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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
510.2.a.a \(1\) \(4.072\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(2\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
510.2.a.b \(1\) \(4.072\) \(\Q\) None \(-1\) \(1\) \(1\) \(-2\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
510.2.a.c \(1\) \(4.072\) \(\Q\) None \(1\) \(-1\) \(-1\) \(-4\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-4q^{7}+\cdots\)
510.2.a.d \(1\) \(4.072\) \(\Q\) None \(1\) \(-1\) \(-1\) \(2\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots\)
510.2.a.e \(1\) \(4.072\) \(\Q\) None \(1\) \(-1\) \(1\) \(0\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
510.2.a.f \(1\) \(4.072\) \(\Q\) None \(1\) \(1\) \(-1\) \(0\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
510.2.a.g \(1\) \(4.072\) \(\Q\) None \(1\) \(1\) \(1\) \(2\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+2q^{7}+\cdots\)
510.2.a.h \(2\) \(4.072\) \(\Q(\sqrt{6}) \) None \(-2\) \(-2\) \(2\) \(0\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+\beta q^{7}+\cdots\)
510.2.c.a \(2\) \(4.072\) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+iq^{3}+q^{4}-iq^{5}-iq^{6}-q^{8}+\cdots\)
510.2.c.b \(2\) \(4.072\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+iq^{3}+q^{4}+iq^{5}+iq^{6}+2iq^{7}+\cdots\)
510.2.c.c \(4\) \(4.072\) \(\Q(i, \sqrt{13})\) None \(-4\) \(0\) \(0\) \(0\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{5}+\beta _{1}q^{6}+\cdots\)
510.2.c.d \(4\) \(4.072\) \(\Q(\zeta_{8})\) None \(4\) \(0\) \(0\) \(0\) \(q+q^{2}+\zeta_{8}q^{3}+q^{4}-\zeta_{8}q^{5}+\zeta_{8}q^{6}+\cdots\)
510.2.d.a \(2\) \(4.072\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}+(-2+i)q^{5}+\cdots\)
510.2.d.b \(4\) \(4.072\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}-\beta _{2}q^{5}-q^{6}+\cdots\)
510.2.d.c \(4\) \(4.072\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(4\) \(0\) \(q+\beta _{2}q^{2}+\beta _{2}q^{3}-q^{4}+(1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
510.2.d.d \(6\) \(4.072\) 6.0.5161984.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}+\beta _{3}q^{3}-q^{4}+\beta _{5}q^{5}+q^{6}+\cdots\)
510.2.f.a \(4\) \(4.072\) \(\Q(i, \sqrt{6})\) None \(0\) \(-4\) \(4\) \(-8\) \(q+\beta _{2}q^{2}-q^{3}-q^{4}+(1+\beta _{2}-\beta _{3})q^{5}+\cdots\)
510.2.f.b \(4\) \(4.072\) \(\Q(i, \sqrt{6})\) None \(0\) \(4\) \(-4\) \(8\) \(q+\beta _{2}q^{2}+q^{3}-q^{4}+(-1-\beta _{2}-\beta _{3})q^{5}+\cdots\)
510.2.f.c \(6\) \(4.072\) 6.0.350464.1 None \(0\) \(-6\) \(-2\) \(4\) \(q+\beta _{4}q^{2}-q^{3}-q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
510.2.f.d \(6\) \(4.072\) 6.0.350464.1 None \(0\) \(6\) \(2\) \(-4\) \(q-\beta _{4}q^{2}+q^{3}-q^{4}+(-\beta _{1}-\beta _{5})q^{5}+\cdots\)
510.2.i.a \(72\) \(4.072\) None \(0\) \(0\) \(0\) \(0\)
510.2.l.a \(4\) \(4.072\) \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(-12\) \(q+\zeta_{8}q^{2}+(1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)
510.2.l.b \(4\) \(4.072\) \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(8\) \(q+\zeta_{8}q^{2}+(1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)
510.2.l.c \(4\) \(4.072\) \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(0\) \(q+\zeta_{8}q^{2}+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)
510.2.l.d \(8\) \(4.072\) 8.0.4030726144.1 None \(0\) \(-8\) \(4\) \(8\) \(q-\beta _{6}q^{2}+(-1-\beta _{4}+\beta _{6})q^{3}-\beta _{2}q^{4}+\cdots\)
510.2.l.e \(8\) \(4.072\) 8.0.4030726144.1 None \(0\) \(0\) \(-4\) \(8\) \(q+\beta _{4}q^{2}+(-\beta _{2}+\beta _{4}+\beta _{6})q^{3}+\beta _{2}q^{4}+\cdots\)
510.2.l.f \(8\) \(4.072\) \(\Q(\zeta_{24})\) None \(0\) \(4\) \(0\) \(-8\) \(q+(\zeta_{24}-\zeta_{24}^{5})q^{2}+(1-\zeta_{24}^{2}-\zeta_{24}^{3}+\cdots)q^{3}+\cdots\)
510.2.l.g \(28\) \(4.072\) None \(0\) \(0\) \(0\) \(4\)
510.2.m.a \(8\) \(4.072\) 8.0.110166016.2 None \(-8\) \(0\) \(-8\) \(-4\) \(q-q^{2}+\beta _{2}q^{3}+q^{4}+(-1+\beta _{3}-\beta _{7})q^{5}+\cdots\)
510.2.m.b \(8\) \(4.072\) 8.0.110166016.2 None \(8\) \(0\) \(0\) \(4\) \(q+q^{2}-\beta _{3}q^{3}+q^{4}+(\beta _{1}-\beta _{3}-\beta _{5}+\cdots)q^{5}+\cdots\)
510.2.m.c \(12\) \(4.072\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-12\) \(0\) \(4\) \(4\) \(q-q^{2}-\beta _{7}q^{3}+q^{4}-\beta _{2}q^{5}+\beta _{7}q^{6}+\cdots\)
510.2.m.d \(12\) \(4.072\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(12\) \(0\) \(-4\) \(-4\) \(q+q^{2}+\beta _{7}q^{3}+q^{4}+\beta _{5}q^{5}+\beta _{7}q^{6}+\cdots\)
510.2.p.a \(4\) \(4.072\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-8\) \(q-\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}+\zeta_{8}q^{5}-\zeta_{8}^{3}q^{6}+\cdots\)
510.2.p.b \(4\) \(4.072\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(8\) \(q+\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}-\zeta_{8}q^{5}+\zeta_{8}^{3}q^{6}+\cdots\)
510.2.p.c \(8\) \(4.072\) 8.0.18939904.2 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}+\beta _{2}q^{3}-q^{4}-\beta _{2}q^{5}-\beta _{3}q^{6}+\cdots\)
510.2.p.d \(8\) \(4.072\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{2}q^{2}+\zeta_{16}^{4}q^{3}-q^{4}+\zeta_{16}^{4}q^{5}+\cdots\)
510.2.q.a \(72\) \(4.072\) None \(0\) \(0\) \(0\) \(0\)
510.2.t.a \(72\) \(4.072\) None \(0\) \(0\) \(0\) \(0\)
510.2.u.a \(8\) \(4.072\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(-8\) \(q-\zeta_{16}^{2}q^{2}+\zeta_{16}^{3}q^{3}+\zeta_{16}^{4}q^{4}+\cdots\)
510.2.u.b \(8\) \(4.072\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(8\) \(q+\zeta_{16}^{6}q^{2}+\zeta_{16}q^{3}-\zeta_{16}^{4}q^{4}-\zeta_{16}^{5}q^{5}+\cdots\)
510.2.u.c \(16\) \(4.072\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(-8\) \(q-\beta _{5}q^{2}-\beta _{7}q^{3}+\beta _{1}q^{4}+\beta _{6}q^{5}+\cdots\)
510.2.u.d \(16\) \(4.072\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(8\) \(q+\beta _{3}q^{2}-\beta _{9}q^{3}+\beta _{5}q^{4}-\beta _{1}q^{5}+\cdots\)
510.2.w.a \(4\) \(4.072\) \(\Q(\zeta_{8})\) None \(-4\) \(0\) \(8\) \(-8\) \(q-q^{2}+(\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+q^{4}+\cdots\)
510.2.w.b \(4\) \(4.072\) \(\Q(\zeta_{8})\) None \(4\) \(-4\) \(-8\) \(-8\) \(q+q^{2}+(-1+\zeta_{8}+\zeta_{8}^{2})q^{3}+q^{4}+\cdots\)
510.2.w.c \(68\) \(4.072\) None \(-68\) \(0\) \(-8\) \(8\)
510.2.w.d \(68\) \(4.072\) None \(68\) \(4\) \(8\) \(8\)
510.2.z.a \(4\) \(4.072\) \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(4\) \(q+\zeta_{8}^{2}q^{2}+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots\)
510.2.z.b \(4\) \(4.072\) \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(4\) \(q-\zeta_{8}^{2}q^{2}+(1-\zeta_{8}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots\)
510.2.z.c \(68\) \(4.072\) None \(0\) \(-4\) \(-8\) \(-4\)
510.2.z.d \(68\) \(4.072\) None \(0\) \(-4\) \(8\) \(-4\)
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