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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 273 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
784.1.d.a	$784$	$1$	784.d	4.b	$2$	$2$	$2$	$0.391$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta q^{5}+q^{9}+\beta q^{13}+\beta q^{17}+q^{25}+\cdots$
784.1.k.a	$784$	$1$	784.k	16.f	$4$	$2$	$1$	$0.391$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{2}-q^{4}+iq^{8}-iq^{9}+(1-i+\cdots)q^{11}+\cdots$
784.1.r.a	$784$	$1$	784.r	28.g	$6$	$4$	$2$	$0.391$	$\Q(\sqrt{2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\beta _{1}q^{5}+(-1-\beta _{2})q^{9}+\beta _{3}q^{13}+\cdots$
784.1.v.a	$784$	$1$	784.v	112.u	$12$	$4$	$1$	$0.391$	$\Q(\zeta_{12})$	$D_{4}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{8}+\zeta_{12}q^{9}+\cdots$
784.1.y.a	$784$	$1$	784.y	112.x	$12$	$4$	$1$	$0.391$	$\Q(\zeta_{12})$	$D_{4}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{3}q^{8}+\cdots$
784.2.a.a	$784$	$2$	784.a	1.a	$1$	$1$	$1$	$6.260$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{5}+6q^{9}+q^{11}+2q^{13}+\cdots$
784.2.a.b	$784$	$2$	784.a	1.a	$1$	$1$	$1$	$6.260$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{9}+4q^{13}-6q^{17}+2q^{19}+\cdots$
784.2.a.c	$784$	$2$	784.a	1.a	$1$	$1$	$1$	$6.260$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{9}-3q^{11}+6q^{13}+\cdots$
784.2.a.d	$784$	$2$	784.a	1.a	$1$	$1$	$1$	$6.260$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}-2q^{9}+3q^{11}+2q^{13}+\cdots$
784.2.a.e	$784$	$2$	784.a	1.a	$1$	$1$	$1$	$6.260$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}-3q^{9}+4q^{11}-2q^{13}+6q^{17}+\cdots$
784.2.a.f	$784$	$2$	784.a	1.a	$1$	$1$	$1$	$6.260$	$\Q$	$_{}$	$\Q(\sqrt{-7}) $	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$N(\mathrm{U}(1))$	$q-3q^{9}-4q^{11}-8q^{23}-5q^{25}+2q^{29}+\cdots$
784.2.a.g	$784$	$2$	784.a	1.a	$1$	$1$	$1$	$6.260$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}-2q^{9}+3q^{11}-2q^{13}+\cdots$
784.2.a.h	$784$	$2$	784.a	1.a	$1$	$1$	$1$	$6.260$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{9}-3q^{11}-6q^{13}+\cdots$
784.2.a.i	$784$	$2$	784.a	1.a	$1$	$1$	$1$	$6.260$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+4q^{5}+q^{9}+8q^{15}+2q^{17}+\cdots$
784.2.a.j	$784$	$2$	784.a	1.a	$1$	$1$	$1$	$6.260$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+q^{5}+6q^{9}+q^{11}-2q^{13}+\cdots$
784.2.a.k	$784$	$2$	784.a	1.a	$1$	$2$	$2$	$6.260$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-2\beta q^{5}-q^{9}-6q^{11}+4\beta q^{13}+\cdots$
784.2.a.l	$784$	$2$	784.a	1.a	$1$	$2$	$2$	$6.260$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+2\beta q^{5}-q^{9}+2q^{11}+4q^{15}+\cdots$
784.2.a.m	$784$	$2$	784.a	1.a	$1$	$2$	$2$	$6.260$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2\beta q^{3}+\beta q^{5}+5q^{9}-4q^{11}+3\beta q^{13}+\cdots$
784.2.a.n	$784$	$2$	784.a	1.a	$1$	$2$	$2$	$6.260$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{3}-\beta q^{5}+5q^{9}+4q^{11}+\beta q^{13}+\cdots$
784.2.f.a	$784$	$2$	784.f	28.d	$2$	$2$	$2$	$6.260$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$0$	$-2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+\zeta_{6}q^{5}-2q^{9}-\zeta_{6}q^{11}-\zeta_{6}q^{15}+\cdots$
784.2.f.b	$784$	$2$	784.f	28.d	$2$	$2$	$2$	$6.260$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+\zeta_{6}q^{5}-2q^{9}+\zeta_{6}q^{11}+\zeta_{6}q^{15}+\cdots$
784.2.f.c	$784$	$2$	784.f	28.d	$2$	$4$	$4$	$6.260$	4.0.2048.2	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$7^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{5}-3q^{9}+(\beta _{1}+\beta _{2})q^{13}+(\beta _{1}+\cdots)q^{17}+\cdots$
784.2.f.d	$784$	$2$	784.f	28.d	$2$	$4$	$4$	$6.260$	$\Q(\sqrt{-3}, \sqrt{7})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{2}q^{5}+4q^{9}+\beta _{3}q^{11}+\cdots$
784.2.f.e	$784$	$2$	784.f	28.d	$2$	$8$	$8$	$6.260$	8.0.339738624.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+(\beta _{2}-\beta _{4})q^{5}+(3-3\beta _{1})q^{9}+\cdots$
784.2.i.a	$784$	$2$	784.i	7.c	$3$	$2$	$1$	$6.260$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-3$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{5}-6\zeta_{6}q^{9}+\cdots$
784.2.i.b	$784$	$2$	784.i	7.c	$3$	$2$	$1$	$6.260$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{3}-4\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$
784.2.i.c	$784$	$2$	784.i	7.c	$3$	$2$	$1$	$6.260$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{9}-4q^{13}+\cdots$
784.2.i.d	$784$	$2$	784.i	7.c	$3$	$2$	$1$	$6.260$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$3$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+3\zeta_{6}q^{5}+2\zeta_{6}q^{9}+\cdots$
784.2.i.e	$784$	$2$	784.i	7.c	$3$	$2$	$1$	$6.260$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-2\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(-4+4\zeta_{6})q^{11}+\cdots$
784.2.i.f	$784$	$2$	784.i	7.c	$3$	$2$	$1$	$6.260$	$\Q(\sqrt{-3}) $	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{3}]$	$q+3\zeta_{6}q^{9}+(4-4\zeta_{6})q^{11}+8\zeta_{6}q^{23}+\cdots$
784.2.i.g	$784$	$2$	784.i	7.c	$3$	$2$	$1$	$6.260$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(-4+4\zeta_{6})q^{11}+\cdots$
784.2.i.h	$784$	$2$	784.i	7.c	$3$	$2$	$1$	$6.260$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(3+\cdots)q^{11}+\cdots$
784.2.i.i	$784$	$2$	784.i	7.c	$3$	$2$	$1$	$6.260$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{3}-\zeta_{6}q^{9}+4q^{13}+(6+\cdots)q^{17}+\cdots$
784.2.i.j	$784$	$2$	784.i	7.c	$3$	$2$	$1$	$6.260$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{3}+4\zeta_{6}q^{5}-\zeta_{6}q^{9}+8q^{15}+\cdots$
784.2.i.k	$784$	$2$	784.i	7.c	$3$	$4$	$2$	$6.260$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+5\beta _{2}q^{9}+(-4+\cdots)q^{11}+\cdots$
784.2.i.l	$784$	$2$	784.i	7.c	$3$	$4$	$2$	$6.260$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{5}+5\beta _{2}q^{9}+\cdots$
784.2.i.m	$784$	$2$	784.i	7.c	$3$	$4$	$2$	$6.260$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{3}+(-2\beta _{1}-2\beta _{3})q^{5}-\beta _{2}q^{9}+\cdots$
784.2.i.n	$784$	$2$	784.i	7.c	$3$	$4$	$2$	$6.260$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{3}+(2\beta _{1}+2\beta _{3})q^{5}-\beta _{2}q^{9}+\cdots$
784.2.j.a	$784$	$2$	784.j	112.j	$4$	$56$	$28$	$6.260$		$_{}$	None	None		$4$	$0$	$4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
784.2.j.b	$784$	$2$	784.j	112.j	$4$	$96$	$48$	$6.260$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
784.2.m.a	$784$	$2$	784.m	16.e	$4$	$2$	$1$	$6.260$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$-2$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+i)q^{2}-2iq^{4}+(-2-2i)q^{5}+\cdots$
784.2.m.b	$784$	$2$	784.m	16.e	$4$	$2$	$1$	$6.260$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$-2$	$2$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-i)q^{2}+(1-i)q^{3}+2iq^{4}+\cdots$
784.2.m.c	$784$	$2$	784.m	16.e	$4$	$2$	$1$	$6.260$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$-2$	$4$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+i)q^{2}+(2-2i)q^{3}-2iq^{4}+\cdots$
784.2.m.d	$784$	$2$	784.m	16.e	$4$	$4$	$2$	$6.260$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$1$	$-2$	$-2$	$-6$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+\zeta_{12}^{3}q^{3}+\cdots$
784.2.m.e	$784$	$2$	784.m	16.e	$4$	$4$	$2$	$6.260$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$-2$	$2$	$6$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\zeta_{12})q^{2}+(1-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{3}+\cdots$
784.2.m.f	$784$	$2$	784.m	16.e	$4$	$4$	$2$	$6.260$	$\Q(i, \sqrt{7})$	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}-2\beta _{3})q^{8}+\cdots$
784.2.m.g	$784$	$2$	784.m	16.e	$4$	$8$	$4$	$6.260$	8.0.214798336.3	$_{}$	None	None		$2$	$0$	$2$	$0$	$4$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{3}q^{2}+(\beta _{1}+\beta _{4})q^{3}+(1+\beta _{4}-\beta _{6}+\cdots)q^{4}+\cdots$
784.2.m.h	$784$	$2$	784.m	16.e	$4$	$12$	$6$	$6.260$	12.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$2$	$-4$	$-4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{2}+(\beta _{2}-\beta _{10})q^{3}+\beta _{1}q^{4}+(-1+\cdots)q^{5}+\cdots$
784.2.m.i	$784$	$2$	784.m	16.e	$4$	$20$	$10$	$6.260$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{11}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{4}q^{2}+\beta _{9}q^{3}-\beta _{17}q^{4}+\beta _{2}q^{5}+\cdots$
784.2.m.j	$784$	$2$	784.m	16.e	$4$	$24$	$12$	$6.260$		$_{}$	None	None		$2$	$0$	$4$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{4}]$

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