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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
570.2.a.a \(1\) \(4.551\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(-2\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots\)
570.2.a.b \(1\) \(4.551\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(2\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
570.2.a.c \(1\) \(4.551\) \(\Q\) None \(-1\) \(-1\) \(1\) \(-2\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
570.2.a.d \(1\) \(4.551\) \(\Q\) None \(-1\) \(1\) \(-1\) \(4\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+4q^{7}+\cdots\)
570.2.a.e \(1\) \(4.551\) \(\Q\) None \(-1\) \(1\) \(1\) \(-4\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-4q^{7}+\cdots\)
570.2.a.f \(1\) \(4.551\) \(\Q\) None \(-1\) \(1\) \(1\) \(2\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots\)
570.2.a.g \(1\) \(4.551\) \(\Q\) None \(1\) \(-1\) \(-1\) \(0\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
570.2.a.h \(1\) \(4.551\) \(\Q\) None \(1\) \(-1\) \(1\) \(-2\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
570.2.a.i \(1\) \(4.551\) \(\Q\) None \(1\) \(-1\) \(1\) \(4\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+4q^{7}+\cdots\)
570.2.a.j \(1\) \(4.551\) \(\Q\) None \(1\) \(1\) \(-1\) \(2\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
570.2.a.k \(1\) \(4.551\) \(\Q\) None \(1\) \(1\) \(-1\) \(2\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
570.2.a.l \(1\) \(4.551\) \(\Q\) None \(1\) \(1\) \(1\) \(-2\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
570.2.a.m \(1\) \(4.551\) \(\Q\) None \(1\) \(1\) \(1\) \(4\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots\)
570.2.c.a \(4\) \(4.551\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots\)
570.2.c.b \(4\) \(4.551\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots\)
570.2.c.c \(8\) \(4.551\) 8.0.1499238400.2 None \(0\) \(-4\) \(0\) \(0\) \(q+\beta _{6}q^{2}+(-1-\beta _{3}+\beta _{4}+\beta _{6}+\beta _{7})q^{3}+\cdots\)
570.2.c.d \(8\) \(4.551\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}q^{2}-\zeta_{24}^{4}q^{3}-q^{4}+(-\zeta_{24}^{2}+\cdots)q^{5}+\cdots\)
570.2.c.e \(8\) \(4.551\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}q^{2}+(-\zeta_{24}-\zeta_{24}^{6})q^{3}-q^{4}+\cdots\)
570.2.c.f \(8\) \(4.551\) 8.0.1499238400.2 None \(0\) \(4\) \(0\) \(0\) \(q+\beta _{6}q^{2}+(-\beta _{3}+\beta _{4}+\beta _{6}+\beta _{7})q^{3}+\cdots\)
570.2.d.a \(2\) \(4.551\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}+(-1-2i)q^{5}+\cdots\)
570.2.d.b \(2\) \(4.551\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}+(2+i)q^{5}-q^{6}+\cdots\)
570.2.d.c \(6\) \(4.551\) 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{3}q^{5}-q^{6}+\cdots\)
570.2.d.d \(6\) \(4.551\) 6.0.350464.1 None \(0\) \(0\) \(2\) \(0\) \(q+\beta _{1}q^{2}-\beta _{1}q^{3}-q^{4}-\beta _{5}q^{5}+q^{6}+\cdots\)
570.2.f.a \(4\) \(4.551\) \(\Q(\zeta_{8})\) None \(-4\) \(-4\) \(0\) \(8\) \(q-q^{2}+(-1-\zeta_{8}^{2})q^{3}+q^{4}+\zeta_{8}q^{5}+\cdots\)
570.2.f.b \(4\) \(4.551\) \(\Q(\zeta_{8})\) None \(4\) \(4\) \(0\) \(8\) \(q+q^{2}+(1+\zeta_{8}^{2})q^{3}+q^{4}+\zeta_{8}q^{5}+\cdots\)
570.2.f.c \(8\) \(4.551\) 8.0.7278137344.1 None \(-8\) \(2\) \(0\) \(4\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)
570.2.f.d \(8\) \(4.551\) 8.0.7278137344.1 None \(8\) \(-2\) \(0\) \(4\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)
570.2.i.a \(2\) \(4.551\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(1\) \(-2\) \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
570.2.i.b \(2\) \(4.551\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(1\) \(-2\) \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
570.2.i.c \(2\) \(4.551\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(1\) \(6\) \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
570.2.i.d \(2\) \(4.551\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(1\) \(-2\) \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
570.2.i.e \(2\) \(4.551\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(-1\) \(-10\) \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
570.2.i.f \(4\) \(4.551\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-2\) \(2\) \(-2\) \(4\) \(q+(-1+\beta _{1})q^{2}+(1-\beta _{1})q^{3}-\beta _{1}q^{4}+\cdots\)
570.2.i.g \(4\) \(4.551\) \(\Q(\sqrt{-3}, \sqrt{73})\) None \(2\) \(-2\) \(-2\) \(-4\) \(q+(1-\beta _{2})q^{2}+(-1+\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots\)
570.2.i.h \(4\) \(4.551\) \(\Q(\sqrt{-3}, \sqrt{19})\) None \(2\) \(-2\) \(2\) \(0\) \(q+(1+\beta _{2})q^{2}+(-1-\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots\)
570.2.i.i \(4\) \(4.551\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(2\) \(2\) \(2\) \(0\) \(q+(1+\beta _{2})q^{2}+(1+\beta _{2})q^{3}+\beta _{2}q^{4}+\cdots\)
570.2.i.j \(6\) \(4.551\) 6.0.29654208.1 None \(-3\) \(-3\) \(-3\) \(2\) \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{1})q^{3}-\beta _{1}q^{4}+\cdots\)
570.2.k.a \(36\) \(4.551\) None \(0\) \(4\) \(0\) \(-12\)
570.2.k.b \(36\) \(4.551\) None \(0\) \(4\) \(0\) \(20\)
570.2.m.a \(20\) \(4.551\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(-4\) \(-4\) \(q+\beta _{2}q^{2}+\beta _{11}q^{3}+\beta _{4}q^{4}+\beta _{6}q^{5}+\cdots\)
570.2.m.b \(20\) \(4.551\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(12\) \(-4\) \(q+\beta _{7}q^{2}-\beta _{10}q^{3}+\beta _{2}q^{4}+(1+\beta _{6}+\cdots)q^{5}+\cdots\)
570.2.n.a \(80\) \(4.551\) None \(0\) \(0\) \(0\) \(0\)
570.2.q.a \(8\) \(4.551\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(4\) \(0\) \(q+(\zeta_{24}-\zeta_{24}^{4})q^{2}+(\zeta_{24}-\zeta_{24}^{4})q^{3}+\cdots\)
570.2.q.b \(12\) \(4.551\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{3}-\beta _{4})q^{2}+(-\beta _{3}-\beta _{4})q^{3}+\cdots\)
570.2.q.c \(20\) \(4.551\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{11}q^{2}+\beta _{11}q^{3}+(1-\beta _{12})q^{4}+\cdots\)
570.2.s.a \(24\) \(4.551\) None \(-12\) \(4\) \(0\) \(-12\)
570.2.s.b \(24\) \(4.551\) None \(12\) \(2\) \(0\) \(-12\)
570.2.u.a \(6\) \(4.551\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(-6\) \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
570.2.u.b \(6\) \(4.551\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(-6\) \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
570.2.u.c \(6\) \(4.551\) \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(-3\) \(q+(-\zeta_{18}+\zeta_{18}^{4})q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+\cdots\)
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