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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
630.2.a.a \(1\) \(5.031\) \(\Q\) None \(-1\) \(0\) \(-1\) \(-1\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
630.2.a.b \(1\) \(5.031\) \(\Q\) None \(-1\) \(0\) \(-1\) \(1\) \(+\) \(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
630.2.a.c \(1\) \(5.031\) \(\Q\) None \(-1\) \(0\) \(-1\) \(1\) \(-\) \(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
630.2.a.d \(1\) \(5.031\) \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) \(+\) \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
630.2.a.e \(1\) \(5.031\) \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
630.2.a.f \(1\) \(5.031\) \(\Q\) None \(-1\) \(0\) \(1\) \(1\) \(-\) \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
630.2.a.g \(1\) \(5.031\) \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) \(-\) \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
630.2.a.h \(1\) \(5.031\) \(\Q\) None \(1\) \(0\) \(-1\) \(1\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
630.2.a.i \(1\) \(5.031\) \(\Q\) None \(1\) \(0\) \(1\) \(-1\) \(-\) \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
630.2.a.j \(1\) \(5.031\) \(\Q\) None \(1\) \(0\) \(1\) \(1\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
630.2.b.a \(8\) \(5.031\) 8.0.7442857984.4 None \(0\) \(0\) \(-8\) \(-4\) \(q+\beta _{3}q^{2}-q^{4}-q^{5}+\beta _{6}q^{7}-\beta _{3}q^{8}+\cdots\)
630.2.b.b \(8\) \(5.031\) 8.0.7442857984.4 None \(0\) \(0\) \(8\) \(-4\) \(q-\beta _{3}q^{2}-q^{4}+q^{5}+\beta _{6}q^{7}+\beta _{3}q^{8}+\cdots\)
630.2.d.a \(4\) \(5.031\) \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(-4\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}+\beta _{3}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)
630.2.d.b \(4\) \(5.031\) \(\Q(\sqrt{-2}, \sqrt{5})\) None \(-4\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}+\beta _{3}q^{5}+(-\beta _{1}-\beta _{3})q^{7}+\cdots\)
630.2.d.c \(4\) \(5.031\) \(\Q(\sqrt{-2}, \sqrt{5})\) None \(4\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}-\beta _{3}q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots\)
630.2.d.d \(4\) \(5.031\) \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(4\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}-\beta _{3}q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots\)
630.2.g.a \(2\) \(5.031\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+iq^{2}-q^{4}+(-2-i)q^{5}+iq^{7}+\cdots\)
630.2.g.b \(2\) \(5.031\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{2}-q^{4}+(-1+2i)q^{5}-iq^{7}+\cdots\)
630.2.g.c \(2\) \(5.031\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{2}-q^{4}+(-1-2i)q^{5}+iq^{7}+\cdots\)
630.2.g.d \(2\) \(5.031\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{2}-q^{4}+(1+2i)q^{5}-iq^{7}-iq^{8}+\cdots\)
630.2.g.e \(2\) \(5.031\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{2}-q^{4}+(1+2i)q^{5}+iq^{7}-iq^{8}+\cdots\)
630.2.g.f \(2\) \(5.031\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+iq^{2}-q^{4}+(2-i)q^{5}-iq^{7}-iq^{8}+\cdots\)
630.2.g.g \(4\) \(5.031\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(-4\) \(0\) \(q-\beta _{2}q^{2}-q^{4}+(-1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
630.2.i.a \(2\) \(5.031\) \(\Q(\sqrt{-3}) \) None \(-2\) \(-3\) \(-1\) \(-1\) \(q-q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
630.2.i.b \(2\) \(5.031\) \(\Q(\sqrt{-3}) \) None \(-2\) \(-3\) \(1\) \(-4\) \(q-q^{2}+(-2+\zeta_{6})q^{3}+q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
630.2.i.c \(2\) \(5.031\) \(\Q(\sqrt{-3}) \) None \(2\) \(3\) \(-1\) \(-5\) \(q+q^{2}+(1+\zeta_{6})q^{3}+q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
630.2.i.d \(2\) \(5.031\) \(\Q(\sqrt{-3}) \) None \(2\) \(3\) \(1\) \(-4\) \(q+q^{2}+(2-\zeta_{6})q^{3}+q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
630.2.i.e \(4\) \(5.031\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(4\) \(-6\) \(2\) \(-2\) \(q+q^{2}+(-2-\beta _{1})q^{3}+q^{4}-\beta _{1}q^{5}+\cdots\)
630.2.i.f \(12\) \(5.031\) 12.0.\(\cdots\).1 None \(-12\) \(2\) \(-6\) \(4\) \(q-q^{2}+(\beta _{4}-\beta _{7})q^{3}+q^{4}+(-1+\beta _{6}+\cdots)q^{5}+\cdots\)
630.2.i.g \(12\) \(5.031\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(0\) \(-6\) \(4\) \(q+q^{2}-\beta _{8}q^{3}+q^{4}+(-1-\beta _{6})q^{5}+\cdots\)
630.2.i.h \(12\) \(5.031\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(2\) \(6\) \(8\) \(q+q^{2}+(-\beta _{2}+\beta _{6})q^{3}+q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
630.2.i.i \(16\) \(5.031\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-16\) \(2\) \(8\) \(4\) \(q-q^{2}+(-\beta _{1}+\beta _{7})q^{3}+q^{4}+(1-\beta _{4}+\cdots)q^{5}+\cdots\)
630.2.j.a \(2\) \(5.031\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(-1\) \(q+(-1+\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
630.2.j.b \(2\) \(5.031\) \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(1\) \(-1\) \(q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
630.2.j.c \(2\) \(5.031\) \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(1\) \(1\) \(q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
630.2.j.d \(2\) \(5.031\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(-1\) \(q+(1-\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
630.2.j.e \(2\) \(5.031\) \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(1\) \(-1\) \(q+(1-\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
630.2.j.f \(4\) \(5.031\) \(\Q(\zeta_{12})\) None \(2\) \(0\) \(-2\) \(2\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{3}+(-1+\zeta_{12}+\cdots)q^{4}+\cdots\)
630.2.j.g \(4\) \(5.031\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(2\) \(1\) \(2\) \(2\) \(q+(1-\beta _{2})q^{2}-\beta _{3}q^{3}-\beta _{2}q^{4}+\beta _{2}q^{5}+\cdots\)
630.2.j.h \(4\) \(5.031\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(2\) \(2\) \(-2\) \(-2\) \(q+\beta _{2}q^{2}+(-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
630.2.j.i \(6\) \(5.031\) 6.0.954288.1 None \(-3\) \(-1\) \(-3\) \(3\) \(q+\beta _{3}q^{2}+(-\beta _{2}+\beta _{5})q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots\)
630.2.j.j \(6\) \(5.031\) 6.0.954288.1 None \(-3\) \(-1\) \(3\) \(-3\) \(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
630.2.j.k \(6\) \(5.031\) 6.0.954288.1 None \(-3\) \(1\) \(-3\) \(-3\) \(q+(-1-\beta _{3})q^{2}+\beta _{1}q^{3}+\beta _{3}q^{4}+\beta _{3}q^{5}+\cdots\)
630.2.j.l \(8\) \(5.031\) 8.0.856615824.2 None \(-4\) \(-3\) \(4\) \(4\) \(q+(-1+\beta _{1})q^{2}+\beta _{6}q^{3}-\beta _{1}q^{4}+\beta _{1}q^{5}+\cdots\)
630.2.k.a \(2\) \(5.031\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(-4\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots\)
630.2.k.b \(2\) \(5.031\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(-1\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
630.2.k.c \(2\) \(5.031\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(4\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
630.2.k.d \(2\) \(5.031\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(-4\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots\)
630.2.k.e \(2\) \(5.031\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(-4\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
630.2.k.f \(2\) \(5.031\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
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