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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
663.1.g.a \(1\) \(0.331\) \(\Q\) \(\Q(\sqrt{-51}) \), \(\Q(\sqrt{-663}) \) \(\Q(\sqrt{13}) \) \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}-q^{4}+q^{9}+q^{12}+q^{13}+q^{16}+\cdots\)
663.1.g.b \(1\) \(0.331\) \(\Q\) \(\Q(\sqrt{-51}) \), \(\Q(\sqrt{-663}) \) \(\Q(\sqrt{13}) \) \(0\) \(1\) \(0\) \(0\) \(q+q^{3}-q^{4}+q^{9}-q^{12}+q^{13}+q^{16}+\cdots\)
663.1.g.c \(2\) \(0.331\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-663}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-\beta q^{2}-q^{3}+q^{4}+\beta q^{6}-\beta q^{7}+q^{9}+\cdots\)
663.1.g.d \(2\) \(0.331\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-663}) \) None \(0\) \(2\) \(0\) \(0\) \(q-\beta q^{2}+q^{3}+q^{4}-\beta q^{6}+\beta q^{7}+q^{9}+\cdots\)
663.1.v.a \(2\) \(0.331\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-51}) \) None \(0\) \(-1\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{4}+(-\zeta_{6}-\zeta_{6}^{2})q^{5}+\cdots\)
663.1.v.b \(2\) \(0.331\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-51}) \) None \(0\) \(1\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{3}+\zeta_{6}q^{4}+(\zeta_{6}+\zeta_{6}^{2})q^{5}+\cdots\)
663.1.bb.a \(2\) \(0.331\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-51}) \) None \(0\) \(-1\) \(-2\) \(0\) \(q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-q^{5}+\zeta_{6}^{2}q^{9}+\cdots\)
663.1.bb.b \(2\) \(0.331\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-51}) \) None \(0\) \(1\) \(2\) \(0\) \(q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+\zeta_{6}^{2}q^{9}+\cdots\)
663.2.a.a \(1\) \(5.294\) \(\Q\) None None \(-1\) \(-1\) \(-2\) \(0\) \(+\) \(q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+3q^{8}+\cdots\)
663.2.a.b \(1\) \(5.294\) \(\Q\) None None \(-1\) \(1\) \(0\) \(-2\) \(+\) \(q-q^{2}+q^{3}-q^{4}-q^{6}-2q^{7}+3q^{8}+\cdots\)
663.2.a.c \(1\) \(5.294\) \(\Q\) None None \(1\) \(-1\) \(-4\) \(2\) \(-\) \(q+q^{2}-q^{3}-q^{4}-4q^{5}-q^{6}+2q^{7}+\cdots\)
663.2.a.d \(3\) \(5.294\) 3.3.148.1 None None \(-3\) \(3\) \(-6\) \(-2\) \(+\) \(q+(-1-\beta _{2})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
663.2.a.e \(3\) \(5.294\) 3.3.148.1 None None \(-1\) \(-3\) \(0\) \(-4\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
663.2.a.f \(5\) \(5.294\) 5.5.1004368.1 None None \(1\) \(-5\) \(2\) \(8\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)
663.2.a.g \(5\) \(5.294\) 5.5.153424.1 None None \(3\) \(5\) \(0\) \(2\) \(-\) \(q+(1+\beta _{3})q^{2}+q^{3}+(2+\beta _{3}-\beta _{4})q^{4}+\cdots\)
663.2.a.h \(6\) \(5.294\) 6.6.83831632.1 None None \(2\) \(-6\) \(0\) \(2\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
663.2.a.i \(6\) \(5.294\) 6.6.15187408.1 None None \(4\) \(6\) \(4\) \(2\) \(-\) \(q+(1-\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
663.2.b.a \(2\) \(5.294\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}+2q^{4}+(1-2\zeta_{6})q^{5}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
663.2.b.b \(2\) \(5.294\) \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(0\) \(0\) \(q+iq^{2}+q^{3}+q^{4}+iq^{6}-4iq^{7}+\cdots\)
663.2.b.c \(6\) \(5.294\) 6.0.31337472.1 None None \(0\) \(-6\) \(0\) \(0\) \(q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(\beta _{1}-\beta _{5})q^{5}+\cdots\)
663.2.b.d \(8\) \(5.294\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(-8\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{7})q^{2}-q^{3}+(-2+\beta _{5}+\cdots)q^{4}+\cdots\)
663.2.b.e \(8\) \(5.294\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(8\) \(0\) \(0\) \(q+\beta _{1}q^{2}+q^{3}+(-1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
663.2.b.f \(10\) \(5.294\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(10\) \(0\) \(0\) \(q+\beta _{1}q^{2}+q^{3}+(-2+\beta _{2})q^{4}-\beta _{8}q^{5}+\cdots\)
663.2.e.a \(40\) \(5.294\) None None \(0\) \(0\) \(0\) \(0\)
663.2.f.a \(2\) \(5.294\) \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+iq^{3}-q^{4}+4iq^{5}+iq^{6}+\cdots\)
663.2.f.b \(16\) \(5.294\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}+\beta _{9}q^{3}+(1-\beta _{5})q^{4}+(\beta _{8}+\cdots)q^{5}+\cdots\)
663.2.f.c \(18\) \(5.294\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(-2\) \(0\) \(0\) \(0\) \(q-\beta _{11}q^{2}-\beta _{7}q^{3}+(2-\beta _{1}+\beta _{10}+\cdots)q^{4}+\cdots\)
663.2.i.a \(2\) \(5.294\) \(\Q(\sqrt{-3}) \) None None \(-2\) \(-1\) \(-6\) \(2\) \(q+(-2+2\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots\)
663.2.i.b \(2\) \(5.294\) \(\Q(\sqrt{-3}) \) None None \(-2\) \(1\) \(8\) \(3\) \(q+(-2+2\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots\)
663.2.i.c \(2\) \(5.294\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(1\) \(-2\) \(-2\) \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
663.2.i.d \(2\) \(5.294\) \(\Q(\sqrt{-3}) \) None None \(2\) \(1\) \(4\) \(4\) \(q+(2-2\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots\)
663.2.i.e \(12\) \(5.294\) 12.0.\(\cdots\).1 None None \(2\) \(-6\) \(8\) \(-5\) \(q+\beta _{1}q^{2}+(-1-\beta _{9})q^{3}+(-\beta _{3}-\beta _{8}+\cdots)q^{4}+\cdots\)
663.2.i.f \(16\) \(5.294\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(8\) \(-2\) \(2\) \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-1+\beta _{4}+\beta _{7}+\cdots)q^{4}+\cdots\)
663.2.i.g \(18\) \(5.294\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(1\) \(9\) \(-10\) \(-3\) \(q+\beta _{1}q^{2}+\beta _{12}q^{3}+(-2+\beta _{3}-\beta _{8}+\cdots)q^{4}+\cdots\)
663.2.i.h \(22\) \(5.294\) None None \(0\) \(-11\) \(0\) \(-3\)
663.2.j.a \(32\) \(5.294\) None None \(0\) \(0\) \(-4\) \(0\)
663.2.j.b \(40\) \(5.294\) None None \(0\) \(0\) \(-4\) \(8\)
663.2.m.a \(160\) \(5.294\) None None \(0\) \(-4\) \(0\) \(-8\)
663.2.n.a \(76\) \(5.294\) None None \(0\) \(0\) \(-2\) \(-8\)
663.2.n.b \(76\) \(5.294\) None None \(0\) \(0\) \(2\) \(-8\)
663.2.q.a \(8\) \(5.294\) 8.0.\(\cdots\).9 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{6}q^{3}+5\beta _{3}q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots\)
663.2.q.b \(8\) \(5.294\) 8.0.1731891456.1 \(\Q(\sqrt{-51}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+2\beta _{5}q^{4}+(-\beta _{1}-\beta _{4}-\beta _{6}+\cdots)q^{5}+\cdots\)
663.2.q.c \(144\) \(5.294\) None None \(0\) \(0\) \(0\) \(0\)
663.2.r.a \(160\) \(5.294\) None None \(0\) \(-4\) \(0\) \(0\)
663.2.u.a \(80\) \(5.294\) None None \(0\) \(0\) \(0\) \(0\)
663.2.w.a \(4\) \(5.294\) \(\Q(\zeta_{12})\) None None \(4\) \(0\) \(0\) \(0\) \(q+2\zeta_{12}^{2}q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+(-2+\cdots)q^{4}+\cdots\)
663.2.w.b \(8\) \(5.294\) \(\Q(\zeta_{24})\) None None \(-4\) \(0\) \(0\) \(0\) \(q+(-1+\zeta_{24}^{2}+\zeta_{24}^{4}-\zeta_{24}^{7})q^{2}+\cdots\)
663.2.w.c \(76\) \(5.294\) None None \(4\) \(0\) \(0\) \(0\)
663.2.z.a \(2\) \(5.294\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(0\) \(6\) \(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{4}+(1-2\zeta_{6})q^{5}+\cdots\)
663.2.z.b \(4\) \(5.294\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(-2\) \(0\) \(-12\) \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+(-1+2\beta _{2}+\cdots)q^{5}+\cdots\)
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