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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	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
704.1.b.a	$704$	$1$	704.b	88.b	$2$	$2$	$2$	$0.351$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-11}) $	$\Q(\sqrt{22}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{3}-3q^{9}-iq^{11}+q^{25}+4iq^{27}+\cdots$
704.1.b.b	$704$	$1$	704.b	88.b	$2$	$4$	$4$	$0.351$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-11}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$		$q-\zeta_{12}^{3}q^{3}+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{5}+\cdots$
704.1.h.a	$704$	$1$	704.h	11.b	$2$	$1$	$1$	$0.351$	$\Q$	$D_{3}$	$\Q(\sqrt{-11}) $	None	✓	$2$	$0$	$0$	$-1$	$1$	$0$		$1$		$q-q^{3}+q^{5}+q^{11}-q^{15}+q^{23}+q^{27}+\cdots$
704.1.h.b	$704$	$1$	704.h	11.b	$2$	$1$	$1$	$0.351$	$\Q$	$D_{3}$	$\Q(\sqrt{-11}) $	None	✓	$2$	$0$	$0$	$1$	$1$	$0$		$1$		$q+q^{3}+q^{5}-q^{11}+q^{15}-q^{23}-q^{27}+\cdots$
704.1.x.a	$704$	$1$	704.x	88.p	$10$	$8$	$2$	$0.351$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-2}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{20}^{7}-\zeta_{20}^{9})q^{3}+(-\zeta_{20}^{4}+\zeta_{20}^{6}+\cdots)q^{9}+\cdots$
704.2.a.a	$704$	$2$	704.a	1.a	$1$	$1$	$1$	$5.621$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-q^{5}+6q^{9}+q^{11}+6q^{13}+\cdots$
704.2.a.b	$704$	$2$	704.a	1.a	$1$	$1$	$1$	$5.621$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+3q^{5}+2q^{7}+6q^{9}-q^{11}+\cdots$
704.2.a.c	$704$	$2$	704.a	1.a	$1$	$1$	$1$	$5.621$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+2q^{7}-2q^{9}+q^{11}-4q^{13}+\cdots$
704.2.a.d	$704$	$2$	704.a	1.a	$1$	$1$	$1$	$5.621$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+4q^{7}-2q^{9}-q^{11}+2q^{13}+\cdots$
704.2.a.e	$704$	$2$	704.a	1.a	$1$	$1$	$1$	$5.621$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}-4q^{7}-2q^{9}-q^{11}+\cdots$
704.2.a.f	$704$	$2$	704.a	1.a	$1$	$1$	$1$	$5.621$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}+2q^{7}-2q^{9}+q^{11}+\cdots$
704.2.a.g	$704$	$2$	704.a	1.a	$1$	$1$	$1$	$5.621$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-4q^{7}-2q^{9}+q^{11}+2q^{13}+\cdots$
704.2.a.h	$704$	$2$	704.a	1.a	$1$	$1$	$1$	$5.621$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{7}-2q^{9}-q^{11}-4q^{13}+\cdots$
704.2.a.i	$704$	$2$	704.a	1.a	$1$	$1$	$1$	$5.621$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}-2q^{7}-2q^{9}-q^{11}+\cdots$
704.2.a.j	$704$	$2$	704.a	1.a	$1$	$1$	$1$	$5.621$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}+4q^{7}-2q^{9}+q^{11}+\cdots$
704.2.a.k	$704$	$2$	704.a	1.a	$1$	$1$	$1$	$5.621$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-q^{5}+6q^{9}-q^{11}+6q^{13}+\cdots$
704.2.a.l	$704$	$2$	704.a	1.a	$1$	$1$	$1$	$5.621$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+3q^{5}-2q^{7}+6q^{9}+q^{11}+\cdots$
704.2.a.m	$704$	$2$	704.a	1.a	$1$	$2$	$2$	$5.621$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-2+\beta )q^{5}-2\beta q^{7}+(1+\beta )q^{9}+\cdots$
704.2.a.n	$704$	$2$	704.a	1.a	$1$	$2$	$2$	$5.621$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-2+\beta )q^{5}+(1+\beta )q^{9}-q^{11}+\cdots$
704.2.a.o	$704$	$2$	704.a	1.a	$1$	$2$	$2$	$5.621$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-2+\beta )q^{5}+(1+\beta )q^{9}+q^{11}+\cdots$
704.2.a.p	$704$	$2$	704.a	1.a	$1$	$2$	$2$	$5.621$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-2+\beta )q^{5}+2\beta q^{7}+(1+\beta )q^{9}+\cdots$
704.2.c.a	$704$	$2$	704.c	8.b	$2$	$4$	$4$	$5.621$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}+2q^{9}+\zeta_{12}q^{11}+\cdots$
704.2.c.b	$704$	$2$	704.c	8.b	$2$	$4$	$4$	$5.621$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}-2\zeta_{12}^{3}q^{7}+\cdots$
704.2.c.c	$704$	$2$	704.c	8.b	$2$	$12$	$12$	$5.621$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{3}-\beta _{7}q^{5}-\beta _{9}q^{7}+(-3+\beta _{1}+\cdots)q^{9}+\cdots$
704.2.e.a	$704$	$2$	704.e	44.c	$2$	$2$	$2$	$5.621$	$\Q(\sqrt{-11}) $	$_{}$	$\Q(\sqrt{-11}) $	None		$4$	$1$	$0$	$0$	$-6$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{3}-3q^{5}-8q^{9}+\beta q^{11}+3\beta q^{15}+\cdots$
704.2.e.b	$704$	$2$	704.e	44.c	$2$	$4$	$4$	$5.621$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$4$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+q^{5}+\beta _{1}q^{7}+(\beta _{1}+\beta _{2})q^{11}+\cdots$
704.2.e.c	$704$	$2$	704.e	44.c	$2$	$4$	$4$	$5.621$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$6$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}+(2-\beta _{3})q^{5}+(-1+\beta _{3})q^{9}+\cdots$
704.2.e.d	$704$	$2$	704.e	44.c	$2$	$12$	$12$	$5.621$	12.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{15}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+\beta _{5}q^{5}+\beta _{8}q^{7}+\beta _{3}q^{9}+\cdots$
704.2.g.a	$704$	$2$	704.g	88.g	$2$	$4$	$4$	$5.621$	$\Q(i, \sqrt{11})$	$_{}$	$\Q(\sqrt{-22}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{9}+\beta _{3}q^{11}-\beta _{2}q^{13}+2\beta _{3}q^{19}+\cdots$
704.2.g.b	$704$	$2$	704.g	88.g	$2$	$4$	$4$	$5.621$	$\Q(i, \sqrt{11})$	$_{}$	$\Q(\sqrt{-11}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{3}-\beta _{3}q^{5}+8q^{9}+\beta _{2}q^{11}+\cdots$
704.2.g.c	$704$	$2$	704.g	88.g	$2$	$8$	$8$	$5.621$	$\Q(\zeta_{24})$	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{24}^{4}q^{3}+\zeta_{24}^{2}q^{5}+\zeta_{24}^{5}q^{7}+\cdots$
704.2.g.d	$704$	$2$	704.g	88.g	$2$	$8$	$8$	$5.621$	8.0.303595776.1	$_{}$	$\Q(\sqrt{-11}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{U}(1)[D_{2}]$	$q+(\beta _{3}+\beta _{5})q^{3}+\beta _{1}q^{5}+(1-\beta _{4})q^{9}+\cdots$
704.2.i.a	$704$	$2$	704.i	176.i	$4$	$44$	$22$	$5.621$		$_{}$	None	None		$4$	$0$	$0$	$4$	$-4$	$0$			$\mathrm{SU}(2)[C_{4}]$
704.2.j.a	$704$	$2$	704.j	16.e	$4$	$40$	$20$	$5.621$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
704.2.m.a	$704$	$2$	704.m	11.c	$5$	$4$	$1$	$5.621$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$-4$	$6$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\zeta_{10}+2\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+(2+\cdots)q^{5}+\cdots$
704.2.m.b	$704$	$2$	704.m	11.c	$5$	$4$	$1$	$5.621$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$-3$	$-3$	$-3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+(-1+\cdots)q^{5}+\cdots$
704.2.m.c	$704$	$2$	704.m	11.c	$5$	$4$	$1$	$5.621$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$-2$	$6$	$10$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\zeta_{10}-\zeta_{10}^{3})q^{3}+(2+2\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
704.2.m.d	$704$	$2$	704.m	11.c	$5$	$4$	$1$	$5.621$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$-1$	$-3$	$7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\zeta_{10}-\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+(-1+\cdots)q^{5}+\cdots$
704.2.m.e	$704$	$2$	704.m	11.c	$5$	$4$	$1$	$5.621$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$1$	$-3$	$-7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+(-1-\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
704.2.m.f	$704$	$2$	704.m	11.c	$5$	$4$	$1$	$5.621$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$2$	$6$	$-10$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\zeta_{10}+\zeta_{10}^{3})q^{3}+(2+2\zeta_{10}^{2})q^{5}+\cdots$
704.2.m.g	$704$	$2$	704.m	11.c	$5$	$4$	$1$	$5.621$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$3$	$-3$	$3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+(-1-\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
704.2.m.h	$704$	$2$	704.m	11.c	$5$	$4$	$1$	$5.621$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$4$	$6$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+(2+2\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
704.2.m.i	$704$	$2$	704.m	11.c	$5$	$8$	$2$	$5.621$	8.0.682515625.5	$_{}$	None	None		$2$	$0$	$0$	$-1$	$3$	$-7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{1}+\beta _{4}-\beta _{6})q^{3}+(-\beta _{3}+\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots$
704.2.m.j	$704$	$2$	704.m	11.c	$5$	$8$	$2$	$5.621$	8.0.484000000.6	$_{}$	None	None		$4$	$0$	$0$	$0$	$-14$	$0$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-2\beta _{1}+\beta _{6}-\beta _{7})q^{3}+(-1-\beta _{2}+\cdots)q^{5}+\cdots$
704.2.m.k	$704$	$2$	704.m	11.c	$5$	$8$	$2$	$5.621$	8.0.484000000.9	$_{}$	None	None		$4$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{1}q^{3}+(-\beta _{2}-\beta _{3}-\beta _{5})q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots$
704.2.m.l	$704$	$2$	704.m	11.c	$5$	$8$	$2$	$5.621$	8.0.682515625.5	$_{}$	None	None		$2$	$0$	$0$	$1$	$3$	$7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{1}-\beta _{4}+\beta _{6})q^{3}+(-\beta _{3}+\beta _{4}+\cdots)q^{5}+\cdots$
704.2.m.m	$704$	$2$	704.m	11.c	$5$	$12$	$3$	$5.621$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{5}+\beta _{8})q^{3}-\beta _{9}q^{5}+(-1+\beta _{4}+\cdots)q^{7}+\cdots$
704.2.m.n	$704$	$2$	704.m	11.c	$5$	$12$	$3$	$5.621$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{5}-\beta _{8})q^{3}-\beta _{9}q^{5}+(1-\beta _{4}-\beta _{6}+\cdots)q^{7}+\cdots$
704.2.s.a	$704$	$2$	704.s	88.k	$10$	$8$	$2$	$5.621$	$\Q(\zeta_{20})$	$_{}$	None	None		$4$	$0$	$0$	$-8$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{10}]$	$q+(-2+\zeta_{20}^{2}-\zeta_{20}^{4}+2\zeta_{20}^{6})q^{3}+\cdots$
704.2.s.b	$704$	$2$	704.s	88.k	$10$	$8$	$2$	$5.621$	$\Q(\zeta_{20})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-10$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-\zeta_{20}^{5}-\zeta_{20}^{7})q^{3}+(-1-\zeta_{20}^{6}+\cdots)q^{5}+\cdots$

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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.