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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
64.2.a.a \(1\) \(0.511\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(2\) \(0\) \(-\) \(q+2q^{5}-3q^{9}-6q^{13}+2q^{17}-q^{25}+\cdots\)
64.2.b.a \(2\) \(0.511\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-q^{9}-3iq^{11}-6q^{17}+iq^{19}+\cdots\)
64.2.e.a \(2\) \(0.511\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-2\) \(0\) \(q+(1-i)q^{3}+(-1-i)q^{5}+2iq^{7}+\cdots\)
64.2.i.a \(56\) \(0.511\) None \(-8\) \(-8\) \(-8\) \(-8\)
64.3.c.a \(1\) \(1.744\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(6\) \(0\) \(q+6q^{5}+9q^{9}-10q^{13}-30q^{17}+\cdots\)
64.3.c.b \(2\) \(1.744\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+iq^{3}-2q^{5}+2iq^{7}-7q^{9}-iq^{11}+\cdots\)
64.3.d.a \(4\) \(1.744\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}+3q^{9}+\cdots\)
64.3.f.a \(6\) \(1.744\) 6.0.399424.1 None \(0\) \(2\) \(-2\) \(4\) \(q-\beta _{5}q^{3}+(-1-\beta _{1}-\beta _{3}-\beta _{5})q^{5}+\cdots\)
64.3.j.a \(120\) \(1.744\) None \(-8\) \(-8\) \(-8\) \(-8\)
64.4.a.a \(1\) \(3.776\) \(\Q\) None \(0\) \(-8\) \(10\) \(16\) \(+\) \(q-8q^{3}+10q^{5}+2^{4}q^{7}+37q^{9}+40q^{11}+\cdots\)
64.4.a.b \(1\) \(3.776\) \(\Q\) None \(0\) \(-4\) \(2\) \(-24\) \(-\) \(q-4q^{3}+2q^{5}-24q^{7}-11q^{9}-44q^{11}+\cdots\)
64.4.a.c \(1\) \(3.776\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-22\) \(0\) \(-\) \(q-22q^{5}-3^{3}q^{9}+18q^{13}-94q^{17}+\cdots\)
64.4.a.d \(1\) \(3.776\) \(\Q\) None \(0\) \(4\) \(2\) \(24\) \(+\) \(q+4q^{3}+2q^{5}+24q^{7}-11q^{9}+44q^{11}+\cdots\)
64.4.a.e \(1\) \(3.776\) \(\Q\) None \(0\) \(8\) \(10\) \(-16\) \(+\) \(q+8q^{3}+10q^{5}-2^{4}q^{7}+37q^{9}-40q^{11}+\cdots\)
64.4.b.a \(2\) \(3.776\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) \(q+5iq^{3}-73q^{9}+9iq^{11}+90q^{17}+\cdots\)
64.4.b.b \(4\) \(3.776\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{5}+\zeta_{12}^{3}q^{7}+23q^{9}+\cdots\)
64.4.e.a \(10\) \(3.776\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(2\) \(-2\) \(0\) \(q+\beta _{5}q^{3}+\beta _{3}q^{5}+(3\beta _{1}-\beta _{4})q^{7}+(5\beta _{1}+\cdots)q^{9}+\cdots\)
64.4.i.a \(184\) \(3.776\) None \(-8\) \(-8\) \(-8\) \(-8\)
64.5.c.a \(1\) \(6.616\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(14\) \(0\) \(q+14q^{5}+3^{4}q^{9}+238q^{13}+322q^{17}+\cdots\)
64.5.c.b \(2\) \(6.616\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-52\) \(0\) \(q+iq^{3}-26q^{5}-22iq^{7}+65q^{9}+\cdots\)
64.5.c.c \(2\) \(6.616\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-36\) \(0\) \(q-\zeta_{6}q^{3}-18q^{5}-2\zeta_{6}q^{7}-111q^{9}+\cdots\)
64.5.c.d \(2\) \(6.616\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(76\) \(0\) \(q+3iq^{3}+38q^{5}-2iq^{7}-63q^{9}+\cdots\)
64.5.d.a \(4\) \(6.616\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}-3\zeta_{12}^{2}q^{5}+5\zeta_{12}^{3}q^{7}+\cdots\)
64.5.d.b \(4\) \(6.616\) \(\Q(i, \sqrt{51})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}-\beta _{3}q^{5}+7\beta _{2}q^{7}+123q^{9}+\cdots\)
64.5.f.a \(14\) \(6.616\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(2\) \(-2\) \(4\) \(q+\beta _{2}q^{3}+\beta _{3}q^{5}+\beta _{9}q^{7}+(19\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
64.5.j.a \(248\) \(6.616\) None \(-8\) \(-8\) \(-8\) \(-8\)
64.6.a.a \(1\) \(10.265\) \(\Q\) None \(0\) \(-20\) \(74\) \(-24\) \(+\) \(q-20q^{3}+74q^{5}-24q^{7}+157q^{9}+\cdots\)
64.6.a.b \(1\) \(10.265\) \(\Q\) None \(0\) \(-12\) \(-54\) \(88\) \(-\) \(q-12q^{3}-54q^{5}+88q^{7}-99q^{9}+\cdots\)
64.6.a.c \(1\) \(10.265\) \(\Q\) None \(0\) \(-8\) \(-14\) \(208\) \(+\) \(q-8q^{3}-14q^{5}+208q^{7}-179q^{9}+\cdots\)
64.6.a.d \(1\) \(10.265\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(82\) \(0\) \(-\) \(q+82q^{5}-3^{5}q^{9}+1194q^{13}+2242q^{17}+\cdots\)
64.6.a.e \(1\) \(10.265\) \(\Q\) None \(0\) \(8\) \(-14\) \(-208\) \(+\) \(q+8q^{3}-14q^{5}-208q^{7}-179q^{9}+\cdots\)
64.6.a.f \(1\) \(10.265\) \(\Q\) None \(0\) \(12\) \(-54\) \(-88\) \(+\) \(q+12q^{3}-54q^{5}-88q^{7}-99q^{9}+\cdots\)
64.6.a.g \(1\) \(10.265\) \(\Q\) None \(0\) \(20\) \(74\) \(24\) \(-\) \(q+20q^{3}+74q^{5}+24q^{7}+157q^{9}+\cdots\)
64.6.a.h \(2\) \(10.265\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-92\) \(0\) \(-\) \(q+\beta q^{3}-46q^{5}+6\beta q^{7}+525q^{9}+\cdots\)
64.6.b.a \(2\) \(10.265\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+239q^{9}+237iq^{11}+1914q^{17}+\cdots\)
64.6.b.b \(8\) \(10.265\) 8.0.\(\cdots\).15 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}+\beta _{1}q^{5}-\beta _{6}q^{7}+(-161+\cdots)q^{9}+\cdots\)
64.6.e.a \(18\) \(10.265\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(2\) \(-2\) \(0\) \(q+\beta _{6}q^{3}-\beta _{5}q^{5}+(-11\beta _{1}+\beta _{4})q^{7}+\cdots\)
64.6.i.a \(312\) \(10.265\) None \(-8\) \(-8\) \(-8\) \(-8\)
64.7.c.a \(1\) \(14.723\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-234\) \(0\) \(q-234q^{5}+3^{6}q^{9}+4070q^{13}-990q^{17}+\cdots\)
64.7.c.b \(2\) \(14.723\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-100\) \(0\) \(q+iq^{3}-50q^{5}-46iq^{7}+713q^{9}+\cdots\)
64.7.c.c \(2\) \(14.723\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(-20\) \(0\) \(q-\beta q^{3}-10q^{5}-10\beta q^{7}-231q^{9}+\cdots\)
64.7.c.d \(2\) \(14.723\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(300\) \(0\) \(q-\zeta_{6}q^{3}+150q^{5}+22\zeta_{6}q^{7}-39q^{9}+\cdots\)
64.7.c.e \(4\) \(14.723\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(56\) \(0\) \(q-\beta _{1}q^{3}+(14+\beta _{3})q^{5}+(-2\beta _{1}+5\beta _{2}+\cdots)q^{7}+\cdots\)
64.7.d.a \(4\) \(14.723\) \(\Q(i, \sqrt{11})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}-5\beta _{3}q^{5}-11\beta _{2}q^{7}-333q^{9}+\cdots\)
64.7.d.b \(8\) \(14.723\) 8.0.\(\cdots\).9 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{3}-\beta _{3}q^{5}+(-\beta _{6}+\beta _{7})q^{7}+\cdots\)
64.7.f.a \(22\) \(14.723\) None \(0\) \(2\) \(-2\) \(4\)
64.7.j.a \(376\) \(14.723\) None \(-8\) \(-8\) \(-8\) \(-8\)
64.8.a.a \(1\) \(19.993\) \(\Q\) None \(0\) \(-84\) \(82\) \(456\) \(-\) \(q-84q^{3}+82q^{5}+456q^{7}+4869q^{9}+\cdots\)
64.8.a.b \(1\) \(19.993\) \(\Q\) None \(0\) \(-44\) \(-430\) \(-1224\) \(+\) \(q-44q^{3}-430q^{5}-1224q^{7}-251q^{9}+\cdots\)
64.8.a.c \(1\) \(19.993\) \(\Q\) None \(0\) \(-12\) \(210\) \(1016\) \(+\) \(q-12q^{3}+210q^{5}+1016q^{7}-2043q^{9}+\cdots\)
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