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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
273.1.o.a 273.o 273.o $2$ $0.136$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+iq^{4}-iq^{7}-q^{9}-q^{12}+\cdots\)
273.1.o.b 273.o 273.o $2$ $0.136$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q-iq^{3}+iq^{4}+q^{7}-q^{9}+q^{12}-iq^{13}+\cdots\)
273.1.s.a 273.s 273.s $2$ $0.136$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q+\zeta_{6}^{2}q^{3}+q^{4}+\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots\)
273.1.s.b 273.s 273.s $4$ $0.136$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(-2\) \(q-\zeta_{12}^{3}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{5}q^{5}+\cdots\)
273.1.x.a 273.x 273.x $2$ $0.136$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(-1\) \(q-q^{3}-\zeta_{6}^{2}q^{4}-\zeta_{6}q^{7}+q^{9}+\zeta_{6}^{2}q^{12}+\cdots\)
273.1.bm.a 273.bm 273.am $2$ $0.136$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(-1\) \(q+q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{7}+q^{9}+\zeta_{6}^{2}q^{12}+\cdots\)
273.1.bm.b 273.bm 273.am $4$ $0.136$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{12}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{5}q^{5}+\zeta_{12}^{4}q^{6}+\cdots\)
273.1.bp.a 273.bp 273.ap $2$ $0.136$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(1\) \(q-\zeta_{6}^{2}q^{3}-q^{4}-\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots\)
273.1.bs.a 273.bs 273.as $4$ $0.136$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{3}-\zeta_{12}^{3}q^{4}-\zeta_{12}q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
273.1.ch.a 273.ch 273.bh $4$ $0.136$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-\zeta_{12}^{3}q^{3}-\zeta_{12}^{5}q^{4}+\zeta_{12}^{4}q^{7}+\cdots\)
273.2.a.a 273.a 1.a $1$ $2.180$ \(\Q\) None None \(-2\) \(-1\) \(-1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}+q^{7}+\cdots\)
273.2.a.b 273.a 1.a $1$ $2.180$ \(\Q\) None None \(2\) \(1\) \(1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}-q^{7}+\cdots\)
273.2.a.c 273.a 1.a $2$ $2.180$ \(\Q(\sqrt{2}) \) None None \(2\) \(-2\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}+(-1+\cdots)q^{6}+\cdots\)
273.2.a.d 273.a 1.a $3$ $2.180$ 3.3.316.1 None None \(-2\) \(-3\) \(-3\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-q^{3}+(2-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
273.2.a.e 273.a 1.a $4$ $2.180$ 4.4.17428.1 None None \(1\) \(4\) \(-3\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
273.2.c.a 273.c 13.b $2$ $2.180$ \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}+q^{3}-2q^{4}+3iq^{5}+2iq^{6}+\cdots\)
273.2.c.b 273.c 13.b $6$ $2.180$ 6.0.350464.1 None None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+q^{3}+(-\beta _{1}+\beta _{2})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)
273.2.c.c 273.c 13.b $8$ $2.180$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-q^{3}+(-2+\beta _{2})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)
273.2.e.a 273.e 21.c $32$ $2.180$ None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$
273.2.g.a 273.g 273.g $32$ $2.180$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
273.2.i.a 273.i 7.c $2$ $2.180$ \(\Q(\sqrt{-3}) \) None None \(1\) \(-1\) \(-4\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
273.2.i.b 273.i 7.c $6$ $2.180$ \(\Q(\zeta_{18})\) None None \(0\) \(3\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\zeta_{18}+\zeta_{18}^{2}+\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+\cdots\)
273.2.i.c 273.i 7.c $6$ $2.180$ 6.0.64827.1 None None \(2\) \(-3\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{4})q^{2}-\beta _{5}q^{3}+(2\beta _{1}-2\beta _{2}+\cdots)q^{4}+\cdots\)
273.2.i.d 273.i 7.c $8$ $2.180$ 8.0.4868829729.1 None None \(1\) \(-4\) \(-3\) \(9\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{3}+\beta _{6})q^{2}+\beta _{4}q^{3}+(\beta _{3}+\cdots)q^{4}+\cdots\)
273.2.i.e 273.i 7.c $10$ $2.180$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(5\) \(3\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{4}-\beta _{8})q^{2}+(1-\beta _{2})q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
273.2.j.a 273.j 91.g $2$ $2.180$ \(\Q(\sqrt{-3}) \) None None \(0\) \(2\) \(0\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{3}+(2-2\zeta_{6})q^{4}+(3-\zeta_{6})q^{7}+q^{9}+\cdots\)
273.2.j.b 273.j 91.g $16$ $2.180$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(-16\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}-q^{3}+(-\beta _{3}+\beta _{5}-\beta _{9}+\beta _{14}+\cdots)q^{4}+\cdots\)
273.2.j.c 273.j 91.g $20$ $2.180$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(20\) \(0\) \(-9\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{4})q^{2}+q^{3}+(-\beta _{2}-2\beta _{7}+\cdots)q^{4}+\cdots\)
273.2.k.a 273.k 13.c $6$ $2.180$ \(\Q(\zeta_{18})\) None None \(0\) \(-3\) \(12\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\zeta_{18}-\zeta_{18}^{2}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots\)
273.2.k.b 273.k 13.c $6$ $2.180$ 6.0.6040683.1 None None \(0\) \(3\) \(4\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{2})q^{2}+(1-\beta _{4})q^{3}+(\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
273.2.k.c 273.k 13.c $6$ $2.180$ 6.0.64827.1 None None \(2\) \(-3\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{4})q^{2}+(-1+\beta _{5})q^{3}+(2\beta _{1}+\cdots)q^{4}+\cdots\)
273.2.k.d 273.k 13.c $6$ $2.180$ 6.0.771147.1 None None \(2\) \(3\) \(0\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}-\beta _{4}q^{3}+\cdots\)
273.2.l.a 273.l 91.h $2$ $2.180$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{3}-2q^{4}+(-3+2\zeta_{6})q^{7}+(-1+\cdots)q^{9}+\cdots\)
273.2.l.b 273.l 91.h $16$ $2.180$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(8\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{2})q^{2}+\beta _{9}q^{3}+(1+\beta _{3}+\cdots)q^{4}+\cdots\)
273.2.l.c 273.l 91.h $20$ $2.180$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(-10\) \(0\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{4}q^{2}+(-1+\beta _{7})q^{3}+(2+\beta _{2})q^{4}+\cdots\)
273.2.n.a 273.n 39.f $4$ $2.180$ \(\Q(\zeta_{8})\) None None \(-4\) \(-4\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\zeta_{8}^{2})q^{2}+(-1+\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
273.2.n.b 273.n 39.f $4$ $2.180$ \(\Q(\zeta_{8})\) None None \(4\) \(-4\) \(8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-\zeta_{8}^{2})q^{2}+(-1+\zeta_{8}+\zeta_{8}^{2})q^{3}+\cdots\)
273.2.n.c 273.n 39.f $48$ $2.180$ None None \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
273.2.p.a 273.p 91.i $4$ $2.180$ \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(-8\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(-2+2\beta _{2}+\cdots)q^{5}+\cdots\)
273.2.p.b 273.p 91.i $4$ $2.180$ \(\Q(i, \sqrt{10})\) None None \(0\) \(0\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{3}+2\beta _{2}q^{4}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
273.2.p.c 273.p 91.i $4$ $2.180$ \(\Q(i, \sqrt{10})\) None None \(0\) \(0\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{3}-2\beta _{2}q^{4}+(1-\beta _{2}+\beta _{3})q^{5}+\cdots\)
273.2.p.d 273.p 91.i $4$ $2.180$ \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}+(2-2\beta _{2}+\cdots)q^{5}+\cdots\)
273.2.p.e 273.p 91.i $12$ $2.180$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(-12\) \(12\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{8}q^{2}-\beta _{4}q^{3}+(3\beta _{4}-\beta _{6}-\beta _{11})q^{4}+\cdots\)
273.2.p.f 273.p 91.i $12$ $2.180$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(12\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{8}q^{2}+\beta _{4}q^{3}+(3\beta _{4}-\beta _{6}-\beta _{11})q^{4}+\cdots\)
273.2.r.a 273.r 273.r $2$ $2.180$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(0\) \(4\) $\mathrm{U}(1)[D_{6}]$ \(q+(-1-\zeta_{6})q^{3}+2q^{4}+(1+2\zeta_{6})q^{7}+\cdots\)
273.2.r.b 273.r 273.r $64$ $2.180$ None None \(0\) \(0\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{6}]$
273.2.t.a 273.t 91.k $2$ $2.180$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-6\) \(5\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+2\zeta_{6})q^{2}+\zeta_{6}q^{3}-q^{4}+(-4+\cdots)q^{5}+\cdots\)
273.2.t.b 273.t 91.k $4$ $2.180$ \(\Q(\sqrt{-3}, \sqrt{-7})\) None None \(0\) \(-2\) \(6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
273.2.t.c 273.t 91.k $12$ $2.180$ 12.0.\(\cdots\).1 None None \(0\) \(-6\) \(-6\) \(-3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}+\beta _{3}+\beta _{6})q^{2}+(-1-\beta _{4})q^{3}+\cdots\)
273.2.t.d 273.t 91.k $20$ $2.180$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(10\) \(6\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{2}+\beta _{3})q^{2}+\beta _{11}q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)
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