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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
574.2.a.a \(1\) \(4.583\) \(\Q\) None \(-1\) \(-2\) \(4\) \(1\) \(-\) \(q-q^{2}-2q^{3}+q^{4}+4q^{5}+2q^{6}+q^{7}+\cdots\)
574.2.a.b \(1\) \(4.583\) \(\Q\) None \(-1\) \(-1\) \(1\) \(-1\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
574.2.a.c \(1\) \(4.583\) \(\Q\) None \(-1\) \(1\) \(-3\) \(1\) \(+\) \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}+q^{7}+\cdots\)
574.2.a.d \(1\) \(4.583\) \(\Q\) None \(-1\) \(2\) \(-2\) \(-1\) \(+\) \(q-q^{2}+2q^{3}+q^{4}-2q^{5}-2q^{6}-q^{7}+\cdots\)
574.2.a.e \(1\) \(4.583\) \(\Q\) None \(-1\) \(2\) \(2\) \(1\) \(-\) \(q-q^{2}+2q^{3}+q^{4}+2q^{5}-2q^{6}+q^{7}+\cdots\)
574.2.a.f \(1\) \(4.583\) \(\Q\) None \(-1\) \(3\) \(-1\) \(1\) \(-\) \(q-q^{2}+3q^{3}+q^{4}-q^{5}-3q^{6}+q^{7}+\cdots\)
574.2.a.g \(1\) \(4.583\) \(\Q\) None \(1\) \(-3\) \(-1\) \(1\) \(+\) \(q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}+q^{7}+\cdots\)
574.2.a.h \(1\) \(4.583\) \(\Q\) None \(1\) \(-1\) \(-1\) \(-1\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
574.2.a.i \(1\) \(4.583\) \(\Q\) None \(1\) \(-1\) \(1\) \(1\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
574.2.a.j \(1\) \(4.583\) \(\Q\) None \(1\) \(0\) \(-4\) \(1\) \(+\) \(q+q^{2}+q^{4}-4q^{5}+q^{7}+q^{8}-3q^{9}+\cdots\)
574.2.a.k \(2\) \(4.583\) \(\Q(\sqrt{3}) \) None \(2\) \(4\) \(2\) \(2\) \(-\) \(q+q^{2}+2q^{3}+q^{4}+(1+\beta )q^{5}+2q^{6}+\cdots\)
574.2.a.l \(3\) \(4.583\) 3.3.568.1 None \(3\) \(1\) \(1\) \(-3\) \(-\) \(q+q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{1}q^{5}-\beta _{2}q^{6}+\cdots\)
574.2.a.m \(4\) \(4.583\) 4.4.11348.1 None \(-4\) \(-1\) \(3\) \(-4\) \(-\) \(q-q^{2}-\beta _{2}q^{3}+q^{4}+(1-\beta _{2}+\beta _{3})q^{5}+\cdots\)
574.2.c.a \(2\) \(4.583\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(2\) \(0\) \(q+q^{2}+iq^{3}+q^{4}+q^{5}+iq^{6}+iq^{7}+\cdots\)
574.2.c.b \(8\) \(4.583\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(8\) \(0\) \(6\) \(0\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{6})q^{5}+\beta _{1}q^{6}+\cdots\)
574.2.c.c \(10\) \(4.583\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(-10\) \(0\) \(-4\) \(0\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{4}-\beta _{8})q^{5}+\cdots\)
574.2.e.a \(2\) \(4.583\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-2\) \(2\) \(5\) \(q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
574.2.e.b \(2\) \(4.583\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(1\) \(5\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
574.2.e.c \(2\) \(4.583\) \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(1\) \(-1\) \(q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
574.2.e.d \(4\) \(4.583\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(2\) \(-1\) \(1\) \(-10\) \(q+(1-\beta _{1})q^{2}-\beta _{3}q^{3}-\beta _{1}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
574.2.e.e \(6\) \(4.583\) 6.0.309123.1 None \(-3\) \(3\) \(-4\) \(-4\) \(q+(-1+\beta _{4})q^{2}+\beta _{4}q^{3}-\beta _{4}q^{4}+(-1+\cdots)q^{5}+\cdots\)
574.2.e.f \(8\) \(4.583\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(4\) \(-4\) \(-3\) \(5\) \(q+\beta _{2}q^{2}+(-1+\beta _{2})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
574.2.e.g \(12\) \(4.583\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(6\) \(-1\) \(0\) \(-1\) \(q-\beta _{8}q^{2}+\beta _{2}q^{3}+(-1-\beta _{8})q^{4}+\beta _{10}q^{5}+\cdots\)
574.2.e.h \(20\) \(4.583\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-10\) \(1\) \(-2\) \(1\) \(q+\beta _{10}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-1-\beta _{10}+\cdots)q^{4}+\cdots\)
574.2.f.a \(20\) \(4.583\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(-4\) \(0\) \(0\) \(q+\beta _{14}q^{2}+\beta _{13}q^{3}-q^{4}+\beta _{4}q^{5}+\cdots\)
574.2.f.b \(24\) \(4.583\) None \(0\) \(0\) \(0\) \(0\)
574.2.h.a \(4\) \(4.583\) \(\Q(\zeta_{10})\) None \(-1\) \(-2\) \(1\) \(-1\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
574.2.h.b \(4\) \(4.583\) \(\Q(\zeta_{10})\) None \(-1\) \(0\) \(4\) \(-1\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
574.2.h.c \(4\) \(4.583\) \(\Q(\zeta_{10})\) None \(1\) \(-12\) \(-2\) \(-1\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-3q^{3}+\cdots\)
574.2.h.d \(4\) \(4.583\) \(\Q(\zeta_{10})\) None \(1\) \(2\) \(6\) \(-1\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(1+\cdots)q^{3}+\cdots\)
574.2.h.e \(4\) \(4.583\) \(\Q(\zeta_{10})\) None \(1\) \(4\) \(-2\) \(-1\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(2+\cdots)q^{3}+\cdots\)
574.2.h.f \(4\) \(4.583\) \(\Q(\zeta_{10})\) None \(1\) \(6\) \(-1\) \(1\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(2+\cdots)q^{3}+\cdots\)
574.2.h.g \(8\) \(4.583\) 8.0.4709390625.5 None \(-2\) \(-4\) \(3\) \(-2\) \(q-\beta _{4}q^{2}+(-\beta _{3}+\beta _{5})q^{3}+\beta _{5}q^{4}+\cdots\)
574.2.h.h \(8\) \(4.583\) 8.0.123765625.1 None \(-2\) \(-2\) \(1\) \(2\) \(q+\beta _{2}q^{2}+(-1-\beta _{3}+\beta _{4}-\beta _{7})q^{3}+\cdots\)
574.2.h.i \(8\) \(4.583\) 8.0.511890625.1 None \(-2\) \(12\) \(-1\) \(2\) \(q-\beta _{2}q^{2}+(1+\beta _{2}+\beta _{7})q^{3}+\beta _{4}q^{4}+\cdots\)
574.2.h.j \(12\) \(4.583\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(3\) \(6\) \(-4\) \(-3\) \(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+\beta _{6}q^{4}+\cdots\)
574.2.h.k \(20\) \(4.583\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(5\) \(-6\) \(-1\) \(5\) \(q-\beta _{4}q^{2}-\beta _{6}q^{3}+\beta _{3}q^{4}+\beta _{18}q^{5}+\cdots\)
574.2.j.a \(28\) \(4.583\) None \(-14\) \(0\) \(0\) \(0\)
574.2.j.b \(28\) \(4.583\) None \(14\) \(0\) \(4\) \(0\)
574.2.m.a \(56\) \(4.583\) None \(0\) \(0\) \(0\) \(-4\)
574.2.m.b \(56\) \(4.583\) None \(0\) \(0\) \(0\) \(4\)
574.2.n.a \(40\) \(4.583\) None \(-10\) \(0\) \(-8\) \(0\)
574.2.n.b \(40\) \(4.583\) None \(10\) \(0\) \(4\) \(0\)
574.2.r.a \(8\) \(4.583\) \(\Q(\zeta_{24})\) None \(0\) \(-4\) \(0\) \(12\) \(q+(\zeta_{24}^{2}-\zeta_{24}^{6})q^{2}+(-1+\zeta_{24}^{2}+\cdots)q^{3}+\cdots\)
574.2.r.b \(8\) \(4.583\) 8.0.303595776.1 None \(0\) \(-2\) \(0\) \(6\) \(q+\beta _{2}q^{2}+(\beta _{3}+\beta _{4}-\beta _{5})q^{3}-\beta _{4}q^{4}+\cdots\)
574.2.r.c \(40\) \(4.583\) None \(0\) \(4\) \(0\) \(-12\)
574.2.r.d \(56\) \(4.583\) None \(0\) \(2\) \(0\) \(-6\)
574.2.s.a \(112\) \(4.583\) None \(-14\) \(2\) \(0\) \(2\)
574.2.s.b \(112\) \(4.583\) None \(14\) \(-2\) \(4\) \(-2\)
574.2.u.a \(80\) \(4.583\) None \(0\) \(4\) \(0\) \(0\)
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