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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
280.1.c.a 280.c 280.c $4$ $0.140$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}+(-\zeta_{8}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots\)
280.1.bi.a 280.bi 280.ai $2$ $0.140$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-10}) \) None \(-1\) \(0\) \(-1\) \(2\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+q^{7}+\cdots\)
280.1.bi.b 280.bi 280.ai $2$ $0.140$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-10}) \) None \(1\) \(0\) \(1\) \(-2\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}-q^{7}+\cdots\)
280.2.a.a 280.a 1.a $1$ $2.236$ \(\Q\) None None \(0\) \(-3\) \(1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+q^{5}+q^{7}+6q^{9}-5q^{11}+\cdots\)
280.2.a.b 280.a 1.a $1$ $2.236$ \(\Q\) None None \(0\) \(-1\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-q^{7}-2q^{9}-5q^{11}+q^{13}+\cdots\)
280.2.a.c 280.a 1.a $2$ $2.236$ \(\Q(\sqrt{33}) \) None None \(0\) \(-1\) \(-2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-q^{5}-q^{7}+(5+\beta )q^{9}+(4-\beta )q^{11}+\cdots\)
280.2.a.d 280.a 1.a $2$ $2.236$ \(\Q(\sqrt{17}) \) None None \(0\) \(1\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}+q^{7}+(1+\beta )q^{9}-\beta q^{11}+\cdots\)
280.2.b.a 280.b 8.b $2$ $2.236$ \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+i)q^{2}+2iq^{3}+2iq^{4}-iq^{5}+\cdots\)
280.2.b.b 280.b 8.b $2$ $2.236$ \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+i)q^{2}+2iq^{3}+2iq^{4}+iq^{5}+\cdots\)
280.2.b.c 280.b 8.b $8$ $2.236$ 8.0.18939904.2 None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{6}q^{2}+(-\beta _{5}+\beta _{7})q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
280.2.b.d 280.b 8.b $12$ $2.236$ 12.0.\(\cdots\).1 None None \(-2\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{2}+(\beta _{1}-\beta _{3}+\beta _{7})q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots\)
280.2.g.a 280.g 5.b $2$ $2.236$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(2-i)q^{5}+iq^{7}+2q^{9}-q^{11}+\cdots\)
280.2.g.b 280.g 5.b $6$ $2.236$ 6.0.5161984.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{3}+(\beta _{1}-\beta _{5})q^{5}+\beta _{4}q^{7}+(-1+\cdots)q^{9}+\cdots\)
280.2.h.a 280.h 56.e $16$ $2.236$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(1\) \(0\) \(-16\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}+\beta _{4}q^{3}+\beta _{9}q^{4}-q^{5}+\beta _{6}q^{6}+\cdots\)
280.2.h.b 280.h 56.e $16$ $2.236$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(1\) \(0\) \(16\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}-\beta _{4}q^{3}+\beta _{9}q^{4}+q^{5}-\beta _{6}q^{6}+\cdots\)
280.2.l.a 280.l 40.f $36$ $2.236$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
280.2.n.a 280.n 280.n $4$ $2.236$ \(\Q(\sqrt{2}, \sqrt{-5})\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{2}+2q^{4}+\beta _{3}q^{5}+(-\beta _{1}+\beta _{3})q^{7}+\cdots\)
280.2.n.b 280.n 280.n $40$ $2.236$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
280.2.q.a 280.q 7.c $2$ $2.236$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots\)
280.2.q.b 280.q 7.c $2$ $2.236$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
280.2.q.c 280.q 7.c $2$ $2.236$ \(\Q(\sqrt{-3}) \) None None \(0\) \(2\) \(1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
280.2.q.d 280.q 7.c $4$ $2.236$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(2\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
280.2.q.e 280.q 7.c $6$ $2.236$ 6.0.11337408.1 None None \(0\) \(0\) \(-3\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{5}q^{3}+(-1+\beta _{2})q^{5}+(1-\beta _{1}-\beta _{5})q^{7}+\cdots\)
280.2.s.a 280.s 280.s $8$ $2.236$ 8.0.\(\cdots\).8 \(\Q(\sqrt{-14}) \) None \(-8\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1-\beta _{3})q^{2}+(-\beta _{1}-\beta _{4})q^{3}+2\beta _{3}q^{4}+\cdots\)
280.2.s.b 280.s 280.s $8$ $2.236$ 8.0.\(\cdots\).8 \(\Q(\sqrt{-14}) \) None \(8\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(1+\beta _{4})q^{2}+\beta _{1}q^{3}+2\beta _{4}q^{4}-\beta _{5}q^{5}+\cdots\)
280.2.s.c 280.s 280.s $72$ $2.236$ None None \(-4\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$
280.2.w.a 280.w 40.k $72$ $2.236$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
280.2.x.a 280.x 35.f $24$ $2.236$ None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$
280.2.ba.a 280.ba 280.aa $8$ $2.236$ 8.0.3317760000.3 \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+\beta _{4}q^{2}-2\beta _{3}q^{4}+\beta _{6}q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
280.2.ba.b 280.ba 280.aa $80$ $2.236$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
280.2.bf.a 280.bf 280.af $88$ $2.236$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
280.2.bg.a 280.bg 35.j $24$ $2.236$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
280.2.bj.a 280.bj 56.m $4$ $2.236$ \(\Q(\zeta_{12})\) None None \(-4\) \(-6\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}^{2})q^{3}+\cdots\)
280.2.bj.b 280.bj 56.m $4$ $2.236$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(-6\) \(-2\) \(-10\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{3}q^{2}+(-2-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+\cdots\)
280.2.bj.c 280.bj 56.m $4$ $2.236$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(-6\) \(2\) \(10\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
280.2.bj.d 280.bj 56.m $4$ $2.236$ \(\Q(\zeta_{12})\) None None \(2\) \(-6\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-2+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
280.2.bj.e 280.bj 56.m $24$ $2.236$ None None \(-3\) \(12\) \(12\) \(-10\) $\mathrm{SU}(2)[C_{6}]$
280.2.bj.f 280.bj 56.m $24$ $2.236$ None None \(3\) \(12\) \(-12\) \(10\) $\mathrm{SU}(2)[C_{6}]$
280.2.bl.a 280.bl 56.p $4$ $2.236$ \(\Q(\zeta_{12})\) None None \(-2\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots\)
280.2.bl.b 280.bl 56.p $60$ $2.236$ None None \(4\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$
280.2.bo.a 280.bo 35.k $48$ $2.236$ None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{12}]$
280.2.br.a 280.br 280.ar $176$ $2.236$ None None \(-2\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
280.2.bv.a 280.bv 280.av $4$ $2.236$ \(\Q(\zeta_{12})\) None None \(-4\) \(-2\) \(-4\) \(-10\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1+\zeta_{12}^{3})q^{2}+(-\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
280.2.bv.b 280.bv 280.av $4$ $2.236$ \(\Q(\zeta_{12})\) None None \(-2\) \(2\) \(4\) \(-10\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1+\zeta_{12}+\zeta_{12}^{2})q^{2}+(\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
280.2.bv.c 280.bv 280.av $4$ $2.236$ \(\Q(\zeta_{12})\) None None \(2\) \(-4\) \(4\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1-\zeta_{12}-\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}+\cdots)q^{3}+\cdots\)
280.2.bv.d 280.bv 280.av $4$ $2.236$ \(\Q(\zeta_{12})\) None None \(4\) \(4\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
280.2.bv.e 280.bv 280.av $160$ $2.236$ None None \(-2\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{12}]$
280.3.c.a 280.c 280.c $1$ $7.629$ \(\Q\) \(\Q(\sqrt{-70}) \) None \(-2\) \(0\) \(-5\) \(-7\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{2}+4q^{4}-5q^{5}-7q^{7}-8q^{8}+\cdots\)
280.3.c.b 280.c 280.c $1$ $7.629$ \(\Q\) \(\Q(\sqrt{-70}) \) None \(-2\) \(0\) \(5\) \(7\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{2}+4q^{4}+5q^{5}+7q^{7}-8q^{8}+\cdots\)
280.3.c.c 280.c 280.c $1$ $7.629$ \(\Q\) \(\Q(\sqrt{-70}) \) None \(2\) \(0\) \(-5\) \(7\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{2}+4q^{4}-5q^{5}+7q^{7}+8q^{8}+\cdots\)
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