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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
143.1.d.a 143.d 143.d $2$ $0.071$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-143}) \) None \(-1\) \(-1\) \(0\) \(-1\) \(q+(-1+\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots\)
143.1.d.b 143.d 143.d $2$ $0.071$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-143}) \) None \(1\) \(-1\) \(0\) \(1\) \(q+(1-\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots\)
143.2.a.a 143.a 1.a $1$ $1.142$ \(\Q\) None None \(0\) \(-1\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-q^{5}-2q^{7}-2q^{9}-q^{11}+\cdots\)
143.2.a.b 143.a 1.a $4$ $1.142$ 4.4.1957.1 None None \(3\) \(0\) \(0\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1}+\beta _{2})q^{2}+(-\beta _{2}-\beta _{3})q^{3}+\cdots\)
143.2.a.c 143.a 1.a $6$ $1.142$ 6.6.194616205.1 None None \(0\) \(3\) \(1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
143.2.b.a 143.b 13.b $12$ $1.142$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(-1+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
143.2.e.a 143.e 13.c $6$ $1.142$ 6.0.1714608.1 None None \(-3\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{4})q^{2}+(-\beta _{3}+\beta _{5})q^{3}-\beta _{4}q^{4}+\cdots\)
143.2.e.b 143.e 13.c $6$ $1.142$ 6.0.3518667.1 None None \(1\) \(-1\) \(-2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-3+\beta _{2}-2\beta _{3}+\cdots)q^{4}+\cdots\)
143.2.e.c 143.e 13.c $12$ $1.142$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(-1\) \(-12\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{6}q^{2}+(\beta _{6}+\beta _{8})q^{3}+(-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
143.2.g.a 143.g 143.g $24$ $1.142$ None None \(0\) \(-8\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$
143.2.h.a 143.h 11.c $4$ $1.142$ \(\Q(\zeta_{10})\) None None \(-5\) \(-4\) \(-4\) \(-8\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1-\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
143.2.h.b 143.h 11.c $16$ $1.142$ 16.0.\(\cdots\).1 None None \(2\) \(5\) \(5\) \(9\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{14}q^{2}+(\beta _{2}-\beta _{4}-\beta _{5}-\beta _{11})q^{3}+\cdots\)
143.2.h.c 143.h 11.c $28$ $1.142$ None None \(-3\) \(-7\) \(-7\) \(-7\) $\mathrm{SU}(2)[C_{5}]$
143.2.j.a 143.j 13.e $4$ $1.142$ \(\Q(\zeta_{12})\) None None \(6\) \(2\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-\zeta_{12}^{2})q^{2}+(-\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
143.2.j.b 143.j 13.e $16$ $1.142$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(-6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{2}q^{2}+(-\beta _{1}-\beta _{2}-\beta _{4}-\beta _{6}+\beta _{8}+\cdots)q^{3}+\cdots\)
143.2.n.a 143.n 143.n $48$ $1.142$ None None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
143.2.o.a 143.o 143.o $48$ $1.142$ None None \(0\) \(-4\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{12}]$
143.2.q.a 143.q 143.q $96$ $1.142$ None None \(-3\) \(-3\) \(-12\) \(-3\) $\mathrm{SU}(2)[C_{15}]$
143.2.s.a 143.s 143.s $96$ $1.142$ None None \(-10\) \(-12\) \(-6\) \(-10\) $\mathrm{SU}(2)[C_{20}]$
143.2.u.a 143.u 143.u $96$ $1.142$ None None \(-9\) \(-3\) \(0\) \(-9\) $\mathrm{SU}(2)[C_{30}]$
143.2.w.a 143.w 143.w $192$ $1.142$ None None \(-20\) \(-6\) \(-12\) \(-20\) $\mathrm{SU}(2)[C_{60}]$
143.3.c.a 143.c 11.b $24$ $3.896$ None None \(0\) \(6\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$
143.3.d.a 143.d 143.d $5$ $3.896$ 5.5.63903125.1 \(\Q(\sqrt{-143}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{3}q^{2}+\beta _{2}q^{3}+(4-\beta _{1}-\beta _{4})q^{4}+\cdots\)
143.3.d.b 143.d 143.d $5$ $3.896$ 5.5.63903125.1 \(\Q(\sqrt{-143}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{3}q^{2}+\beta _{2}q^{3}+(4-\beta _{1}-\beta _{4})q^{4}+\cdots\)
143.3.d.c 143.d 143.d $8$ $3.896$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-\beta _{1}q^{3}+(-1+\beta _{1})q^{4}+\beta _{2}q^{5}+\cdots\)
143.3.d.d 143.d 143.d $8$ $3.896$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1-2\beta _{3})q^{4}-\beta _{2}q^{5}+\cdots\)
143.3.f.a 143.f 13.d $44$ $3.896$ None None \(4\) \(0\) \(-20\) \(20\) $\mathrm{SU}(2)[C_{4}]$
143.3.i.a 143.i 143.i $52$ $3.896$ None None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
143.3.k.a 143.k 143.k $52$ $3.896$ None None \(0\) \(-2\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{6}]$
143.3.l.a 143.l 143.l $104$ $3.896$ None None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
143.3.m.a 143.m 11.d $96$ $3.896$ None None \(0\) \(-6\) \(2\) \(-30\) $\mathrm{SU}(2)[C_{10}]$
143.3.p.a 143.p 13.f $96$ $3.896$ None None \(-4\) \(0\) \(20\) \(-40\) $\mathrm{SU}(2)[C_{12}]$
143.3.r.a 143.r 143.r $208$ $3.896$ None None \(-6\) \(-12\) \(-6\) \(-6\) $\mathrm{SU}(2)[C_{20}]$
143.3.t.a 143.t 143.t $208$ $3.896$ None None \(-5\) \(-3\) \(-12\) \(-5\) $\mathrm{SU}(2)[C_{30}]$
143.3.v.a 143.v 143.v $208$ $3.896$ None None \(-15\) \(-3\) \(0\) \(-15\) $\mathrm{SU}(2)[C_{30}]$
143.3.x.a 143.x 143.x $416$ $3.896$ None None \(-12\) \(-6\) \(-12\) \(-12\) $\mathrm{SU}(2)[C_{60}]$
143.4.a.a 143.a 1.a $4$ $8.437$ 4.4.297133.1 None None \(0\) \(-4\) \(-6\) \(-17\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(2+\beta _{1}+2\beta _{2}+\cdots)q^{4}+\cdots\)
143.4.a.b 143.a 1.a $6$ $8.437$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(-6\) \(-6\) \(-8\) \(-53\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{4})q^{3}+(4+\cdots)q^{4}+\cdots\)
143.4.a.c 143.a 1.a $9$ $8.437$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(0\) \(8\) \(30\) \(25\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(5-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
143.4.a.d 143.a 1.a $11$ $8.437$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None None \(6\) \(6\) \(-4\) \(45\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1-\beta _{5})q^{3}+(6-\beta _{1}+\cdots)q^{4}+\cdots\)
143.4.b.a 143.b 13.b $36$ $8.437$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
143.4.e.a 143.e 13.c $34$ $8.437$ None None \(-4\) \(6\) \(32\) \(6\) $\mathrm{SU}(2)[C_{3}]$
143.4.e.b 143.e 13.c $34$ $8.437$ None None \(0\) \(6\) \(-48\) \(62\) $\mathrm{SU}(2)[C_{3}]$
143.4.g.a 143.g 143.g $80$ $8.437$ None None \(0\) \(-8\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$
143.4.h.a 143.h 11.c $68$ $8.437$ None None \(4\) \(12\) \(24\) \(8\) $\mathrm{SU}(2)[C_{5}]$
143.4.h.b 143.h 11.c $76$ $8.437$ None None \(4\) \(-12\) \(-16\) \(56\) $\mathrm{SU}(2)[C_{5}]$
143.4.j.a 143.j 13.e $72$ $8.437$ None None \(0\) \(-12\) \(0\) \(-36\) $\mathrm{SU}(2)[C_{6}]$
143.4.n.a 143.n 143.n $160$ $8.437$ None None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
143.4.o.a 143.o 143.o $160$ $8.437$ None None \(0\) \(-4\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{12}]$
143.4.q.a 143.q 143.q $320$ $8.437$ None None \(-3\) \(-3\) \(-12\) \(-3\) $\mathrm{SU}(2)[C_{15}]$
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