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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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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	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	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
722.2.a.a	$722$	$2$	722.a	1.a	$1$	$1$	$1$	$5.765$	$\Q$	None	✓	$1$	$1$	$-1$	$-3$	$2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-3q^{3}+q^{4}+2q^{5}+3q^{6}-3q^{7}+\cdots$
722.2.a.b	$722$	$2$	722.a	1.a	$1$	$1$	$1$	$5.765$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$-4$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-4q^{5}-q^{6}+3q^{7}+\cdots$
722.2.a.c	$722$	$2$	722.a	1.a	$1$	$1$	$1$	$5.765$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-4q^{7}-q^{8}+\cdots$
722.2.a.d	$722$	$2$	722.a	1.a	$1$	$1$	$1$	$5.765$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots$
722.2.a.e	$722$	$2$	722.a	1.a	$1$	$1$	$1$	$5.765$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots$
722.2.a.f	$722$	$2$	722.a	1.a	$1$	$1$	$1$	$5.765$	$\Q$	None	✓	$1$	$0$	$1$	$3$	$2$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}+q^{4}+2q^{5}+3q^{6}-3q^{7}+\cdots$
722.2.a.g	$722$	$2$	722.a	1.a	$1$	$2$	$2$	$5.765$	$\Q(\sqrt{7}) $	None	✓	$1$	$0$	$-2$	$0$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}+(1+\beta )q^{5}-\beta q^{6}+\cdots$
722.2.a.h	$722$	$2$	722.a	1.a	$1$	$2$	$2$	$5.765$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$2$	$-5$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2\beta q^{3}+q^{4}+(-3+\beta )q^{5}+\cdots$
722.2.a.i	$722$	$2$	722.a	1.a	$1$	$2$	$2$	$5.765$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$-2$	$-5$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2\beta q^{3}+q^{4}+(-3+\beta )q^{5}+\cdots$
722.2.a.j	$722$	$2$	722.a	1.a	$1$	$2$	$2$	$5.765$	$\Q(\sqrt{7}) $	None	✓	$1$	$0$	$2$	$0$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}+(1-\beta )q^{5}+\beta q^{6}+\cdots$
722.2.a.k	$722$	$2$	722.a	1.a	$1$	$3$	$3$	$5.765$	$\Q(\zeta_{18})^+$	None	✓	$1$	$0$	$-3$	$0$	$6$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+2q^{5}-\beta _{1}q^{6}+\cdots$
722.2.a.l	$722$	$2$	722.a	1.a	$1$	$3$	$3$	$5.765$	$\Q(\zeta_{18})^+$	None	✓	$1$	$0$	$3$	$0$	$6$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}+2q^{5}-\beta _{1}q^{6}+\cdots$
722.2.a.m	$722$	$2$	722.a	1.a	$1$	$4$	$4$	$5.765$	$\Q(\zeta_{20})^+$	None	✓	$1$	$1$	$-4$	$-2$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1-\beta _{2}-\beta _{3})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots$
722.2.a.n	$722$	$2$	722.a	1.a	$1$	$4$	$4$	$5.765$	$\Q(\zeta_{20})^+$	None	✓	$1$	$0$	$4$	$2$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta _{2}+\beta _{3})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots$
722.2.c.a	$722$	$2$	722.c	19.c	$3$	$2$	$1$	$5.765$	$\Q(\sqrt{-3}) $	None		$2$	$1$	$-1$	$-3$	$-2$	$-6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
722.2.c.b	$722$	$2$	722.c	19.c	$3$	$2$	$1$	$5.765$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$1$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
722.2.c.c	$722$	$2$	722.c	19.c	$3$	$2$	$1$	$5.765$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$1$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
722.2.c.d	$722$	$2$	722.c	19.c	$3$	$2$	$1$	$5.765$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$1$	$4$	$6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
722.2.c.e	$722$	$2$	722.c	19.c	$3$	$2$	$1$	$5.765$	$\Q(\sqrt{-3}) $	None		$2$	$1$	$1$	$-1$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
722.2.c.f	$722$	$2$	722.c	19.c	$3$	$2$	$1$	$5.765$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$-1$	$4$	$6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
722.2.c.g	$722$	$2$	722.c	19.c	$3$	$2$	$1$	$5.765$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$3$	$-2$	$-6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
722.2.c.h	$722$	$2$	722.c	19.c	$3$	$4$	$2$	$5.765$	$\Q(\sqrt{-3}, \sqrt{5})$	None		$2$	$0$	$-2$	$2$	$5$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{3})q^{2}+2\beta _{1}q^{3}+\beta _{3}q^{4}+\cdots$
722.2.c.i	$722$	$2$	722.c	19.c	$3$	$4$	$2$	$5.765$	$\Q(\sqrt{-3}, \sqrt{5})$	None		$2$	$0$	$2$	$-2$	$5$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{3})q^{2}-2\beta _{1}q^{3}+\beta _{3}q^{4}+(3+\cdots)q^{5}+\cdots$
722.2.c.j	$722$	$2$	722.c	19.c	$3$	$4$	$2$	$5.765$	$\Q(\sqrt{-3}, \sqrt{7})$	None		$2$	$0$	$2$	$0$	$-2$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{2})q^{2}-\beta _{1}q^{3}+\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots$
722.2.c.k	$722$	$2$	722.c	19.c	$3$	$6$	$3$	$5.765$	$\Q(\zeta_{18})$	None		$2$	$0$	$-3$	$0$	$-6$	$12$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{18})q^{2}+(\zeta_{18}^{2}-\zeta_{18}^{3})q^{3}+\cdots$
722.2.c.l	$722$	$2$	722.c	19.c	$3$	$6$	$3$	$5.765$	$\Q(\zeta_{18})$	None		$2$	$0$	$3$	$0$	$-6$	$12$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{18}q^{2}+(-\zeta_{18}^{2}+\zeta_{18}^{3}+\zeta_{18}^{4}+\cdots)q^{3}+\cdots$
722.2.c.m	$722$	$2$	722.c	19.c	$3$	$8$	$4$	$5.765$	8.0.324000000.2	None		$2$	$0$	$-4$	$-2$	$2$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{4})q^{2}+(\beta _{3}+\beta _{6})q^{3}+\beta _{4}q^{4}+\cdots$
722.2.c.n	$722$	$2$	722.c	19.c	$3$	$8$	$4$	$5.765$	8.0.324000000.2	None		$2$	$0$	$4$	$2$	$2$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{4})q^{2}+(-\beta _{3}-\beta _{6})q^{3}+\beta _{4}q^{4}+\cdots$
722.2.e.a	$722$	$2$	722.e	19.e	$9$	$6$	$1$	$5.765$	$\Q(\zeta_{18})$	None		$2$	$0$	$0$	$-6$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+(-1-\zeta_{18}^{2}+\cdots)q^{3}+\cdots$
722.2.e.b	$722$	$2$	722.e	19.e	$9$	$6$	$1$	$5.765$	$\Q(\zeta_{18})$	None		$2$	$0$	$0$	$-3$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+(-1+\zeta_{18}^{3}-\zeta_{18}^{5})q^{3}+\cdots$
722.2.e.c	$722$	$2$	722.e	19.e	$9$	$6$	$1$	$5.765$	$\Q(\zeta_{18})$	None		$6$	$0$	$0$	$0$	$0$	$-9$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$
722.2.e.d	$722$	$2$	722.e	19.e	$9$	$6$	$1$	$5.765$	$\Q(\zeta_{18})$	None		$6$	$0$	$0$	$0$	$0$	$-9$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$
722.2.e.e	$722$	$2$	722.e	19.e	$9$	$6$	$1$	$5.765$	$\Q(\zeta_{18})$	None		$6$	$0$	$0$	$0$	$0$	$3$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$
722.2.e.f	$722$	$2$	722.e	19.e	$9$	$6$	$1$	$5.765$	$\Q(\zeta_{18})$	None		$6$	$0$	$0$	$0$	$0$	$3$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$
722.2.e.g	$722$	$2$	722.e	19.e	$9$	$6$	$1$	$5.765$	$\Q(\zeta_{18})$	None		$6$	$0$	$0$	$0$	$0$	$9$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(\zeta_{18}-\zeta_{18}^{4})q^{2}-3\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$
722.2.e.h	$722$	$2$	722.e	19.e	$9$	$6$	$1$	$5.765$	$\Q(\zeta_{18})$	None		$6$	$0$	$0$	$0$	$0$	$9$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+3\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$
722.2.e.i	$722$	$2$	722.e	19.e	$9$	$6$	$1$	$5.765$	$\Q(\zeta_{18})$	None		$6$	$0$	$0$	$0$	$0$	$12$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$
722.2.e.j	$722$	$2$	722.e	19.e	$9$	$6$	$1$	$5.765$	$\Q(\zeta_{18})$	None		$6$	$0$	$0$	$0$	$0$	$12$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots$
722.2.e.k	$722$	$2$	722.e	19.e	$9$	$6$	$1$	$5.765$	$\Q(\zeta_{18})$	None		$2$	$0$	$0$	$3$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{3}+\cdots)q^{3}+\cdots$
722.2.e.l	$722$	$2$	722.e	19.e	$9$	$6$	$1$	$5.765$	$\Q(\zeta_{18})$	None		$2$	$0$	$0$	$3$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+(1-\zeta_{18}^{3}+\zeta_{18}^{5})q^{3}+\cdots$
722.2.e.m	$722$	$2$	722.e	19.e	$9$	$6$	$1$	$5.765$	$\Q(\zeta_{18})$	None		$2$	$0$	$0$	$6$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(\zeta_{18}-\zeta_{18}^{4})q^{2}+(1+\zeta_{18}^{2})q^{3}+\cdots$
722.2.e.n	$722$	$2$	722.e	19.e	$9$	$12$	$2$	$5.765$	12.0.$\cdots$.3	None		$6$	$0$	$0$	$0$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+\beta _{10}q^{2}+(-\beta _{1}-\beta _{7})q^{3}+\beta _{2}q^{4}+\cdots$
722.2.e.o	$722$	$2$	722.e	19.e	$9$	$12$	$2$	$5.765$	12.0.$\cdots$.3	None		$6$	$0$	$0$	$0$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q-\beta _{10}q^{2}+(-\beta _{1}-\beta _{7})q^{3}+\beta _{2}q^{4}+\cdots$
722.2.e.p	$722$	$2$	722.e	19.e	$9$	$12$	$2$	$5.765$	12.0.$\cdots$.1	None		$6$	$0$	$0$	$0$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q-\beta _{9}q^{2}-2\beta _{7}q^{3}-\beta _{11}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
722.2.e.q	$722$	$2$	722.e	19.e	$9$	$12$	$2$	$5.765$	12.0.$\cdots$.1	None		$6$	$0$	$0$	$0$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{9}]$	$q+(\beta _{3}-\beta _{9})q^{2}-2\beta _{1}q^{3}+(-\beta _{5}+\beta _{11})q^{4}+\cdots$
722.2.e.r	$722$	$2$	722.e	19.e	$9$	$24$	$4$	$5.765$		None		$6$	$0$	$0$	$0$	$0$	$6$			$\mathrm{SU}(2)[C_{9}]$
722.2.e.s	$722$	$2$	722.e	19.e	$9$	$24$	$4$	$5.765$		None		$6$	$0$	$0$	$0$	$0$	$6$			$\mathrm{SU}(2)[C_{9}]$
722.2.g.a	$722$	$2$	722.g	361.g	$19$	$288$	$16$	$5.765$		None		$2$	$0$	$16$	$-1$	$1$	$2$			$\mathrm{SU}(2)[C_{19}]$
722.2.g.b	$722$	$2$	722.g	361.g	$19$	$306$	$17$	$5.765$		None		$2$	$0$	$-17$	$16$	$-1$	$-10$			$\mathrm{SU}(2)[C_{19}]$
722.2.i.a	$722$	$2$	722.i	361.i	$57$	$576$	$16$	$5.765$		None		$2$	$0$	$-16$	$1$	$-1$	$10$			$\mathrm{SU}(2)[C_{57}]$

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