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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
714.2.a.a \(1\) \(5.701\) \(\Q\) None \(-1\) \(-1\) \(-2\) \(1\) \(+\) \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
714.2.a.b \(1\) \(5.701\) \(\Q\) None \(-1\) \(-1\) \(1\) \(-1\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
714.2.a.c \(1\) \(5.701\) \(\Q\) None \(-1\) \(-1\) \(1\) \(1\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
714.2.a.d \(1\) \(5.701\) \(\Q\) None \(-1\) \(-1\) \(2\) \(-1\) \(+\) \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots\)
714.2.a.e \(1\) \(5.701\) \(\Q\) None \(1\) \(-1\) \(-2\) \(-1\) \(+\) \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
714.2.a.f \(1\) \(5.701\) \(\Q\) None \(1\) \(-1\) \(-2\) \(1\) \(-\) \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{7}+\cdots\)
714.2.a.g \(1\) \(5.701\) \(\Q\) None \(1\) \(-1\) \(3\) \(-1\) \(-\) \(q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}-q^{7}+\cdots\)
714.2.a.h \(1\) \(5.701\) \(\Q\) None \(1\) \(-1\) \(3\) \(1\) \(-\) \(q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}+q^{7}+\cdots\)
714.2.a.i \(1\) \(5.701\) \(\Q\) None \(1\) \(1\) \(-3\) \(1\) \(-\) \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{7}+\cdots\)
714.2.a.j \(2\) \(5.701\) \(\Q(\sqrt{33}) \) None \(-2\) \(2\) \(-3\) \(2\) \(-\) \(q-q^{2}+q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
714.2.a.k \(2\) \(5.701\) \(\Q(\sqrt{41}) \) None \(-2\) \(2\) \(1\) \(-2\) \(-\) \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}-q^{7}+\cdots\)
714.2.a.l \(2\) \(5.701\) \(\Q(\sqrt{17}) \) None \(2\) \(2\) \(3\) \(-2\) \(-\) \(q+q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
714.2.a.m \(2\) \(5.701\) \(\Q(\sqrt{6}) \) None \(2\) \(2\) \(4\) \(2\) \(-\) \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots\)
714.2.b.a \(2\) \(5.701\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+iq^{3}+q^{4}+3iq^{5}+iq^{6}+\cdots\)
714.2.b.b \(2\) \(5.701\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+iq^{3}+q^{4}+3iq^{5}+iq^{6}+\cdots\)
714.2.b.c \(2\) \(5.701\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+iq^{3}+q^{4}-2iq^{5}+iq^{6}+\cdots\)
714.2.b.d \(2\) \(5.701\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+iq^{3}+q^{4}-2iq^{5}+iq^{6}+\cdots\)
714.2.b.e \(4\) \(5.701\) \(\Q(i, \sqrt{17})\) None \(-4\) \(0\) \(0\) \(0\) \(q-q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{1}q^{5}+\beta _{2}q^{6}+\cdots\)
714.2.b.f \(8\) \(5.701\) 8.0.\(\cdots\).23 None \(-8\) \(0\) \(0\) \(0\) \(q-q^{2}-\beta _{3}q^{3}+q^{4}+\beta _{6}q^{5}+\beta _{3}q^{6}+\cdots\)
714.2.e.a \(48\) \(5.701\) None \(0\) \(0\) \(0\) \(0\)
714.2.f.a \(20\) \(5.701\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(4\) \(q+\beta _{1}q^{2}+\beta _{9}q^{3}-q^{4}+\beta _{14}q^{5}+\beta _{6}q^{6}+\cdots\)
714.2.f.b \(20\) \(5.701\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(4\) \(q-\beta _{1}q^{2}-\beta _{4}q^{3}-q^{4}-\beta _{14}q^{5}+\beta _{10}q^{6}+\cdots\)
714.2.i.a \(2\) \(5.701\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(1\) \(-4\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.b \(2\) \(5.701\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(1\) \(5\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.c \(2\) \(5.701\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-3\) \(4\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.d \(2\) \(5.701\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-1\) \(-4\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.e \(2\) \(5.701\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-1\) \(1\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.f \(2\) \(5.701\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(3\) \(5\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.g \(2\) \(5.701\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-3\) \(-4\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.h \(2\) \(5.701\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(3\) \(-4\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.i \(2\) \(5.701\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(-1\) \(-4\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.j \(2\) \(5.701\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(-1\) \(1\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.k \(2\) \(5.701\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(-1\) \(5\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
714.2.i.l \(4\) \(5.701\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(-2\) \(-2\) \(-2\) \(-3\) \(q-\beta _{2}q^{2}+(-1+\beta _{2})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
714.2.i.m \(4\) \(5.701\) \(\Q(\sqrt{-3}, \sqrt{17})\) None \(-2\) \(-2\) \(0\) \(2\) \(q-\beta _{2}q^{2}+(-1+\beta _{2})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
714.2.i.n \(4\) \(5.701\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(-2\) \(2\) \(2\) \(q+(1+\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
714.2.i.o \(6\) \(5.701\) 6.0.11337408.1 None \(3\) \(3\) \(3\) \(-6\) \(q+\beta _{2}q^{2}+(1-\beta _{2})q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
714.2.k.a \(8\) \(5.701\) 8.0.40960000.1 None \(-8\) \(0\) \(0\) \(-8\) \(q-q^{2}+(-\beta _{1}+\beta _{6}+\beta _{7})q^{3}+q^{4}+\cdots\)
714.2.k.b \(8\) \(5.701\) 8.0.40960000.1 None \(8\) \(0\) \(0\) \(-8\) \(q+q^{2}+(-\beta _{4}+\beta _{7})q^{3}+q^{4}+2\beta _{1}q^{5}+\cdots\)
714.2.k.c \(40\) \(5.701\) None \(-40\) \(0\) \(0\) \(8\)
714.2.k.d \(40\) \(5.701\) None \(40\) \(0\) \(0\) \(8\)
714.2.m.a \(4\) \(5.701\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-8\) \(0\) \(q+\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}+(-2+\zeta_{8}+\cdots)q^{5}+\cdots\)
714.2.m.b \(4\) \(5.701\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}-\zeta_{8}q^{5}-\zeta_{8}^{3}q^{6}+\cdots\)
714.2.m.c \(8\) \(5.701\) 8.0.836829184.2 None \(0\) \(0\) \(4\) \(0\) \(q+\beta _{5}q^{2}-\beta _{1}q^{3}-q^{4}+(1+\beta _{1}+\beta _{4}+\cdots)q^{5}+\cdots\)
714.2.m.d \(12\) \(5.701\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{7}q^{2}+\beta _{2}q^{3}-q^{4}+\beta _{6}q^{5}-\beta _{3}q^{6}+\cdots\)
714.2.m.e \(12\) \(5.701\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{9}q^{2}+\beta _{5}q^{3}-q^{4}+(-\beta _{5}-\beta _{7}+\cdots)q^{5}+\cdots\)
714.2.p.a \(44\) \(5.701\) None \(0\) \(0\) \(0\) \(10\)
714.2.p.b \(44\) \(5.701\) None \(0\) \(0\) \(0\) \(10\)
714.2.q.a \(96\) \(5.701\) None \(0\) \(0\) \(0\) \(0\)
714.2.t.a \(4\) \(5.701\) \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{2}+\zeta_{12}q^{3}+(-1+\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
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