}q^{5}+\zeta_{8}^{3}q^{7}+\cdots$
1540.1.bj.a	$1540$	$1$	1540.bj	1540.aj	$6$	$8$	$4$	$0.769$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{24}^{9}q^{2}-\zeta_{24}^{6}q^{4}+\zeta_{24}^{10}q^{5}+\cdots$
1540.1.bj.b	$1540$	$1$	1540.bj	1540.aj	$6$	$8$	$4$	$0.769$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}-\zeta_{24}^{10}q^{5}+\cdots$
1705.1.y.a	$1705$	$1$	1705.y	1705.y	$6$	$2$	$1$	$0.851$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-55}) $	None		$4$	$0$	$-2$	$0$	$-1$	$1$	$1$		$q-q^{2}-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+q^{8}-\zeta_{6}q^{9}+\cdots$
1705.1.y.d	$1705$	$1$	1705.y	1705.y	$6$	$2$	$1$	$0.851$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-55}) $	None		$4$	$0$	$2$	$0$	$-1$	$-1$	$1$		$q+q^{2}-\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}-q^{8}-\zeta_{6}q^{9}+\cdots$
1705.1.y.e	$1705$	$1$	1705.y	1705.y	$6$	$4$	$2$	$0.851$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$2$	$0$	$3$		$q+(\zeta_{12}-\zeta_{12}^{5})q^{2}+(1+\zeta_{12}^{2}-\zeta_{12}^{4}+\cdots)q^{4}+\cdots$
1705.1.bk.a	$1705$	$1$	1705.bk	1705.ak	$10$	$4$	$1$	$0.851$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-55}) $	None		$4$	$0$	$-2$	$0$	$4$	$3$	$1$		$q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}+(\zeta_{10}^{2}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots$
1705.1.bk.d	$1705$	$1$	1705.bk	1705.ak	$10$	$4$	$1$	$0.851$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-55}) $	None		$4$	$0$	$2$	$0$	$4$	$-3$	$1$		$q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+(\zeta_{10}^{2}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots$
1705.1.bk.e	$1705$	$1$	1705.bk	1705.ak	$10$	$8$	$2$	$0.851$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$-8$	$0$	$5$		$q+(\zeta_{20}^{7}+\zeta_{20}^{9})q^{2}+(-\zeta_{20}^{4}-\zeta_{20}^{6}+\cdots)q^{4}+\cdots$
1705.1.ek.a	$1705$	$1$	1705.ek	1705.dk	$30$	$8$	$1$	$0.851$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-55}) $	None		$4$	$0$	$-2$	$0$	$-4$	$-9$	$1$		$q+(\zeta_{30}-\zeta_{30}^{8})q^{2}+(-\zeta_{30}+\zeta_{30}^{2}+\cdots)q^{4}+\cdots$
1705.1.ek.d	$1705$	$1$	1705.ek	1705.dk	$30$	$8$	$1$	$0.851$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-55}) $	None		$4$	$0$	$2$	$0$	$-4$	$9$	$1$		$q+(-\zeta_{30}+\zeta_{30}^{8})q^{2}+(-\zeta_{30}+\zeta_{30}^{2}+\cdots)q^{4}+\cdots$
1705.1.ek.e	$1705$	$1$	1705.ek	1705.dk	$30$	$16$	$2$	$0.851$	$\Q(\zeta_{60})$	$D_{30}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$8$	$0$	$1$		$q+(\zeta_{60}^{11}+\zeta_{60}^{13})q^{2}+(\zeta_{60}^{22}+\zeta_{60}^{24}+\cdots)q^{4}+\cdots$
1760.1.o.e	$1760$	$1$	1760.o	440.o	$2$	$4$	$4$	$0.878$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2$		$q-\zeta_{8}^{2}q^{5}+(\zeta_{8}-\zeta_{8}^{3})q^{7}-q^{9}+\zeta_{8}^{2}q^{11}+\cdots$
1760.1.bw.a	$1760$	$1$	1760.bw	1760.aw	$8$	$16$	$4$	$0.878$	$\Q(\zeta_{32})$	$D_{16}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{32}^{3}q^{2}+\zeta_{32}^{6}q^{4}+\zeta_{32}^{10}q^{5}+\cdots$
1925.1.l.a	$1925$	$1$	1925.l	385.l	$4$	$4$	$2$	$0.961$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-35}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{77}) $		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}^{2}q^{4}-\zeta_{8}q^{7}-\zeta_{8}^{2}q^{9}-q^{11}+\cdots$
1925.1.l.b	$1925$	$1$	1925.l	385.l	$4$	$4$	$2$	$0.961$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-55}) $	$\Q(\sqrt{385}) $		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{3}q^{2}-3\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{7}+2\zeta_{8}q^{8}+\cdots$
1925.1.w.a	$1925$	$1$	1925.w	77.h	$6$	$2$	$1$	$0.961$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-55}) $	None		$4$	$0$	$-3$	$0$	$0$	$2$	$1$		$q+(-1+\zeta_{6}^{2})q^{2}+(1-\zeta_{6}-\zeta_{6}^{2})q^{4}+\cdots$
1925.1.w.b	$1925$	$1$	1925.w	77.h	$6$	$2$	$1$	$0.961$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-55}) $	None		$4$	$0$	$3$	$0$	$0$	$-2$	$1$		$q+(1-\zeta_{6}^{2})q^{2}+(1-\zeta_{6}-\zeta_{6}^{2})q^{4}+\cdots$
1925.1.w.c	$1925$	$1$	1925.w	77.h	$6$	$4$	$2$	$0.961$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}-\zeta_{12}^{3}q^{7}+\zeta_{12}^{3}q^{8}-\zeta_{12}^{4}q^{9}+\cdots$
1925.1.ct.a	$1925$	$1$	1925.ct	385.af	$12$	$8$	$2$	$0.961$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-55}) $	None		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{24}^{7}q^{2}+\zeta_{24}^{3}q^{7}-\zeta_{24}^{9}q^{8}+\cdots$

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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.