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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
16.2.e.a \(2\) \(0.128\) \(\Q(\sqrt{-1}) \) None \(-2\) \(-2\) \(-2\) \(0\) \(q+(-1-i)q^{2}+(-1+i)q^{3}+2iq^{4}+\cdots\)
16.3.c.a \(1\) \(0.436\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-6\) \(0\) \(q-6q^{5}+9q^{9}+10q^{13}-30q^{17}+\cdots\)
16.3.f.a \(6\) \(0.436\) 6.0.399424.1 None \(-2\) \(-2\) \(-2\) \(-4\) \(q+\beta _{2}q^{2}+(-1-\beta _{2}+\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots\)
16.4.a.a \(1\) \(0.944\) \(\Q\) None \(0\) \(4\) \(-2\) \(-24\) \(+\) \(q+4q^{3}-2q^{5}-24q^{7}-11q^{9}+44q^{11}+\cdots\)
16.4.e.a \(10\) \(0.944\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(-2\) \(-2\) \(0\) \(q-\beta _{4}q^{2}-\beta _{5}q^{3}+(1-\beta _{2}+\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots\)
16.5.c.a \(2\) \(1.654\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(36\) \(0\) \(q-\zeta_{6}q^{3}+18q^{5}+2\zeta_{6}q^{7}-111q^{9}+\cdots\)
16.5.f.a \(14\) \(1.654\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-2\) \(-2\) \(-2\) \(-4\) \(q+\beta _{4}q^{2}-\beta _{6}q^{3}+(-1+2\beta _{3}-\beta _{11}+\cdots)q^{4}+\cdots\)
16.6.a.a \(1\) \(2.566\) \(\Q\) None \(0\) \(-20\) \(-74\) \(24\) \(+\) \(q-20q^{3}-74q^{5}+24q^{7}+157q^{9}+\cdots\)
16.6.a.b \(1\) \(2.566\) \(\Q\) None \(0\) \(12\) \(54\) \(88\) \(-\) \(q+12q^{3}+54q^{5}+88q^{7}-99q^{9}+\cdots\)
16.6.e.a \(18\) \(2.566\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-2\) \(-2\) \(-2\) \(0\) \(q+\beta _{5}q^{2}-\beta _{4}q^{3}+(-1+\beta _{1}+\beta _{9}+\cdots)q^{4}+\cdots\)
16.7.c.a \(1\) \(3.681\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(234\) \(0\) \(q+234q^{5}+3^{6}q^{9}-4070q^{13}-990q^{17}+\cdots\)
16.7.c.b \(2\) \(3.681\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-300\) \(0\) \(q-\zeta_{6}q^{3}-150q^{5}-22\zeta_{6}q^{7}-39q^{9}+\cdots\)
16.7.f.a \(22\) \(3.681\) None \(-2\) \(-2\) \(-2\) \(-4\)
16.8.a.a \(1\) \(4.998\) \(\Q\) None \(0\) \(-44\) \(430\) \(1224\) \(+\) \(q-44q^{3}+430q^{5}+1224q^{7}-251q^{9}+\cdots\)
16.8.a.b \(1\) \(4.998\) \(\Q\) None \(0\) \(-12\) \(-210\) \(-1016\) \(-\) \(q-12q^{3}-210q^{5}-1016q^{7}-2043q^{9}+\cdots\)
16.8.a.c \(1\) \(4.998\) \(\Q\) None \(0\) \(84\) \(-82\) \(456\) \(+\) \(q+84q^{3}-82q^{5}+456q^{7}+4869q^{9}+\cdots\)
16.8.e.a \(26\) \(4.998\) None \(-2\) \(-2\) \(-2\) \(0\)
16.9.c.a \(2\) \(6.518\) \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(-1020\) \(0\) \(q-\beta q^{3}-510q^{5}+18\beta q^{7}-13599q^{9}+\cdots\)
16.9.c.b \(2\) \(6.518\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(516\) \(0\) \(q-\zeta_{6}q^{3}+258q^{5}-238\zeta_{6}q^{7}+6369q^{9}+\cdots\)
16.9.f.a \(30\) \(6.518\) None \(-2\) \(-2\) \(-2\) \(-4\)
16.10.a.a \(1\) \(8.241\) \(\Q\) None \(0\) \(-228\) \(-666\) \(6328\) \(-\) \(q-228q^{3}-666q^{5}+6328q^{7}+32301q^{9}+\cdots\)
16.10.a.b \(1\) \(8.241\) \(\Q\) None \(0\) \(-68\) \(1510\) \(-10248\) \(+\) \(q-68q^{3}+1510q^{5}-10248q^{7}-15059q^{9}+\cdots\)
16.10.a.c \(1\) \(8.241\) \(\Q\) None \(0\) \(60\) \(-2074\) \(4344\) \(+\) \(q+60q^{3}-2074q^{5}+4344q^{7}-16083q^{9}+\cdots\)
16.10.a.d \(1\) \(8.241\) \(\Q\) None \(0\) \(156\) \(870\) \(952\) \(-\) \(q+156q^{3}+870q^{5}+952q^{7}+4653q^{9}+\cdots\)
16.10.e.a \(34\) \(8.241\) None \(-2\) \(-2\) \(-2\) \(0\)
16.11.c.a \(1\) \(10.166\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(474\) \(0\) \(q+474q^{5}+3^{10}q^{9}+683050q^{13}+\cdots\)
16.11.c.b \(4\) \(10.166\) \(\Q(\sqrt{-3}, \sqrt{505})\) None \(0\) \(0\) \(4200\) \(0\) \(q-\beta _{1}q^{3}+(1050+\beta _{2})q^{5}+(-12\beta _{1}+\cdots)q^{7}+\cdots\)
16.11.f.a \(38\) \(10.166\) None \(-2\) \(-2\) \(-2\) \(-4\)
16.12.a.a \(1\) \(12.293\) \(\Q\) None \(0\) \(-252\) \(4830\) \(16744\) \(-\) \(q-252q^{3}+4830q^{5}+16744q^{7}+\cdots\)
16.12.a.b \(1\) \(12.293\) \(\Q\) None \(0\) \(36\) \(-3490\) \(55464\) \(+\) \(q+6^{2}q^{3}-3490q^{5}+55464q^{7}-175851q^{9}+\cdots\)
16.12.a.c \(1\) \(12.293\) \(\Q\) None \(0\) \(516\) \(-10530\) \(-49304\) \(-\) \(q+516q^{3}-10530q^{5}-49304q^{7}+\cdots\)
16.12.a.d \(2\) \(12.293\) \(\Q(\sqrt{109}) \) None \(0\) \(-56\) \(7868\) \(-91056\) \(+\) \(q+(-28-\beta )q^{3}+(3934-12\beta )q^{5}+\cdots\)
16.12.e.a \(42\) \(12.293\) None \(-2\) \(-2\) \(-2\) \(0\)
16.13.c.a \(2\) \(14.624\) \(\Q(\sqrt{-1155}) \) None \(0\) \(0\) \(-540\) \(0\) \(q-\beta q^{3}-270q^{5}-222\beta q^{7}-133839q^{9}+\cdots\)
16.13.c.b \(4\) \(14.624\) \(\Q(\sqrt{-3}, \sqrt{2521})\) None \(0\) \(0\) \(-14904\) \(0\) \(q+\beta _{1}q^{3}+(-3726-\beta _{3})q^{5}+(-162\beta _{1}+\cdots)q^{7}+\cdots\)
16.13.f.a \(46\) \(14.624\) None \(-2\) \(-2\) \(-2\) \(-4\)
16.14.a.a \(1\) \(17.157\) \(\Q\) None \(0\) \(-1236\) \(-57450\) \(-64232\) \(-\) \(q-1236q^{3}-57450q^{5}-64232q^{7}+\cdots\)
16.14.a.b \(1\) \(17.157\) \(\Q\) None \(0\) \(-468\) \(56214\) \(-333032\) \(-\) \(q-468q^{3}+56214q^{5}-333032q^{7}+\cdots\)
16.14.a.c \(1\) \(17.157\) \(\Q\) None \(0\) \(12\) \(-4330\) \(139992\) \(+\) \(q+12q^{3}-4330q^{5}+139992q^{7}+\cdots\)
16.14.a.d \(1\) \(17.157\) \(\Q\) None \(0\) \(1836\) \(3990\) \(433432\) \(-\) \(q+1836q^{3}+3990q^{5}+433432q^{7}+\cdots\)
16.14.a.e \(2\) \(17.157\) \(\Q(\sqrt{781}) \) None \(0\) \(-872\) \(18476\) \(-110928\) \(+\) \(q+(-436-\beta )q^{3}+(9238+12\beta )q^{5}+\cdots\)
16.14.e.a \(50\) \(17.157\) None \(-2\) \(-2\) \(-2\) \(0\)
16.15.c.a \(1\) \(19.893\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-152886\) \(0\) \(q-152886q^{5}+3^{14}q^{9}-46322630q^{13}+\cdots\)
16.15.c.b \(2\) \(19.893\) \(\Q(\sqrt{-3395}) \) None \(0\) \(0\) \(215700\) \(0\) \(q-\beta q^{3}+107850q^{5}+522\beta q^{7}-3039111q^{9}+\cdots\)
16.15.c.c \(4\) \(19.893\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(0\) \(-87000\) \(0\) \(q+\beta _{1}q^{3}+(-21750+\beta _{3})q^{5}+(245\beta _{1}+\cdots)q^{7}+\cdots\)
16.15.f.a \(54\) \(19.893\) None \(-2\) \(-2\) \(-2\) \(-4\)
16.16.a.a \(1\) \(22.831\) \(\Q\) None \(0\) \(-6252\) \(90510\) \(-56\) \(-\) \(q-6252q^{3}+90510q^{5}-56q^{7}+24738597q^{9}+\cdots\)
16.16.a.b \(1\) \(22.831\) \(\Q\) None \(0\) \(-2700\) \(-251890\) \(-1374072\) \(+\) \(q-2700q^{3}-251890q^{5}-1374072q^{7}+\cdots\)
16.16.a.c \(1\) \(22.831\) \(\Q\) None \(0\) \(276\) \(-132210\) \(3585736\) \(-\) \(q+276q^{3}-132210q^{5}+3585736q^{7}+\cdots\)
16.16.a.d \(1\) \(22.831\) \(\Q\) None \(0\) \(3348\) \(52110\) \(-2822456\) \(-\) \(q+3348q^{3}+52110q^{5}-2822456q^{7}+\cdots\)
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