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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
588.1.c.a \(1\) \(0.293\) \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}+q^{9}+q^{13}+q^{19}+q^{25}-q^{27}+\cdots\)
588.1.c.b \(1\) \(0.293\) \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(0\) \(q+q^{3}+q^{9}-q^{13}-q^{19}+q^{25}+q^{27}+\cdots\)
588.1.p.a \(2\) \(0.293\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}+q^{13}-\zeta_{6}q^{19}+\cdots\)
588.1.z.a \(12\) \(0.293\) \(\Q(\zeta_{21})\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(1\) \(q+\zeta_{42}^{10}q^{3}+\zeta_{42}^{8}q^{7}+\zeta_{42}^{20}q^{9}+\cdots\)
588.2.a.a \(1\) \(4.695\) \(\Q\) None None \(0\) \(-1\) \(-2\) \(0\) \(-\) \(q-q^{3}-2q^{5}+q^{9}+2q^{11}-3q^{13}+\cdots\)
588.2.a.b \(1\) \(4.695\) \(\Q\) None None \(0\) \(-1\) \(-2\) \(0\) \(+\) \(q-q^{3}-2q^{5}+q^{9}+2q^{11}+4q^{13}+\cdots\)
588.2.a.c \(1\) \(4.695\) \(\Q\) None None \(0\) \(-1\) \(0\) \(0\) \(+\) \(q-q^{3}+q^{9}-6q^{11}-2q^{13}+4q^{19}+\cdots\)
588.2.a.d \(1\) \(4.695\) \(\Q\) None None \(0\) \(1\) \(-4\) \(0\) \(-\) \(q+q^{3}-4q^{5}+q^{9}+2q^{11}+6q^{13}+\cdots\)
588.2.a.e \(1\) \(4.695\) \(\Q\) None None \(0\) \(1\) \(2\) \(0\) \(-\) \(q+q^{3}+2q^{5}+q^{9}+2q^{11}-4q^{13}+\cdots\)
588.2.a.f \(1\) \(4.695\) \(\Q\) None None \(0\) \(1\) \(2\) \(0\) \(-\) \(q+q^{3}+2q^{5}+q^{9}+2q^{11}+3q^{13}+\cdots\)
588.2.b.a \(8\) \(4.695\) 8.0.562828176.1 None None \(-2\) \(-8\) \(0\) \(0\) \(q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(\beta _{2}-\beta _{5})q^{5}+\cdots\)
588.2.b.b \(8\) \(4.695\) 8.0.562828176.1 None None \(-2\) \(8\) \(0\) \(0\) \(q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots\)
588.2.b.c \(12\) \(4.695\) 12.0.\(\cdots\).1 None None \(4\) \(-12\) \(0\) \(0\) \(q+\beta _{1}q^{2}-q^{3}+(\beta _{5}+\beta _{6})q^{4}+(-1+\cdots)q^{5}+\cdots\)
588.2.b.d \(12\) \(4.695\) 12.0.\(\cdots\).1 None None \(4\) \(12\) \(0\) \(0\) \(q+\beta _{1}q^{2}+q^{3}+(\beta _{5}+\beta _{6})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
588.2.e.a \(4\) \(4.695\) \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-21}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+2q^{4}+\beta _{3}q^{5}+\beta _{3}q^{6}+\cdots\)
588.2.e.b \(8\) \(4.695\) 8.0.3317760000.1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{2}-\beta _{2}q^{3}+(-1-\beta _{3})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
588.2.e.c \(12\) \(4.695\) 12.0.\(\cdots\).2 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+\beta _{10}q^{3}+(-\beta _{3}+\beta _{5})q^{4}+\cdots\)
588.2.e.d \(12\) \(4.695\) 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{8}q^{3}+\beta _{2}q^{4}-\beta _{3}q^{5}+\cdots\)
588.2.e.e \(12\) \(4.695\) 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{8}q^{3}+\beta _{2}q^{4}+\beta _{3}q^{5}+\cdots\)
588.2.e.f \(24\) \(4.695\) None None \(0\) \(0\) \(0\) \(0\)
588.2.f.a \(2\) \(4.695\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(6\) \(0\) \(q+(-1-\zeta_{6})q^{3}+3q^{5}+3\zeta_{6}q^{9}+(-3+\cdots)q^{11}+\cdots\)
588.2.f.b \(2\) \(4.695\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{3}-3q^{9}-3\zeta_{6}q^{13}-5\zeta_{6}q^{19}+\cdots\)
588.2.f.c \(2\) \(4.695\) \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(-6\) \(0\) \(q+(1+\zeta_{6})q^{3}-3q^{5}+3\zeta_{6}q^{9}+(-3+\cdots)q^{11}+\cdots\)
588.2.f.d \(8\) \(4.695\) 8.0.3288334336.2 None None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{6})q^{3}+(-\beta _{1}-\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots\)
588.2.i.a \(2\) \(4.695\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-2\) \(0\) \(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
588.2.i.b \(2\) \(4.695\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-2\) \(0\) \(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
588.2.i.c \(2\) \(4.695\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(0\) \(0\) \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{9}+(6-6\zeta_{6})q^{11}+\cdots\)
588.2.i.d \(2\) \(4.695\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(4\) \(0\) \(q+(-1+\zeta_{6})q^{3}+4\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
588.2.i.e \(2\) \(4.695\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-4\) \(0\) \(q+(1-\zeta_{6})q^{3}-4\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-2+\cdots)q^{11}+\cdots\)
588.2.i.f \(2\) \(4.695\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(0\) \(0\) \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{9}+(6-6\zeta_{6})q^{11}+\cdots\)
588.2.i.g \(2\) \(4.695\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(2\) \(0\) \(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-2+\cdots)q^{11}+\cdots\)
588.2.k.a \(2\) \(4.695\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(0\) \(0\) \(q+(-1-\zeta_{6})q^{3}+3\zeta_{6}q^{9}+(4-8\zeta_{6})q^{13}+\cdots\)
588.2.k.b \(2\) \(4.695\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(0\) \(0\) \(q+(-1-\zeta_{6})q^{3}+3\zeta_{6}q^{9}+(-3+6\zeta_{6})q^{13}+\cdots\)
588.2.k.c \(2\) \(4.695\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(3\) \(0\) \(q+(-1+2\zeta_{6})q^{3}+3\zeta_{6}q^{5}-3q^{9}+\cdots\)
588.2.k.d \(2\) \(4.695\) \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(-3\) \(0\) \(q+(2-\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(3-3\zeta_{6})q^{9}+\cdots\)
588.2.k.e \(2\) \(4.695\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(0\) \(0\) \(q+(1+\zeta_{6})q^{3}+3\zeta_{6}q^{9}+(-4+8\zeta_{6})q^{13}+\cdots\)
588.2.k.f \(16\) \(4.695\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}-\beta _{5}-\beta _{8})q^{3}+(\beta _{1}-2\beta _{7}+\cdots)q^{5}+\cdots\)
588.2.n.a \(4\) \(4.695\) \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-21}) \) None \(0\) \(-6\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-2-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
588.2.n.b \(4\) \(4.695\) \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-21}) \) None \(0\) \(6\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{3}+2\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
588.2.n.c \(16\) \(4.695\) 16.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{9}q^{2}+(-\beta _{1}+\beta _{5}+\beta _{15})q^{3}-\beta _{3}q^{4}+\cdots\)
588.2.n.d \(24\) \(4.695\) None None \(0\) \(0\) \(0\) \(0\)
588.2.n.e \(24\) \(4.695\) None None \(0\) \(0\) \(0\) \(0\)
588.2.n.f \(24\) \(4.695\) None None \(0\) \(0\) \(0\) \(0\)
588.2.n.g \(24\) \(4.695\) None None \(0\) \(0\) \(0\) \(0\)
588.2.n.h \(24\) \(4.695\) None None \(0\) \(0\) \(0\) \(0\)
588.2.o.a \(8\) \(4.695\) 8.0.432972864.2 None None \(1\) \(-4\) \(0\) \(0\) \(q+(-\beta _{1}-\beta _{6})q^{2}+\beta _{2}q^{3}+\beta _{5}q^{4}+\cdots\)
588.2.o.b \(8\) \(4.695\) 8.0.562828176.1 None None \(1\) \(-4\) \(0\) \(0\) \(q+\beta _{6}q^{2}-\beta _{3}q^{3}+(\beta _{1}-\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
588.2.o.c \(8\) \(4.695\) 8.0.432972864.2 None None \(1\) \(4\) \(0\) \(0\) \(q+(-\beta _{1}-\beta _{6})q^{2}-\beta _{2}q^{3}+\beta _{5}q^{4}+\cdots\)
588.2.o.d \(8\) \(4.695\) 8.0.562828176.1 None None \(1\) \(4\) \(0\) \(0\) \(q-\beta _{4}q^{2}+(1-\beta _{3})q^{3}+(\beta _{2}+\beta _{5}-\beta _{7})q^{4}+\cdots\)
588.2.o.e \(24\) \(4.695\) None None \(-4\) \(-12\) \(0\) \(0\)
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