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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
147.1.l.a 147.l 147.l $6$ $0.073$ \(\Q(\zeta_{14})\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q+\zeta_{14}^{2}q^{3}+\zeta_{14}^{6}q^{4}-\zeta_{14}^{3}q^{7}+\cdots\)
147.2.a.a 147.a 1.a $1$ $1.174$ \(\Q\) None None \(-1\) \(-1\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+2q^{5}+q^{6}+3q^{8}+\cdots\)
147.2.a.b 147.a 1.a $1$ $1.174$ \(\Q\) None None \(2\) \(-1\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}+2q^{5}-2q^{6}+\cdots\)
147.2.a.c 147.a 1.a $1$ $1.174$ \(\Q\) None None \(2\) \(1\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}-2q^{5}+2q^{6}+\cdots\)
147.2.a.d 147.a 1.a $2$ $1.174$ \(\Q(\sqrt{2}) \) None None \(-2\) \(-2\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}+(-2+\cdots)q^{5}+\cdots\)
147.2.a.e 147.a 1.a $2$ $1.174$ \(\Q(\sqrt{2}) \) None None \(-2\) \(2\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}+(2+\cdots)q^{5}+\cdots\)
147.2.c.a 147.c 21.c $2$ $1.174$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{6}q^{3}+2q^{4}-3q^{9}-2\zeta_{6}q^{12}+\cdots\)
147.2.c.b 147.c 21.c $8$ $1.174$ 8.0.3288334336.2 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+(\beta _{1}-\beta _{5})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)
147.2.e.a 147.e 7.c $2$ $1.174$ \(\Q(\sqrt{-3}) \) None None \(-2\) \(1\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
147.2.e.b 147.e 7.c $2$ $1.174$ \(\Q(\sqrt{-3}) \) None None \(1\) \(-1\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
147.2.e.c 147.e 7.c $2$ $1.174$ \(\Q(\sqrt{-3}) \) None None \(1\) \(1\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
147.2.e.d 147.e 7.c $4$ $1.174$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(2\) \(-2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{2})q^{2}+\beta _{2}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
147.2.e.e 147.e 7.c $4$ $1.174$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(2\) \(2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{2})q^{2}-\beta _{2}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
147.2.g.a 147.g 21.g $2$ $1.174$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+(1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+3\zeta_{6}q^{9}+\cdots\)
147.2.g.b 147.g 21.g $16$ $1.174$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{13}q^{2}+(\beta _{7}-\beta _{9})q^{3}+(1-\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
147.2.i.a 147.i 49.e $24$ $1.174$ None None \(1\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{7}]$
147.2.i.b 147.i 49.e $36$ $1.174$ None None \(-1\) \(-6\) \(-4\) \(-6\) $\mathrm{SU}(2)[C_{7}]$
147.2.k.a 147.k 147.k $96$ $1.174$ None None \(0\) \(-7\) \(0\) \(-14\) $\mathrm{SU}(2)[C_{14}]$
147.2.m.a 147.m 49.g $48$ $1.174$ None None \(-1\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{21}]$
147.2.m.b 147.m 49.g $60$ $1.174$ None None \(1\) \(5\) \(-2\) \(5\) $\mathrm{SU}(2)[C_{21}]$
147.2.o.a 147.o 147.o $12$ $1.174$ \(\Q(\zeta_{21})\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(0\) \(-1\) $\mathrm{U}(1)[D_{42}]$ \(q+(2\zeta_{21}+\zeta_{21}^{8})q^{3}+(-2\zeta_{21}^{3}-2\zeta_{21}^{10}+\cdots)q^{4}+\cdots\)
147.2.o.b 147.o 147.o $192$ $1.174$ None None \(0\) \(-14\) \(0\) \(-28\) $\mathrm{SU}(2)[C_{42}]$
147.3.b.a 147.b 3.b $1$ $4.005$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-3q^{3}+4q^{4}+9q^{9}-12q^{12}+23q^{13}+\cdots\)
147.3.b.b 147.b 3.b $1$ $4.005$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+3q^{3}+4q^{4}+9q^{9}+12q^{12}-23q^{13}+\cdots\)
147.3.b.c 147.b 3.b $2$ $4.005$ \(\Q(\sqrt{-5}) \) None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+(-2-\beta )q^{3}-q^{4}+\beta q^{5}+\cdots\)
147.3.b.d 147.b 3.b $2$ $4.005$ \(\Q(\sqrt{-5}) \) None None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+(2+\beta )q^{3}-q^{4}-\beta q^{5}+(-5+\cdots)q^{6}+\cdots\)
147.3.b.e 147.b 3.b $4$ $4.005$ \(\Q(\sqrt{-5}, \sqrt{-6})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)
147.3.b.f 147.b 3.b $4$ $4.005$ 4.0.65856.1 None None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(-3+\cdots)q^{4}+\cdots\)
147.3.b.g 147.b 3.b $8$ $4.005$ 8.0.\(\cdots\).7 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(-\beta _{5}-\beta _{7})q^{3}+(-2+\beta _{3}+\cdots)q^{4}+\cdots\)
147.3.d.a 147.d 7.b $2$ $4.005$ \(\Q(\sqrt{-3}) \) None None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2q^{2}-\zeta_{6}q^{3}+2\zeta_{6}q^{5}+2\zeta_{6}q^{6}+\cdots\)
147.3.d.b 147.d 7.b $2$ $4.005$ \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\zeta_{6}q^{3}-3q^{4}+3\zeta_{6}q^{5}+\zeta_{6}q^{6}+\cdots\)
147.3.d.c 147.d 7.b $2$ $4.005$ \(\Q(\sqrt{-3}) \) None None \(6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3q^{2}+\zeta_{6}q^{3}+5q^{4}+3\zeta_{6}q^{5}+3\zeta_{6}q^{6}+\cdots\)
147.3.d.d 147.d 7.b $8$ $4.005$ 8.0.339738624.1 None None \(-8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{2})q^{2}+\beta _{3}q^{3}+(5-\beta _{5})q^{4}+\cdots\)
147.3.f.a 147.f 7.d $2$ $4.005$ \(\Q(\sqrt{-3}) \) None None \(-3\) \(3\) \(-9\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-3\zeta_{6}q^{2}+(1+\zeta_{6})q^{3}+(-5+5\zeta_{6})q^{4}+\cdots\)
147.3.f.b 147.f 7.d $2$ $4.005$ \(\Q(\sqrt{-3}) \) None None \(-1\) \(-3\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(3-3\zeta_{6})q^{4}+\cdots\)
147.3.f.c 147.f 7.d $2$ $4.005$ \(\Q(\sqrt{-3}) \) None None \(-1\) \(-3\) \(9\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(3-3\zeta_{6})q^{4}+\cdots\)
147.3.f.d 147.f 7.d $2$ $4.005$ \(\Q(\sqrt{-3}) \) None None \(-1\) \(3\) \(12\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{6}q^{2}+(1+\zeta_{6})q^{3}+(3-3\zeta_{6})q^{4}+\cdots\)
147.3.f.e 147.f 7.d $2$ $4.005$ \(\Q(\sqrt{-3}) \) None None \(2\) \(3\) \(6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+2\zeta_{6}q^{2}+(1+\zeta_{6})q^{3}+(4-2\zeta_{6})q^{5}+\cdots\)
147.3.f.f 147.f 7.d $8$ $4.005$ 8.0.339738624.1 None None \(4\) \(-12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{3}-\beta _{7})q^{2}+(-1+\beta _{3})q^{3}+(-5+\cdots)q^{4}+\cdots\)
147.3.f.g 147.f 7.d $8$ $4.005$ 8.0.339738624.1 None None \(4\) \(12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{3}-\beta _{7})q^{2}+(1-\beta _{3})q^{3}+(-5+\cdots)q^{4}+\cdots\)
147.3.h.a 147.h 21.h $2$ $4.005$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q-3\zeta_{6}q^{3}-4\zeta_{6}q^{4}+(-9+9\zeta_{6})q^{9}+\cdots\)
147.3.h.b 147.h 21.h $4$ $4.005$ \(\Q(\sqrt{-3}, \sqrt{-5})\) None None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(\beta _{1}+2\beta _{2}-\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots\)
147.3.h.c 147.h 21.h $8$ $4.005$ 8.0.\(\cdots\).8 None None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{5}q^{2}+(\beta _{2}-\beta _{6})q^{3}+(2\beta _{2}-3\beta _{4}+\cdots)q^{4}+\cdots\)
147.3.h.d 147.h 21.h $8$ $4.005$ 8.0.3317760000.3 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(-\beta _{2}+\beta _{6})q^{3}+(1-\beta _{3}+\cdots)q^{4}+\cdots\)
147.3.h.e 147.h 21.h $8$ $4.005$ 8.0.\(\cdots\).8 None None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{5}q^{2}+(-\beta _{2}+\beta _{6})q^{3}+(2\beta _{2}-3\beta _{4}+\cdots)q^{4}+\cdots\)
147.3.h.f 147.h 21.h $16$ $4.005$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(-\beta _{8}-\beta _{9}+\beta _{12})q^{3}+(1+\cdots)q^{4}+\cdots\)
147.3.j.a 147.j 49.f $108$ $4.005$ None None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{14}]$
147.3.l.a 147.l 147.l $216$ $4.005$ None None \(0\) \(-5\) \(0\) \(-14\) $\mathrm{SU}(2)[C_{14}]$
147.3.n.a 147.n 147.n $12$ $4.005$ \(\Q(\zeta_{21})\) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(0\) \(13\) $\mathrm{U}(1)[D_{42}]$ \(q+(3\zeta_{21}^{2}+3\zeta_{21}^{9})q^{3}+(-4+4\zeta_{21}^{2}+\cdots)q^{4}+\cdots\)
147.3.n.b 147.n 147.n $408$ $4.005$ None None \(0\) \(-10\) \(0\) \(-42\) $\mathrm{SU}(2)[C_{42}]$
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