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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
790.2.a.a	$790$	$2$	790.a	1.a	$1$	$1$	$1$	$6.308$	\(\Q\)	None	✓	✓	✓	✓	790.2.a.a	$1$	$1$	\(1\)	\(-2\)	\(1\)	\(-2\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}+q^{4}+q^{5}-2q^{6}-2q^{7}+\cdots\)
790.2.a.b	$790$	$2$	790.a	1.a	$1$	$2$	$2$	$6.308$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓	✓	790.2.a.b	$1$	$1$	\(-2\)	\(0\)	\(2\)	\(0\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta q^{3}+q^{4}+q^{5}-\beta q^{6}-2\beta q^{7}+\cdots\)
790.2.a.c	$790$	$2$	790.a	1.a	$1$	$2$	$2$	$6.308$	\(\Q(\sqrt{3}) \)	None	✓	✓	✓	✓	790.2.a.c	$1$	$0$	\(-2\)	\(2\)	\(-2\)	\(-2\)	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+(1+\beta )q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
790.2.a.d	$790$	$2$	790.a	1.a	$1$	$2$	$2$	$6.308$	\(\Q(\sqrt{3}) \)	None	✓	✓	✓	✓	790.2.a.d	$1$	$1$	\(2\)	\(0\)	\(-2\)	\(-6\)	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+(-3-\beta )q^{7}+q^{8}+\cdots\)
790.2.a.e	$790$	$2$	790.a	1.a	$1$	$4$	$4$	$6.308$	4.4.5744.1	None	✓	✓	✓	✓	790.2.a.e	$1$	$1$	\(-4\)	\(-2\)	\(-4\)	\(-2\)	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
790.2.a.f	$790$	$2$	790.a	1.a	$1$	$4$	$4$	$6.308$	4.4.5744.1	None	✓	✓	✓	✓	790.2.a.f	$1$	$0$	\(-4\)	\(-2\)	\(4\)	\(-4\)	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{2}q^{3}+q^{4}+q^{5}-\beta _{2}q^{6}+\cdots\)
790.2.a.g	$790$	$2$	790.a	1.a	$1$	$4$	$4$	$6.308$	4.4.5744.1	None	✓	✓	✓	✓	790.2.a.g	$1$	$0$	\(4\)	\(2\)	\(-4\)	\(4\)	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
790.2.a.h	$790$	$2$	790.a	1.a	$1$	$6$	$6$	$6.308$	6.6.9372736.1	None	✓	✓	✓	✓	790.2.a.h	$1$	$0$	\(6\)	\(2\)	\(6\)	\(4\)	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{3}q^{3}+q^{4}+q^{5}+\beta _{3}q^{6}+\cdots\)
790.2.b.a	$790$	$2$	790.b	5.b	$2$	$20$	$20$	$6.308$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓			790.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+(\beta _{2}+\beta _{6})q^{3}-q^{4}+\beta _{14}q^{5}+\cdots\)
790.2.b.b	$790$	$2$	790.b	5.b	$2$	$20$	$20$	$6.308$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓			790.2.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{11}q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{9}q^{5}+\beta _{5}q^{6}+\cdots\)
790.2.e.a	$790$	$2$	790.e	79.c	$3$	$2$	$1$	$6.308$	\(\Q(\sqrt{-3}) \)	None		✓			790.2.e.a	$2$	$0$	\(-1\)	\(2\)	\(1\)	\(1\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
790.2.e.b	$790$	$2$	790.e	79.c	$3$	$12$	$6$	$6.308$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			790.2.e.b	$2$	$0$	\(-6\)	\(-2\)	\(6\)	\(-4\)		$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{6})q^{2}+\beta _{2}q^{3}-\beta _{6}q^{4}+\beta _{6}q^{5}+\cdots\)
790.2.e.c	$790$	$2$	790.e	79.c	$3$	$14$	$7$	$6.308$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		✓			790.2.e.c	$2$	$0$	\(-7\)	\(0\)	\(-7\)	\(1\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{10}q^{2}-\beta _{1}q^{3}+(-1-\beta _{10})q^{4}+\cdots\)
790.2.e.d	$790$	$2$	790.e	79.c	$3$	$14$	$7$	$6.308$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		✓			790.2.e.d	$2$	$0$	\(7\)	\(-2\)	\(-7\)	\(-1\)		$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{3})q^{2}-\beta _{1}q^{3}+\beta _{3}q^{4}+\beta _{3}q^{5}+\cdots\)
790.2.e.e	$790$	$2$	790.e	79.c	$3$	$14$	$7$	$6.308$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		✓			790.2.e.e	$2$	$0$	\(7\)	\(2\)	\(7\)	\(-1\)		$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{5})q^{2}+\beta _{1}q^{3}+\beta _{5}q^{4}-\beta _{5}q^{5}+\cdots\)
790.2.g.a	$790$	$2$	790.g	395.f	$4$	$80$	$40$	$6.308$		None		✓	✓	✓	790.2.g.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{4}]$
790.2.j.a	$790$	$2$	790.j	395.j	$6$	$80$	$40$	$6.308$		None		✓	✓	✓	790.2.j.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{6}]$
790.2.k.a	$790$	$2$	790.k	395.l	$12$	$160$	$40$	$6.308$		None		✓	✓	✓	790.2.k.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)			$\mathrm{SU}(2)[C_{12}]$
790.2.m.a	$790$	$2$	790.m	79.e	$13$	$12$	$1$	$6.308$	\(\Q(\zeta_{26})\)	None		✓			790.2.m.a	$2$	$0$	\(1\)	\(-9\)	\(-1\)	\(17\)		$1$	$\mathrm{SU}(2)[C_{13}]$	\(q+\zeta_{26}q^{2}+(-1-\zeta_{26}^{2}+\zeta_{26}^{5}+\zeta_{26}^{7}+\cdots)q^{3}+\cdots\)
790.2.m.b	$790$	$2$	790.m	79.e	$13$	$12$	$1$	$6.308$	\(\Q(\zeta_{26})\)	None		✓			790.2.m.b	$2$	$0$	\(1\)	\(12\)	\(-1\)	\(-4\)		$1$	$\mathrm{SU}(2)[C_{13}]$	\(q+\zeta_{26}q^{2}+(1-\zeta_{26}^{7}-\zeta_{26}^{10})q^{3}+\cdots\)
790.2.m.c	$790$	$2$	790.m	79.e	$13$	$48$	$4$	$6.308$		None		✓			790.2.m.c	$2$	$0$	\(4\)	\(-1\)	\(-4\)	\(-9\)			$\mathrm{SU}(2)[C_{13}]$
790.2.m.d	$790$	$2$	790.m	79.e	$13$	$72$	$6$	$6.308$		None		✓			790.2.m.d	$2$	$0$	\(-6\)	\(-2\)	\(6\)	\(2\)			$\mathrm{SU}(2)[C_{13}]$
790.2.m.e	$790$	$2$	790.m	79.e	$13$	$72$	$6$	$6.308$		None		✓			790.2.m.e	$2$	$0$	\(-6\)	\(4\)	\(-6\)	\(6\)			$\mathrm{SU}(2)[C_{13}]$
790.2.m.f	$790$	$2$	790.m	79.e	$13$	$72$	$6$	$6.308$		None		✓			790.2.m.f	$2$	$0$	\(6\)	\(0\)	\(6\)	\(4\)			$\mathrm{SU}(2)[C_{13}]$
790.2.p.a	$790$	$2$	790.p	395.p	$26$	$480$	$40$	$6.308$		None		✓	✓	✓	790.2.p.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{26}]$
790.2.q.a	$790$	$2$	790.q	79.g	$39$	$168$	$7$	$6.308$		None		✓			790.2.q.a	$2$	$0$	\(-7\)	\(-2\)	\(-7\)	\(1\)			$\mathrm{SU}(2)[C_{39}]$
790.2.q.b	$790$	$2$	790.q	79.g	$39$	$168$	$7$	$6.308$		None		✓			790.2.q.b	$2$	$0$	\(-7\)	\(2\)	\(7\)	\(1\)			$\mathrm{SU}(2)[C_{39}]$
790.2.q.c	$790$	$2$	790.q	79.g	$39$	$168$	$7$	$6.308$		None		✓			790.2.q.c	$2$	$0$	\(7\)	\(0\)	\(-7\)	\(3\)			$\mathrm{SU}(2)[C_{39}]$
790.2.q.d	$790$	$2$	790.q	79.g	$39$	$168$	$7$	$6.308$		None		✓			790.2.q.d	$2$	$0$	\(7\)	\(0\)	\(7\)	\(-1\)			$\mathrm{SU}(2)[C_{39}]$
790.2.r.a	$790$	$2$	790.r	395.s	$52$	$960$	$40$	$6.308$		None		✓	✓	✓	790.2.r.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{52}]$
790.2.t.a	$790$	$2$	790.t	395.t	$78$	$960$	$40$	$6.308$		None		✓	✓	✓	790.2.t.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{78}]$
790.2.x.a	$790$	$2$	790.x	395.w	$156$	$1920$	$40$	$6.308$		None		✓	✓	✓	790.2.x.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(12\)			$\mathrm{SU}(2)[C_{156}]$
790.3.c.a	$790$	$3$	790.c	79.b	$2$	$56$	$56$	$21.526$		None		✓	✓	✓	790.3.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
790.3.d.a	$790$	$3$	790.d	395.c	$2$	$80$	$80$	$21.526$		None		✓	✓	✓	790.3.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)			$\mathrm{SU}(2)[C_{2}]$
790.4.a.a	$790$	$4$	790.a	1.a	$1$	$6$	$6$	$46.612$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓	✓	✓	790.4.a.a	$1$	$1$	\(12\)	\(-6\)	\(30\)	\(-39\)	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+2q^{2}+(-1-\beta _{5})q^{3}+4q^{4}+5q^{5}+\cdots\)
790.4.a.b	$790$	$4$	790.a	1.a	$1$	$9$	$9$	$46.612$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓	✓	✓	790.4.a.b	$1$	$1$	\(-18\)	\(-2\)	\(45\)	\(13\)	$-$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	\(q-2q^{2}-\beta _{1}q^{3}+4q^{4}+5q^{5}+2\beta _{1}q^{6}+\cdots\)
790.4.a.c	$790$	$4$	790.a	1.a	$1$	$9$	$9$	$46.612$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓	✓	✓	790.4.a.c	$1$	$0$	\(-18\)	\(8\)	\(-45\)	\(-1\)	$+$	$2^{3}\cdot 11$	$\mathrm{SU}(2)$	\(q-2q^{2}+(1-\beta _{1})q^{3}+4q^{4}-5q^{5}+\cdots\)
790.4.a.d	$790$	$4$	790.a	1.a	$1$	$9$	$9$	$46.612$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓	✓	✓	790.4.a.d	$1$	$1$	\(18\)	\(-4\)	\(-45\)	\(-43\)	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+2q^{2}-\beta _{1}q^{3}+4q^{4}-5q^{5}-2\beta _{1}q^{6}+\cdots\)
790.4.a.e	$790$	$4$	790.a	1.a	$1$	$11$	$11$	$46.612$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	✓	✓	✓	790.4.a.e	$1$	$0$	\(-22\)	\(-8\)	\(55\)	\(-15\)	$+$	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q-2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+5q^{5}+\cdots\)
790.4.a.f	$790$	$4$	790.a	1.a	$1$	$11$	$11$	$46.612$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	✓	✓	✓	790.4.a.f	$1$	$1$	\(-22\)	\(-4\)	\(-55\)	\(-1\)	$-$	$2$	$\mathrm{SU}(2)$	\(q-2q^{2}-\beta _{1}q^{3}+4q^{4}-5q^{5}+2\beta _{1}q^{6}+\cdots\)
790.4.a.g	$790$	$4$	790.a	1.a	$1$	$11$	$11$	$46.612$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	✓	✓	✓	790.4.a.g	$1$	$0$	\(22\)	\(2\)	\(-55\)	\(27\)	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+2q^{2}+\beta _{1}q^{3}+4q^{4}-5q^{5}+2\beta _{1}q^{6}+\cdots\)
790.4.a.h	$790$	$4$	790.a	1.a	$1$	$12$	$12$	$46.612$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓	✓	790.4.a.h	$1$	$0$	\(24\)	\(18\)	\(60\)	\(59\)	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+2q^{2}+(2-\beta _{1})q^{3}+4q^{4}+5q^{5}+\cdots\)
790.6.a.a	$790$	$6$	790.a	1.a	$1$	$14$	$14$	$126.703$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	✓	✓	✓	790.6.a.a	$1$	$1$	\(56\)	\(-34\)	\(350\)	\(-470\)	$+$	$2^{6}$	$\mathrm{SU}(2)$	\(q+4q^{2}+(-2-\beta _{1})q^{3}+2^{4}q^{4}+5^{2}q^{5}+\cdots\)
790.6.a.b	$790$	$6$	790.a	1.a	$1$	$15$	$15$	$126.703$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	✓	✓	✓	790.6.a.b	$1$	$1$	\(-60\)	\(-4\)	\(375\)	\(192\)	$+$	$2^{6}\cdot 3$	$\mathrm{SU}(2)$	\(q-4q^{2}-\beta _{1}q^{3}+2^{4}q^{4}+5^{2}q^{5}+4\beta _{1}q^{6}+\cdots\)
790.6.a.c	$790$	$6$	790.a	1.a	$1$	$15$	$15$	$126.703$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	✓	✓	✓	790.6.a.c	$1$	$0$	\(-60\)	\(24\)	\(-375\)	\(-56\)	$-$	$2^{6}\cdot 3$	$\mathrm{SU}(2)$	\(q-4q^{2}+(2-\beta _{1})q^{3}+2^{4}q^{4}-5^{2}q^{5}+\cdots\)
790.6.a.d	$790$	$6$	790.a	1.a	$1$	$15$	$15$	$126.703$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	✓	✓	✓	790.6.a.d	$1$	$1$	\(60\)	\(-26\)	\(-375\)	\(-156\)	$+$	$2^{5}\cdot 3$	$\mathrm{SU}(2)$	\(q+4q^{2}+(-2+\beta _{1})q^{3}+2^{4}q^{4}-5^{2}q^{5}+\cdots\)
790.6.a.e	$790$	$6$	790.a	1.a	$1$	$17$	$17$	$126.703$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	✓	✓	✓	790.6.a.e	$1$	$0$	\(-68\)	\(-22\)	\(425\)	\(-4\)	$-$	$2^{8}$	$\mathrm{SU}(2)$	\(q-4q^{2}+(-1-\beta _{1})q^{3}+2^{4}q^{4}+5^{2}q^{5}+\cdots\)
790.6.a.f	$790$	$6$	790.a	1.a	$1$	$17$	$17$	$126.703$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	✓	✓	✓	790.6.a.f	$1$	$1$	\(-68\)	\(-12\)	\(-425\)	\(-56\)	$+$	$2^{7}$	$\mathrm{SU}(2)$	\(q-4q^{2}+(-1+\beta _{1})q^{3}+2^{4}q^{4}-5^{2}q^{5}+\cdots\)
790.6.a.g	$790$	$6$	790.a	1.a	$1$	$17$	$17$	$126.703$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	✓	✓	✓	790.6.a.g	$1$	$0$	\(68\)	\(-8\)	\(-425\)	\(334\)	$-$	$2^{7}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+4q^{2}-\beta _{1}q^{3}+2^{4}q^{4}-5^{2}q^{5}-4\beta _{1}q^{6}+\cdots\)
790.6.a.h	$790$	$6$	790.a	1.a	$1$	$20$	$20$	$126.703$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	✓	✓	✓	790.6.a.h	$1$	$0$	\(80\)	\(38\)	\(500\)	\(216\)	$-$	$2^{12}$	$\mathrm{SU}(2)$	\(q+4q^{2}+(2-\beta _{1})q^{3}+2^{4}q^{4}+5^{2}q^{5}+\cdots\)

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