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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1638.2.a.a \(1\) \(13.079\) \(\Q\) None \(-1\) \(0\) \(-3\) \(-1\) \(-\) \(q-q^{2}+q^{4}-3q^{5}-q^{7}-q^{8}+3q^{10}+\cdots\)
1638.2.a.b \(1\) \(13.079\) \(\Q\) None \(-1\) \(0\) \(-3\) \(1\) \(+\) \(q-q^{2}+q^{4}-3q^{5}+q^{7}-q^{8}+3q^{10}+\cdots\)
1638.2.a.c \(1\) \(13.079\) \(\Q\) None \(-1\) \(0\) \(-2\) \(-1\) \(-\) \(q-q^{2}+q^{4}-2q^{5}-q^{7}-q^{8}+2q^{10}+\cdots\)
1638.2.a.d \(1\) \(13.079\) \(\Q\) None \(-1\) \(0\) \(-2\) \(1\) \(+\) \(q-q^{2}+q^{4}-2q^{5}+q^{7}-q^{8}+2q^{10}+\cdots\)
1638.2.a.e \(1\) \(13.079\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+q^{13}-q^{14}+\cdots\)
1638.2.a.f \(1\) \(13.079\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+3q^{11}+q^{13}+\cdots\)
1638.2.a.g \(1\) \(13.079\) \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
1638.2.a.h \(1\) \(13.079\) \(\Q\) None \(-1\) \(0\) \(1\) \(1\) \(+\) \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
1638.2.a.i \(1\) \(13.079\) \(\Q\) None \(-1\) \(0\) \(3\) \(1\) \(-\) \(q-q^{2}+q^{4}+3q^{5}+q^{7}-q^{8}-3q^{10}+\cdots\)
1638.2.a.j \(1\) \(13.079\) \(\Q\) None \(-1\) \(0\) \(4\) \(-1\) \(-\) \(q-q^{2}+q^{4}+4q^{5}-q^{7}-q^{8}-4q^{10}+\cdots\)
1638.2.a.k \(1\) \(13.079\) \(\Q\) None \(1\) \(0\) \(-4\) \(-1\) \(-\) \(q+q^{2}+q^{4}-4q^{5}-q^{7}+q^{8}-4q^{10}+\cdots\)
1638.2.a.l \(1\) \(13.079\) \(\Q\) None \(1\) \(0\) \(-3\) \(1\) \(+\) \(q+q^{2}+q^{4}-3q^{5}+q^{7}+q^{8}-3q^{10}+\cdots\)
1638.2.a.m \(1\) \(13.079\) \(\Q\) None \(1\) \(0\) \(-3\) \(1\) \(+\) \(q+q^{2}+q^{4}-3q^{5}+q^{7}+q^{8}-3q^{10}+\cdots\)
1638.2.a.n \(1\) \(13.079\) \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) \(+\) \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
1638.2.a.o \(1\) \(13.079\) \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) \(+\) \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
1638.2.a.p \(1\) \(13.079\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+q^{13}+q^{14}+\cdots\)
1638.2.a.q \(1\) \(13.079\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+5q^{11}-q^{13}+\cdots\)
1638.2.a.r \(1\) \(13.079\) \(\Q\) None \(1\) \(0\) \(1\) \(-1\) \(-\) \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
1638.2.a.s \(1\) \(13.079\) \(\Q\) None \(1\) \(0\) \(2\) \(-1\) \(-\) \(q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}+2q^{10}+\cdots\)
1638.2.a.t \(1\) \(13.079\) \(\Q\) None \(1\) \(0\) \(3\) \(1\) \(-\) \(q+q^{2}+q^{4}+3q^{5}+q^{7}+q^{8}+3q^{10}+\cdots\)
1638.2.a.u \(2\) \(13.079\) \(\Q(\sqrt{17}) \) None \(-2\) \(0\) \(-3\) \(-2\) \(+\) \(q-q^{2}+q^{4}+(-1-\beta )q^{5}-q^{7}-q^{8}+\cdots\)
1638.2.a.v \(2\) \(13.079\) \(\Q(\sqrt{33}) \) None \(-2\) \(0\) \(-1\) \(-2\) \(+\) \(q-q^{2}+q^{4}-\beta q^{5}-q^{7}-q^{8}+\beta q^{10}+\cdots\)
1638.2.a.w \(2\) \(13.079\) \(\Q(\sqrt{41}) \) None \(-2\) \(0\) \(1\) \(2\) \(-\) \(q-q^{2}+q^{4}+\beta q^{5}+q^{7}-q^{8}-\beta q^{10}+\cdots\)
1638.2.a.x \(2\) \(13.079\) \(\Q(\sqrt{33}) \) None \(2\) \(0\) \(1\) \(-2\) \(-\) \(q+q^{2}+q^{4}+\beta q^{5}-q^{7}+q^{8}+\beta q^{10}+\cdots\)
1638.2.a.y \(2\) \(13.079\) \(\Q(\sqrt{57}) \) None \(2\) \(0\) \(1\) \(2\) \(-\) \(q+q^{2}+q^{4}+\beta q^{5}+q^{7}+q^{8}+\beta q^{10}+\cdots\)
1638.2.c.a \(2\) \(13.079\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+2iq^{5}-iq^{7}-iq^{8}+\cdots\)
1638.2.c.b \(2\) \(13.079\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+2iq^{5}-iq^{7}-iq^{8}+\cdots\)
1638.2.c.c \(2\) \(13.079\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+2iq^{5}+iq^{7}-iq^{8}+\cdots\)
1638.2.c.d \(2\) \(13.079\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+2iq^{5}-iq^{7}-iq^{8}+\cdots\)
1638.2.c.e \(2\) \(13.079\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{5}-iq^{7}+iq^{8}+\cdots\)
1638.2.c.f \(2\) \(13.079\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{5}+iq^{7}+iq^{8}+\cdots\)
1638.2.c.g \(2\) \(13.079\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+3iq^{5}+iq^{7}+iq^{8}+\cdots\)
1638.2.c.h \(4\) \(13.079\) \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}-q^{4}+(\beta _{1}-\beta _{2})q^{5}-\beta _{2}q^{7}+\cdots\)
1638.2.c.i \(6\) \(13.079\) 6.0.30647296.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{2}-q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{4}q^{7}+\cdots\)
1638.2.c.j \(6\) \(13.079\) 6.0.3356224.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-q^{4}+(-\beta _{1}-\beta _{4})q^{5}+\beta _{1}q^{7}+\cdots\)
1638.2.c.k \(6\) \(13.079\) 6.0.3356224.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-q^{4}+(-\beta _{1}-\beta _{4})q^{5}-\beta _{1}q^{7}+\cdots\)
1638.2.e.a \(16\) \(13.079\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(-16\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}+\beta _{6}q^{5}+\beta _{1}q^{7}-q^{8}+\cdots\)
1638.2.e.b \(16\) \(13.079\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(16\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+\beta _{6}q^{5}-\beta _{2}q^{7}+q^{8}+\cdots\)
1638.2.g.a \(8\) \(13.079\) 8.0.40960000.1 None \(0\) \(0\) \(-8\) \(0\) \(q+\beta _{1}q^{2}-q^{4}+(-1-\beta _{3})q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots\)
1638.2.g.b \(8\) \(13.079\) 8.0.836829184.2 None \(0\) \(0\) \(-8\) \(4\) \(q-\beta _{3}q^{2}-q^{4}+(-2-\beta _{1}-\beta _{6}+\beta _{7})q^{5}+\cdots\)
1638.2.g.c \(8\) \(13.079\) 8.0.40960000.1 None \(0\) \(0\) \(8\) \(0\) \(q-\beta _{1}q^{2}-q^{4}+(1-\beta _{3})q^{5}+(\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
1638.2.g.d \(8\) \(13.079\) 8.0.836829184.2 None \(0\) \(0\) \(8\) \(4\) \(q-\beta _{3}q^{2}-q^{4}+(2+\beta _{1}+\beta _{6}-\beta _{7})q^{5}+\cdots\)
1638.2.j.a \(2\) \(13.079\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-2\) \(-5\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-2\zeta_{6}q^{5}+\cdots\)
1638.2.j.b \(2\) \(13.079\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-2\) \(-1\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-2\zeta_{6}q^{5}+\cdots\)
1638.2.j.c \(2\) \(13.079\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(5\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(2+\zeta_{6})q^{7}+\cdots\)
1638.2.j.d \(2\) \(13.079\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(-5\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots\)
1638.2.j.e \(2\) \(13.079\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(-1\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
1638.2.j.f \(2\) \(13.079\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-4\) \(-1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-4\zeta_{6}q^{5}+\cdots\)
1638.2.j.g \(2\) \(13.079\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-1\) \(-5\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots\)
1638.2.j.h \(2\) \(13.079\) \(\Q(\sqrt{-3}) \) 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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