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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
16.2.e.a 16.e 16.e $2$ $0.128$ \(\Q(\sqrt{-1}) \) None \(-2\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-i)q^{2}+(-1+i)q^{3}+2iq^{4}+\cdots\)
16.3.c.a 16.c 4.b $1$ $0.436$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-6\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-6q^{5}+9q^{9}+10q^{13}-30q^{17}+\cdots\)
16.3.f.a 16.f 16.f $6$ $0.436$ 6.0.399424.1 None \(-2\) \(-2\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{2}+(-1-\beta _{2}+\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots\)
16.4.a.a 16.a 1.a $1$ $0.944$ \(\Q\) None \(0\) \(4\) \(-2\) \(-24\) $+$ $\mathrm{SU}(2)$ \(q+4q^{3}-2q^{5}-24q^{7}-11q^{9}+44q^{11}+\cdots\)
16.4.e.a 16.e 16.e $10$ $0.944$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{4}q^{2}-\beta _{5}q^{3}+(1-\beta _{2}+\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots\)
16.5.c.a 16.c 4.b $2$ $1.654$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(36\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{3}+18q^{5}+2\zeta_{6}q^{7}-111q^{9}+\cdots\)
16.5.f.a 16.f 16.f $14$ $1.654$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-2\) \(-2\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{4}q^{2}-\beta _{6}q^{3}+(-1+2\beta _{3}-\beta _{11}+\cdots)q^{4}+\cdots\)
16.6.a.a 16.a 1.a $1$ $2.566$ \(\Q\) None \(0\) \(-20\) \(-74\) \(24\) $+$ $\mathrm{SU}(2)$ \(q-20q^{3}-74q^{5}+24q^{7}+157q^{9}+\cdots\)
16.6.a.b 16.a 1.a $1$ $2.566$ \(\Q\) None \(0\) \(12\) \(54\) \(88\) $-$ $\mathrm{SU}(2)$ \(q+12q^{3}+54q^{5}+88q^{7}-99q^{9}+\cdots\)
16.6.e.a 16.e 16.e $18$ $2.566$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-2\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{5}q^{2}-\beta _{4}q^{3}+(-1+\beta _{1}+\beta _{9}+\cdots)q^{4}+\cdots\)
16.7.c.a 16.c 4.b $1$ $3.681$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(234\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+234q^{5}+3^{6}q^{9}-4070q^{13}-990q^{17}+\cdots\)
16.7.c.b 16.c 4.b $2$ $3.681$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-300\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{3}-150q^{5}-22\zeta_{6}q^{7}-39q^{9}+\cdots\)
16.7.f.a 16.f 16.f $22$ $3.681$ None \(-2\) \(-2\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{4}]$
16.8.a.a 16.a 1.a $1$ $4.998$ \(\Q\) None \(0\) \(-44\) \(430\) \(1224\) $+$ $\mathrm{SU}(2)$ \(q-44q^{3}+430q^{5}+1224q^{7}-251q^{9}+\cdots\)
16.8.a.b 16.a 1.a $1$ $4.998$ \(\Q\) None \(0\) \(-12\) \(-210\) \(-1016\) $-$ $\mathrm{SU}(2)$ \(q-12q^{3}-210q^{5}-1016q^{7}-2043q^{9}+\cdots\)
16.8.a.c 16.a 1.a $1$ $4.998$ \(\Q\) None \(0\) \(84\) \(-82\) \(456\) $+$ $\mathrm{SU}(2)$ \(q+84q^{3}-82q^{5}+456q^{7}+4869q^{9}+\cdots\)
16.8.e.a 16.e 16.e $26$ $4.998$ None \(-2\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$
16.9.c.a 16.c 4.b $2$ $6.518$ \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(-1020\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{3}-510q^{5}+18\beta q^{7}-13599q^{9}+\cdots\)
16.9.c.b 16.c 4.b $2$ $6.518$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(516\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{3}+258q^{5}-238\zeta_{6}q^{7}+6369q^{9}+\cdots\)
16.9.f.a 16.f 16.f $30$ $6.518$ None \(-2\) \(-2\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{4}]$
16.10.a.a 16.a 1.a $1$ $8.241$ \(\Q\) None \(0\) \(-228\) \(-666\) \(6328\) $-$ $\mathrm{SU}(2)$ \(q-228q^{3}-666q^{5}+6328q^{7}+32301q^{9}+\cdots\)
16.10.a.b 16.a 1.a $1$ $8.241$ \(\Q\) None \(0\) \(-68\) \(1510\) \(-10248\) $+$ $\mathrm{SU}(2)$ \(q-68q^{3}+1510q^{5}-10248q^{7}-15059q^{9}+\cdots\)
16.10.a.c 16.a 1.a $1$ $8.241$ \(\Q\) None \(0\) \(60\) \(-2074\) \(4344\) $+$ $\mathrm{SU}(2)$ \(q+60q^{3}-2074q^{5}+4344q^{7}-16083q^{9}+\cdots\)
16.10.a.d 16.a 1.a $1$ $8.241$ \(\Q\) None \(0\) \(156\) \(870\) \(952\) $-$ $\mathrm{SU}(2)$ \(q+156q^{3}+870q^{5}+952q^{7}+4653q^{9}+\cdots\)
16.10.e.a 16.e 16.e $34$ $8.241$ None \(-2\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$
16.11.c.a 16.c 4.b $1$ $10.166$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(474\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+474q^{5}+3^{10}q^{9}+683050q^{13}+\cdots\)
16.11.c.b 16.c 4.b $4$ $10.166$ \(\Q(\sqrt{-3}, \sqrt{505})\) None \(0\) \(0\) \(4200\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+(1050+\beta _{2})q^{5}+(-12\beta _{1}+\cdots)q^{7}+\cdots\)
16.11.f.a 16.f 16.f $38$ $10.166$ None \(-2\) \(-2\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{4}]$
16.12.a.a 16.a 1.a $1$ $12.293$ \(\Q\) None \(0\) \(-252\) \(4830\) \(16744\) $-$ $\mathrm{SU}(2)$ \(q-252q^{3}+4830q^{5}+16744q^{7}+\cdots\)
16.12.a.b 16.a 1.a $1$ $12.293$ \(\Q\) None \(0\) \(36\) \(-3490\) \(55464\) $+$ $\mathrm{SU}(2)$ \(q+6^{2}q^{3}-3490q^{5}+55464q^{7}-175851q^{9}+\cdots\)
16.12.a.c 16.a 1.a $1$ $12.293$ \(\Q\) None \(0\) \(516\) \(-10530\) \(-49304\) $-$ $\mathrm{SU}(2)$ \(q+516q^{3}-10530q^{5}-49304q^{7}+\cdots\)
16.12.a.d 16.a 1.a $2$ $12.293$ \(\Q(\sqrt{109}) \) None \(0\) \(-56\) \(7868\) \(-91056\) $+$ $\mathrm{SU}(2)$ \(q+(-28-\beta )q^{3}+(3934-12\beta )q^{5}+\cdots\)
16.12.e.a 16.e 16.e $42$ $12.293$ None \(-2\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$
16.13.c.a 16.c 4.b $2$ $14.624$ \(\Q(\sqrt{-1155}) \) None \(0\) \(0\) \(-540\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{3}-270q^{5}-222\beta q^{7}-133839q^{9}+\cdots\)
16.13.c.b 16.c 4.b $4$ $14.624$ \(\Q(\sqrt{-3}, \sqrt{2521})\) None \(0\) \(0\) \(-14904\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-3726-\beta _{3})q^{5}+(-162\beta _{1}+\cdots)q^{7}+\cdots\)
16.13.f.a 16.f 16.f $46$ $14.624$ None \(-2\) \(-2\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{4}]$
16.14.a.a 16.a 1.a $1$ $17.157$ \(\Q\) None \(0\) \(-1236\) \(-57450\) \(-64232\) $-$ $\mathrm{SU}(2)$ \(q-1236q^{3}-57450q^{5}-64232q^{7}+\cdots\)
16.14.a.b 16.a 1.a $1$ $17.157$ \(\Q\) None \(0\) \(-468\) \(56214\) \(-333032\) $-$ $\mathrm{SU}(2)$ \(q-468q^{3}+56214q^{5}-333032q^{7}+\cdots\)
16.14.a.c 16.a 1.a $1$ $17.157$ \(\Q\) None \(0\) \(12\) \(-4330\) \(139992\) $+$ $\mathrm{SU}(2)$ \(q+12q^{3}-4330q^{5}+139992q^{7}+\cdots\)
16.14.a.d 16.a 1.a $1$ $17.157$ \(\Q\) None \(0\) \(1836\) \(3990\) \(433432\) $-$ $\mathrm{SU}(2)$ \(q+1836q^{3}+3990q^{5}+433432q^{7}+\cdots\)
16.14.a.e 16.a 1.a $2$ $17.157$ \(\Q(\sqrt{781}) \) None \(0\) \(-872\) \(18476\) \(-110928\) $+$ $\mathrm{SU}(2)$ \(q+(-436-\beta )q^{3}+(9238+12\beta )q^{5}+\cdots\)
16.14.e.a 16.e 16.e $50$ $17.157$ None \(-2\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$
16.15.c.a 16.c 4.b $1$ $19.893$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-152886\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-152886q^{5}+3^{14}q^{9}-46322630q^{13}+\cdots\)
16.15.c.b 16.c 4.b $2$ $19.893$ \(\Q(\sqrt{-3395}) \) None \(0\) \(0\) \(215700\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{3}+107850q^{5}+522\beta q^{7}-3039111q^{9}+\cdots\)
16.15.c.c 16.c 4.b $4$ $19.893$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(0\) \(-87000\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-21750+\beta _{3})q^{5}+(245\beta _{1}+\cdots)q^{7}+\cdots\)
16.15.f.a 16.f 16.f $54$ $19.893$ None \(-2\) \(-2\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{4}]$
16.16.a.a 16.a 1.a $1$ $22.831$ \(\Q\) None \(0\) \(-6252\) \(90510\) \(-56\) $-$ $\mathrm{SU}(2)$ \(q-6252q^{3}+90510q^{5}-56q^{7}+24738597q^{9}+\cdots\)
16.16.a.b 16.a 1.a $1$ $22.831$ \(\Q\) None \(0\) \(-2700\) \(-251890\) \(-1374072\) $+$ $\mathrm{SU}(2)$ \(q-2700q^{3}-251890q^{5}-1374072q^{7}+\cdots\)
16.16.a.c 16.a 1.a $1$ $22.831$ \(\Q\) None \(0\) \(276\) \(-132210\) \(3585736\) $-$ $\mathrm{SU}(2)$ \(q+276q^{3}-132210q^{5}+3585736q^{7}+\cdots\)
16.16.a.d 16.a 1.a $1$ $22.831$ \(\Q\) None \(0\) \(3348\) \(52110\) \(-2822456\) $-$ $\mathrm{SU}(2)$ \(q+3348q^{3}+52110q^{5}-2822456q^{7}+\cdots\)
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