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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 101 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
3400.1.g.a	$3400$	$1$	3400.g	136.e	$2$	$1$	$1$	$1.697$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-34}) $	$\Q(\sqrt{17}) $	✓	$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}+q^{8}+q^{9}+q^{16}+q^{17}+\cdots$
3400.1.g.b	$3400$	$1$	3400.g	136.e	$2$	$2$	$2$	$1.697$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-q^{2}+(\zeta_{6}+\zeta_{6}^{2})q^{3}+q^{4}+(-\zeta_{6}+\cdots)q^{6}+\cdots$
3400.1.g.c	$3400$	$1$	3400.g	136.e	$2$	$2$	$2$	$1.697$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-34}) $	None	✓	$4$	$0$	$-2$	$0$	$0$	$0$		$1$		$q-q^{2}+q^{4}-\beta q^{7}-q^{8}+q^{9}+\beta q^{14}+\cdots$
3400.1.g.d	$3400$	$1$	3400.g	136.e	$2$	$2$	$2$	$1.697$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-170}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{8}+iq^{12}+\cdots$
3400.1.g.e	$3400$	$1$	3400.g	136.e	$2$	$2$	$2$	$1.697$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-170}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+iq^{2}-iq^{3}-q^{4}+q^{6}-iq^{8}+iq^{12}+\cdots$
3400.1.g.f	$3400$	$1$	3400.g	136.e	$2$	$2$	$2$	$1.697$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}+(\zeta_{6}+\zeta_{6}^{2})q^{3}+q^{4}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{6}+\cdots$
3400.1.g.g	$3400$	$1$	3400.g	136.e	$2$	$2$	$2$	$1.697$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-34}) $	None	✓	$4$	$0$	$2$	$0$	$0$	$0$		$1$		$q+q^{2}+q^{4}-\beta q^{7}+q^{8}+q^{9}-\beta q^{14}+\cdots$
3400.1.k.a	$3400$	$1$	3400.k	680.k	$2$	$2$	$2$	$1.697$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-34}) $	$\Q(\sqrt{17}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{2}-q^{4}+iq^{8}-q^{9}+q^{16}-iq^{17}+\cdots$
3400.1.k.b	$3400$	$1$	3400.k	680.k	$2$	$4$	$4$	$1.697$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-2}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{3}q^{2}+(-\zeta_{12}+\zeta_{12}^{5})q^{3}-q^{4}+\cdots$
3400.1.s.a	$3400$	$1$	3400.s	680.s	$4$	$4$	$2$	$1.697$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{2}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\zeta_{8}^{3})q^{7}+\cdots$
3400.1.y.a	$3400$	$1$	3400.y	136.j	$4$	$2$	$1$	$1.697$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q-iq^{2}+(1-i)q^{3}-q^{4}+(-1-i+\cdots)q^{6}+\cdots$
3400.1.y.b	$3400$	$1$	3400.y	136.j	$4$	$4$	$2$	$1.697$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-\zeta_{12}^{3}q^{2}+(\zeta_{12}^{4}+\zeta_{12}^{5})q^{3}-q^{4}+\cdots$
3400.1.y.c	$3400$	$1$	3400.y	136.j	$4$	$4$	$2$	$1.697$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q+\zeta_{12}^{3}q^{2}+(-\zeta_{12}+\zeta_{12}^{2})q^{3}-q^{4}+\cdots$
3400.1.bc.a	$3400$	$1$	3400.bc	680.ac	$4$	$2$	$1$	$1.697$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-2$	$2$	$0$	$0$		$1$		$q-q^{2}+(1-i)q^{3}+q^{4}+(-1+i)q^{6}+\cdots$
3400.1.bc.b	$3400$	$1$	3400.bc	680.ac	$4$	$2$	$1$	$1.697$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$2$	$-2$	$0$	$0$		$1$		$q+q^{2}+(-1+i)q^{3}+q^{4}+(-1+i+\cdots)q^{6}+\cdots$
3400.1.bc.c	$3400$	$1$	3400.bc	680.ac	$4$	$4$	$2$	$1.697$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-4$	$-2$	$0$	$0$		$1$		$q-q^{2}+(\zeta_{12}^{4}+\zeta_{12}^{5})q^{3}+q^{4}+(-\zeta_{12}^{4}+\cdots)q^{6}+\cdots$
3400.1.bc.d	$3400$	$1$	3400.bc	680.ac	$4$	$4$	$2$	$1.697$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$4$	$2$	$0$	$0$		$1$		$q+q^{2}+(-\zeta_{12}+\zeta_{12}^{2})q^{3}+q^{4}+(-\zeta_{12}+\cdots)q^{6}+\cdots$
3400.1.bk.a	$3400$	$1$	3400.bk	680.ak	$4$	$4$	$2$	$1.697$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{2}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{7}+\cdots$
3400.1.br.a	$3400$	$1$	3400.br	680.aq	$8$	$4$	$1$	$1.697$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-4$	$0$	$0$		$1$		$q+\zeta_{8}^{3}q^{2}+(-1+\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots$
3400.1.br.b	$3400$	$1$	3400.br	680.aq	$8$	$4$	$1$	$1.697$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$4$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{2}+(1-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots$
3400.1.br.c	$3400$	$1$	3400.br	680.aq	$8$	$8$	$2$	$1.697$	$\Q(\zeta_{24})$	$D_{24}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-4$	$0$	$0$		$1$		$q-\zeta_{24}^{3}q^{2}+(-\zeta_{24}^{4}-\zeta_{24}^{11})q^{3}+\cdots$
3400.1.br.d	$3400$	$1$	3400.br	680.aq	$8$	$8$	$2$	$1.697$	$\Q(\zeta_{24})$	$D_{24}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$4$	$0$	$0$		$1$		$q+\zeta_{24}^{3}q^{2}+(\zeta_{24}^{4}+\zeta_{24}^{11})q^{3}+\zeta_{24}^{6}q^{4}+\cdots$
3400.1.ce.a	$3400$	$1$	3400.ce	136.p	$8$	$4$	$1$	$1.697$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{3}q^{2}+(-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots$
3400.1.ce.b	$3400$	$1$	3400.ce	136.p	$8$	$8$	$2$	$1.697$	$\Q(\zeta_{24})$	$D_{24}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{3}q^{2}+(\zeta_{24}^{10}+\zeta_{24}^{11})q^{3}+\cdots$
3400.1.ce.c	$3400$	$1$	3400.ce	136.p	$8$	$8$	$2$	$1.697$	$\Q(\zeta_{24})$	$D_{24}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{3}q^{2}+(-\zeta_{24}^{2}-\zeta_{24}^{7})q^{3}+\cdots$
3400.1.ch.a	$3400$	$1$	3400.ch	3400.bh	$10$	$16$	$4$	$1.697$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-34}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{40}^{18}q^{2}-\zeta_{40}^{16}q^{4}+\zeta_{40}^{15}q^{5}+\cdots$
3400.1.cs.a	$3400$	$1$	3400.cs	3400.bs	$10$	$4$	$1$	$1.697$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-34}) $	None		$4$	$0$	$-1$	$0$	$-4$	$2$		$1$		$q+\zeta_{10}^{2}q^{2}+\zeta_{10}^{4}q^{4}-q^{5}+(-\zeta_{10}^{2}+\cdots)q^{7}+\cdots$
3400.1.cs.b	$3400$	$1$	3400.cs	3400.bs	$10$	$4$	$1$	$1.697$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-34}) $	None		$4$	$0$	$-1$	$0$	$4$	$-2$		$1$		$q+\zeta_{10}^{2}q^{2}+\zeta_{10}^{4}q^{4}+q^{5}+(\zeta_{10}^{2}+\cdots)q^{7}+\cdots$
3400.1.cs.c	$3400$	$1$	3400.cs	3400.bs	$10$	$8$	$2$	$1.697$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-34}) $	None		$8$	$0$	$2$	$0$	$0$	$0$		$1$		$q-\zeta_{20}^{4}q^{2}+\zeta_{20}^{8}q^{4}+\zeta_{20}^{5}q^{5}+\cdots$
3400.1.cx.a	$3400$	$1$	3400.cx	680.bh	$16$	$8$	$1$	$1.697$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{16}^{5}q^{2}+(-\zeta_{16}^{4}-\zeta_{16}^{5})q^{3}+\cdots$
3400.1.cx.b	$3400$	$1$	3400.cx	680.bh	$16$	$8$	$1$	$1.697$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}^{5}q^{2}+(\zeta_{16}^{4}+\zeta_{16}^{5})q^{3}-\zeta_{16}^{2}q^{4}+\cdots$
3400.1.cx.c	$3400$	$1$	3400.cx	680.bh	$16$	$16$	$2$	$1.697$	$\Q(\zeta_{48})$	$D_{48}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{48}^{21}q^{2}+(\zeta_{48}^{13}-\zeta_{48}^{20})q^{3}+\cdots$
3400.1.cx.d	$3400$	$1$	3400.cx	680.bh	$16$	$16$	$2$	$1.697$	$\Q(\zeta_{48})$	$D_{48}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{48}^{21}q^{2}+(\zeta_{48}^{4}+\zeta_{48}^{5})q^{3}-\zeta_{48}^{18}q^{4}+\cdots$
3400.1.dh.a	$3400$	$1$	3400.dh	680.br	$16$	$8$	$1$	$1.697$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-8$	$0$	$0$		$1$		$q+\zeta_{16}q^{2}+(-1-\zeta_{16})q^{3}+\zeta_{16}^{2}q^{4}+\cdots$
3400.1.dh.b	$3400$	$1$	3400.dh	680.br	$16$	$8$	$1$	$1.697$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$8$	$0$	$0$		$1$		$q-\zeta_{16}q^{2}+(1+\zeta_{16})q^{3}+\zeta_{16}^{2}q^{4}+\cdots$
3400.1.dh.c	$3400$	$1$	3400.dh	680.br	$16$	$16$	$2$	$1.697$	$\Q(\zeta_{48})$	$D_{48}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-8$	$0$	$0$		$1$		$q+\zeta_{48}^{9}q^{2}+(\zeta_{48}^{16}+\zeta_{48}^{17})q^{3}+\cdots$
3400.1.dh.d	$3400$	$1$	3400.dh	680.br	$16$	$16$	$2$	$1.697$	$\Q(\zeta_{48})$	$D_{48}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$8$	$0$	$0$		$1$		$q-\zeta_{48}^{9}q^{2}+(-\zeta_{48}+\zeta_{48}^{8})q^{3}+\zeta_{48}^{18}q^{4}+\cdots$
3400.2.a.a	$3400$	$2$	3400.a	1.a	$1$	$1$	$1$	$27.149$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots$
3400.2.a.b	$3400$	$2$	3400.a	1.a	$1$	$1$	$1$	$27.149$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{9}+2q^{11}+6q^{13}+q^{17}+\cdots$
3400.2.a.c	$3400$	$2$	3400.a	1.a	$1$	$1$	$1$	$27.149$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{7}-2q^{9}+2q^{11}-5q^{13}+\cdots$
3400.2.a.d	$3400$	$2$	3400.a	1.a	$1$	$1$	$1$	$27.149$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{9}+2q^{13}-q^{17}-4q^{19}+8q^{23}+\cdots$
3400.2.a.e	$3400$	$2$	3400.a	1.a	$1$	$1$	$1$	$27.149$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}-2q^{9}+4q^{11}+q^{13}+\cdots$
3400.2.a.f	$3400$	$2$	3400.a	1.a	$1$	$1$	$1$	$27.149$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{7}-2q^{9}+2q^{11}+5q^{13}+\cdots$
3400.2.a.g	$3400$	$2$	3400.a	1.a	$1$	$1$	$1$	$27.149$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+2q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots$
3400.2.a.h	$3400$	$2$	3400.a	1.a	$1$	$2$	$2$	$27.149$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-\beta q^{7}-q^{9}+(-2+3\beta )q^{11}+\cdots$
3400.2.a.i	$3400$	$2$	3400.a	1.a	$1$	$2$	$2$	$27.149$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-1-\beta )q^{7}+(3+2\beta )q^{9}+\cdots$
3400.2.a.j	$3400$	$2$	3400.a	1.a	$1$	$2$	$2$	$27.149$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(3-\beta )q^{7}+(1+2\beta )q^{9}+\cdots$
3400.2.a.k	$3400$	$2$	3400.a	1.a	$1$	$3$	$3$	$27.149$	3.3.940.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{3}+(-1+\beta _{2})q^{7}+(3+\cdots)q^{9}+\cdots$
3400.2.a.l	$3400$	$2$	3400.a	1.a	$1$	$3$	$3$	$27.149$	3.3.1016.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-2-\beta _{2})q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots$
3400.2.a.m	$3400$	$2$	3400.a	1.a	$1$	$3$	$3$	$27.149$	3.3.564.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2})q^{7}+(1+\beta _{2})q^{9}+\cdots$

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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.