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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 118 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
676.1.b.a	$676$	$1$	676.b	52.b	$2$	$2$	$2$	$0.337$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{2}-q^{4}+iq^{5}+iq^{8}+q^{9}+q^{10}+\cdots$
676.1.c.a	$676$	$1$	676.c	4.b	$2$	$1$	$1$	$0.337$	$\Q$	$D_{3}$	$\Q(\sqrt{-1}) $	None	✓	$2$	$0$	$-1$	$0$	$1$	$0$		$1$		$q-q^{2}+q^{4}+q^{5}-q^{8}+q^{9}-q^{10}+\cdots$
676.1.c.b	$676$	$1$	676.c	4.b	$2$	$1$	$1$	$0.337$	$\Q$	$D_{3}$	$\Q(\sqrt{-1}) $	None	✓	$2$	$0$	$1$	$0$	$-1$	$0$		$1$		$q+q^{2}+q^{4}-q^{5}+q^{8}+q^{9}-q^{10}+\cdots$
676.1.i.a	$676$	$1$	676.i	52.i	$6$	$4$	$2$	$0.337$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}-\zeta_{12}^{3}q^{8}+\cdots$
676.1.j.a	$676$	$1$	676.j	52.j	$6$	$2$	$1$	$0.337$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$2$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{5}-q^{8}-\zeta_{6}q^{9}+\cdots$
676.1.o.a	$676$	$1$	676.o	676.o	$26$	$12$	$1$	$0.337$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$		$1$		$q+\zeta_{26}^{8}q^{2}-\zeta_{26}^{3}q^{4}+(\zeta_{26}^{2}+\zeta_{26}^{12}+\cdots)q^{5}+\cdots$
676.1.t.a	$676$	$1$	676.t	676.t	$78$	$24$	$1$	$0.337$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$2$	$0$		$1$		$q+\zeta_{78}^{8}q^{2}+\zeta_{78}^{16}q^{4}+(\zeta_{78}^{28}+\zeta_{78}^{38}+\cdots)q^{5}+\cdots$
676.2.a.a	$676$	$2$	676.a	1.a	$1$	$1$	$1$	$5.398$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$-3$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-3q^{5}-4q^{7}+q^{9}+6q^{15}+\cdots$
676.2.a.b	$676$	$2$	676.a	1.a	$1$	$1$	$1$	$5.398$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+3q^{5}+4q^{7}+q^{9}-6q^{15}+\cdots$
676.2.a.c	$676$	$2$	676.a	1.a	$1$	$1$	$1$	$5.398$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+2q^{7}-3q^{9}+2q^{11}+6q^{17}+\cdots$
676.2.a.d	$676$	$2$	676.a	1.a	$1$	$1$	$1$	$5.398$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-2q^{5}-q^{7}+6q^{9}+5q^{11}+\cdots$
676.2.a.e	$676$	$2$	676.a	1.a	$1$	$1$	$1$	$5.398$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+2q^{5}+q^{7}+6q^{9}-5q^{11}+\cdots$
676.2.a.f	$676$	$2$	676.a	1.a	$1$	$2$	$2$	$5.398$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$2$	$1$	$0$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{7}-2q^{9}-3\beta q^{11}-3q^{17}+\cdots$
676.2.a.g	$676$	$2$	676.a	1.a	$1$	$3$	$3$	$5.398$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-8$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{2})q^{3}+(-2-\beta _{1}+\beta _{2})q^{5}+\cdots$
676.2.a.h	$676$	$2$	676.a	1.a	$1$	$3$	$3$	$5.398$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$8$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-\beta _{1}-\beta _{2})q^{3}+(2+\beta _{1}-\beta _{2})q^{5}+\cdots$
676.2.d.a	$676$	$2$	676.d	13.b	$2$	$2$	$2$	$5.398$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-2q^{3}+3iq^{5}-4iq^{7}+q^{9}-6iq^{15}+\cdots$
676.2.d.b	$676$	$2$	676.d	13.b	$2$	$2$	$2$	$5.398$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}-\zeta_{6}q^{7}-2q^{9}+3\zeta_{6}q^{11}+3q^{17}+\cdots$
676.2.d.c	$676$	$2$	676.d	13.b	$2$	$2$	$2$	$5.398$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{5}+iq^{7}-3q^{9}+iq^{11}-6q^{17}+\cdots$
676.2.d.d	$676$	$2$	676.d	13.b	$2$	$2$	$2$	$5.398$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3q^{3}+2iq^{5}-iq^{7}+6q^{9}+5iq^{11}+\cdots$
676.2.d.e	$676$	$2$	676.d	13.b	$2$	$6$	$6$	$5.398$	6.0.153664.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-2\beta _{2}-\beta _{4})q^{3}+(-\beta _{1}+3\beta _{5})q^{5}+\cdots$
676.2.e.a	$676$	$2$	676.e	13.c	$3$	$2$	$1$	$5.398$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$0$	$-3$	$-4$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-3+3\zeta_{6})q^{3}-2q^{5}+\zeta_{6}q^{7}-6\zeta_{6}q^{9}+\cdots$
676.2.e.b	$676$	$2$	676.e	13.c	$3$	$2$	$1$	$5.398$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$0$	$0$	$-4$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2q^{5}-2\zeta_{6}q^{7}+3\zeta_{6}q^{9}+(-2+2\zeta_{6})q^{11}+\cdots$
676.2.e.c	$676$	$2$	676.e	13.c	$3$	$2$	$1$	$5.398$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2q^{5}+2\zeta_{6}q^{7}+3\zeta_{6}q^{9}+(2-2\zeta_{6})q^{11}+\cdots$
676.2.e.d	$676$	$2$	676.e	13.c	$3$	$2$	$1$	$5.398$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$6$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{3}+3q^{5}-4\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$
676.2.e.e	$676$	$2$	676.e	13.c	$3$	$4$	$2$	$5.398$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$0$	$2$	$0$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{12})q^{3}-\zeta_{12}^{2}q^{7}+2\zeta_{12}q^{9}+\cdots$
676.2.e.f	$676$	$2$	676.e	13.c	$3$	$6$	$3$	$5.398$	6.0.64827.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$-16$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4})q^{3}+(-2-\beta _{2}+\cdots)q^{5}+\cdots$
676.2.e.g	$676$	$2$	676.e	13.c	$3$	$6$	$3$	$5.398$	6.0.64827.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$16$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4})q^{3}+(2+\beta _{2}+\cdots)q^{5}+\cdots$
676.2.f.a	$676$	$2$	676.f	52.f	$4$	$2$	$1$	$5.398$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$-2$	$0$	$0$	$-2$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-1+i)q^{2}-2iq^{4}+(-1-i)q^{7}+\cdots$
676.2.f.b	$676$	$2$	676.f	52.f	$4$	$2$	$1$	$5.398$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$6$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-1-i)q^{2}+2iq^{4}+(3+3i)q^{5}+\cdots$
676.2.f.c	$676$	$2$	676.f	52.f	$4$	$2$	$1$	$5.398$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$2$	$0$	$0$	$2$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(1-i)q^{2}-2iq^{4}+(1+i)q^{7}+(-2+\cdots)q^{8}+\cdots$
676.2.f.d	$676$	$2$	676.f	52.f	$4$	$4$	$2$	$5.398$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-4$	$0$	$-6$	$0$		$2$	$\mathrm{U}(1)[D_{4}]$	$q+(-1+\zeta_{12}^{2})q^{2}-2\zeta_{12}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots$
676.2.f.e	$676$	$2$	676.f	52.f	$4$	$4$	$2$	$5.398$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$4$	$0$	$6$	$0$		$2$	$\mathrm{U}(1)[D_{4}]$	$q+(1-\zeta_{12}^{2})q^{2}-2\zeta_{12}^{2}q^{4}+(1-\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
676.2.f.f	$676$	$2$	676.f	52.f	$4$	$8$	$4$	$5.398$	8.0.157351936.1	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(\beta _{6}-\beta _{7})q^{2}+(1-2\beta _{1})q^{3}+(-2\beta _{3}+\cdots)q^{4}+\cdots$
676.2.f.g	$676$	$2$	676.f	52.f	$4$	$8$	$4$	$5.398$	8.0.18939904.2	$_{}$	None	None		$4$	$0$	$4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\beta _{3}+\beta _{6}+\beta _{7})q^{2}+(-1+2\beta _{1}+\cdots)q^{3}+\cdots$
676.2.f.h	$676$	$2$	676.f	52.f	$4$	$16$	$8$	$5.398$	16.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$-2$	$0$	$-12$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{2}q^{2}+(-\beta _{3}-\beta _{6})q^{3}+(-\beta _{5}-\beta _{8}+\cdots)q^{4}+\cdots$
676.2.f.i	$676$	$2$	676.f	52.f	$4$	$16$	$8$	$5.398$	16.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$2$	$0$	$12$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{2}+(-\beta _{3}-\beta _{6})q^{3}+(-\beta _{5}-\beta _{8}+\cdots)q^{4}+\cdots$
676.2.f.j	$676$	$2$	676.f	52.f	$4$	$72$	$36$	$5.398$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
676.2.h.a	$676$	$2$	676.h	13.e	$6$	$2$	$1$	$5.398$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$0$	$3$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\zeta_{6})q^{3}+(2-\zeta_{6})q^{7}+2\zeta_{6}q^{9}+\cdots$
676.2.h.b	$676$	$2$	676.h	13.e	$6$	$4$	$2$	$5.398$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$0$	$-6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-3+3\zeta_{12}^{2})q^{3}-2\zeta_{12}^{3}q^{5}+(\zeta_{12}+\cdots)q^{7}+\cdots$
676.2.h.c	$676$	$2$	676.h	13.e	$6$	$4$	$2$	$5.398$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}^{3}q^{5}-\zeta_{12}q^{7}+(3-3\zeta_{12}^{2}+\cdots)q^{9}+\cdots$
676.2.h.d	$676$	$2$	676.h	13.e	$6$	$4$	$2$	$5.398$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(2-2\zeta_{12}^{2})q^{3}+3\zeta_{12}^{3}q^{5}+(-4\zeta_{12}+\cdots)q^{7}+\cdots$
676.2.h.e	$676$	$2$	676.h	13.e	$6$	$12$	$6$	$5.398$	12.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1+\beta _{4}-\beta _{7}+2\beta _{9})q^{3}+(-3\beta _{6}+\cdots)q^{5}+\cdots$
676.2.l.a	$676$	$2$	676.l	52.l	$12$	$4$	$1$	$5.398$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-1}) $	None		$8$	$1$	$-2$	$0$	$-12$	$0$		$1$	$\mathrm{U}(1)[D_{12}]$	$q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots$
676.2.l.b	$676$	$2$	676.l	52.l	$12$	$4$	$1$	$5.398$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-13}) $	None		$8$	$0$	$-2$	$0$	$0$	$-2$		$1$	$\mathrm{U}(1)[D_{12}]$	$q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}-2\zeta_{12}q^{4}+\cdots$
676.2.l.c	$676$	$2$	676.l	52.l	$12$	$4$	$1$	$5.398$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$6$	$0$		$1$	$\mathrm{U}(1)[D_{12}]$	$q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots$
676.2.l.d	$676$	$2$	676.l	52.l	$12$	$4$	$1$	$5.398$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$2$	$0$	$-6$	$0$		$1$	$\mathrm{U}(1)[D_{12}]$	$q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots$
676.2.l.e	$676$	$2$	676.l	52.l	$12$	$4$	$1$	$5.398$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$2$	$0$	$-6$	$0$		$1$	$\mathrm{U}(1)[D_{12}]$	$q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots$
676.2.l.f	$676$	$2$	676.l	52.l	$12$	$4$	$1$	$5.398$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-13}) $	None		$8$	$0$	$2$	$0$	$0$	$2$		$1$	$\mathrm{U}(1)[D_{12}]$	$q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}-2\zeta_{12}q^{4}+\cdots$
676.2.l.g	$676$	$2$	676.l	52.l	$12$	$4$	$1$	$5.398$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$2$	$0$	$12$	$0$		$1$	$\mathrm{U}(1)[D_{12}]$	$q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots$
676.2.l.h	$676$	$2$	676.l	52.l	$12$	$16$	$4$	$5.398$	16.0.$\cdots$.2	$_{}$	None	None		$8$	$0$	$-4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-\beta _{2}+\beta _{9})q^{2}+(-2\beta _{1}-\beta _{11}-\beta _{13}+\cdots)q^{3}+\cdots$

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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.