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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1650.2.a.a \(1\) \(13.175\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-3\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-3q^{7}-q^{8}+\cdots\)
1650.2.a.b \(1\) \(13.175\) \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
1650.2.a.c \(1\) \(13.175\) \(\Q\) None \(-1\) \(-1\) \(0\) \(2\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots\)
1650.2.a.d \(1\) \(13.175\) \(\Q\) None \(-1\) \(-1\) \(0\) \(2\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots\)
1650.2.a.e \(1\) \(13.175\) \(\Q\) None \(-1\) \(1\) \(0\) \(-4\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-4q^{7}-q^{8}+\cdots\)
1650.2.a.f \(1\) \(13.175\) \(\Q\) None \(-1\) \(1\) \(0\) \(-3\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-3q^{7}-q^{8}+\cdots\)
1650.2.a.g \(1\) \(13.175\) \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
1650.2.a.h \(1\) \(13.175\) \(\Q\) None \(-1\) \(1\) \(0\) \(0\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
1650.2.a.i \(1\) \(13.175\) \(\Q\) None \(-1\) \(1\) \(0\) \(2\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
1650.2.a.j \(1\) \(13.175\) \(\Q\) None \(-1\) \(1\) \(0\) \(2\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
1650.2.a.k \(1\) \(13.175\) \(\Q\) None \(-1\) \(1\) \(0\) \(4\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+4q^{7}-q^{8}+\cdots\)
1650.2.a.l \(1\) \(13.175\) \(\Q\) None \(1\) \(-1\) \(0\) \(-2\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\)
1650.2.a.m \(1\) \(13.175\) \(\Q\) None \(1\) \(-1\) \(0\) \(-2\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\)
1650.2.a.n \(1\) \(13.175\) \(\Q\) None \(1\) \(-1\) \(0\) \(-2\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\)
1650.2.a.o \(1\) \(13.175\) \(\Q\) None \(1\) \(-1\) \(0\) \(1\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
1650.2.a.p \(1\) \(13.175\) \(\Q\) None \(1\) \(-1\) \(0\) \(3\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+3q^{7}+q^{8}+\cdots\)
1650.2.a.q \(1\) \(13.175\) \(\Q\) None \(1\) \(1\) \(0\) \(-2\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\)
1650.2.a.r \(1\) \(13.175\) \(\Q\) None \(1\) \(1\) \(0\) \(0\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
1650.2.a.s \(1\) \(13.175\) \(\Q\) None \(1\) \(1\) \(0\) \(3\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+3q^{7}+q^{8}+\cdots\)
1650.2.a.t \(1\) \(13.175\) \(\Q\) None \(1\) \(1\) \(0\) \(4\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+4q^{7}+q^{8}+\cdots\)
1650.2.a.u \(2\) \(13.175\) \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(0\) \(-4\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+(-2+\beta )q^{7}+\cdots\)
1650.2.a.v \(2\) \(13.175\) \(\Q(\sqrt{73}) \) None \(-2\) \(-2\) \(0\) \(1\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+\beta q^{7}-q^{8}+\cdots\)
1650.2.a.w \(2\) \(13.175\) \(\Q(\sqrt{10}) \) None \(-2\) \(2\) \(0\) \(4\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+(2+\beta )q^{7}+\cdots\)
1650.2.a.x \(2\) \(13.175\) \(\Q(\sqrt{10}) \) None \(2\) \(-2\) \(0\) \(-4\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+(-2+\beta )q^{7}+\cdots\)
1650.2.a.y \(2\) \(13.175\) \(\Q(\sqrt{73}) \) None \(2\) \(2\) \(0\) \(-1\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-\beta q^{7}+q^{8}+\cdots\)
1650.2.a.z \(2\) \(13.175\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(0\) \(4\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+(2+\beta )q^{7}+\cdots\)
1650.2.c.a \(2\) \(13.175\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots\)
1650.2.c.b \(2\) \(13.175\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots\)
1650.2.c.c \(2\) \(13.175\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
1650.2.c.d \(2\) \(13.175\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
1650.2.c.e \(2\) \(13.175\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots\)
1650.2.c.f \(2\) \(13.175\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+3iq^{7}+\cdots\)
1650.2.c.g \(2\) \(13.175\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{8}-q^{9}+\cdots\)
1650.2.c.h \(2\) \(13.175\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
1650.2.c.i \(2\) \(13.175\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{8}-q^{9}+\cdots\)
1650.2.c.j \(2\) \(13.175\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+4iq^{7}+\cdots\)
1650.2.c.k \(2\) \(13.175\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+3iq^{7}+\cdots\)
1650.2.c.l \(2\) \(13.175\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}-iq^{8}-q^{9}+\cdots\)
1650.2.c.m \(2\) \(13.175\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
1650.2.c.n \(2\) \(13.175\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
1650.2.c.o \(4\) \(13.175\) \(\Q(i, \sqrt{73})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}-\beta _{2}q^{3}-q^{4}+q^{6}+\beta _{1}q^{7}+\cdots\)
1650.2.d.a \(2\) \(13.175\) \(\Q(\sqrt{-2}) \) None \(-2\) \(2\) \(0\) \(0\) \(q-q^{2}+(1-\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots\)
1650.2.d.b \(2\) \(13.175\) \(\Q(\sqrt{-2}) \) None \(2\) \(2\) \(0\) \(0\) \(q+q^{2}+(1+\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots\)
1650.2.d.c \(8\) \(13.175\) 8.0.2051727616.3 None \(-8\) \(-2\) \(0\) \(0\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
1650.2.d.d \(8\) \(13.175\) 8.0.\(\cdots\).1 None \(-8\) \(-1\) \(0\) \(0\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}-\beta _{7}q^{7}+\cdots\)
1650.2.d.e \(8\) \(13.175\) 8.0.\(\cdots\).1 None \(-8\) \(1\) \(0\) \(0\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}-\beta _{7}q^{7}+\cdots\)
1650.2.d.f \(8\) \(13.175\) 8.0.2051727616.3 None \(8\) \(-2\) \(0\) \(0\) \(q+q^{2}+(-\beta _{3}-\beta _{4})q^{3}+q^{4}+(-\beta _{3}+\cdots)q^{6}+\cdots\)
1650.2.d.g \(8\) \(13.175\) 8.0.\(\cdots\).1 None \(8\) \(-1\) \(0\) \(0\) \(q+q^{2}+\beta _{4}q^{3}+q^{4}+\beta _{4}q^{6}-\beta _{7}q^{7}+\cdots\)
1650.2.d.h \(8\) \(13.175\) 8.0.\(\cdots\).1 None \(8\) \(1\) \(0\) \(0\) \(q+q^{2}-\beta _{4}q^{3}+q^{4}-\beta _{4}q^{6}-\beta _{7}q^{7}+\cdots\)
1650.2.d.i \(12\) \(13.175\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-12\) \(0\) \(0\) \(0\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}-\beta _{3}q^{7}+\cdots\)
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