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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2394.2.a.a \(1\) \(19.116\) \(\Q\) None \(-1\) \(0\) \(-4\) \(1\) \(+\) \(q-q^{2}+q^{4}-4q^{5}+q^{7}-q^{8}+4q^{10}+\cdots\)
2394.2.a.b \(1\) \(19.116\) \(\Q\) None \(-1\) \(0\) \(-2\) \(-1\) \(+\) \(q-q^{2}+q^{4}-2q^{5}-q^{7}-q^{8}+2q^{10}+\cdots\)
2394.2.a.c \(1\) \(19.116\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(q-q^{2}+q^{4}+q^{7}-q^{8}-6q^{11}+2q^{13}+\cdots\)
2394.2.a.d \(1\) \(19.116\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+2q^{13}-q^{14}+\cdots\)
2394.2.a.e \(1\) \(19.116\) \(\Q\) None \(-1\) \(0\) \(2\) \(-1\) \(+\) \(q-q^{2}+q^{4}+2q^{5}-q^{7}-q^{8}-2q^{10}+\cdots\)
2394.2.a.f \(1\) \(19.116\) \(\Q\) None \(-1\) \(0\) \(4\) \(-1\) \(-\) \(q-q^{2}+q^{4}+4q^{5}-q^{7}-q^{8}-4q^{10}+\cdots\)
2394.2.a.g \(1\) \(19.116\) \(\Q\) None \(1\) \(0\) \(-4\) \(1\) \(+\) \(q+q^{2}+q^{4}-4q^{5}+q^{7}+q^{8}-4q^{10}+\cdots\)
2394.2.a.h \(1\) \(19.116\) \(\Q\) None \(1\) \(0\) \(-2\) \(-1\) \(+\) \(q+q^{2}+q^{4}-2q^{5}-q^{7}+q^{8}-2q^{10}+\cdots\)
2394.2.a.i \(1\) \(19.116\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}-2q^{11}-4q^{13}+\cdots\)
2394.2.a.j \(1\) \(19.116\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(+\) \(q+q^{2}+q^{4}+q^{7}+q^{8}-6q^{11}-4q^{13}+\cdots\)
2394.2.a.k \(1\) \(19.116\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+2q^{13}+q^{14}+\cdots\)
2394.2.a.l \(1\) \(19.116\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+6q^{11}+2q^{13}+\cdots\)
2394.2.a.m \(1\) \(19.116\) \(\Q\) None \(1\) \(0\) \(2\) \(-1\) \(-\) \(q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}+2q^{10}+\cdots\)
2394.2.a.n \(1\) \(19.116\) \(\Q\) None \(1\) \(0\) \(2\) \(1\) \(-\) \(q+q^{2}+q^{4}+2q^{5}+q^{7}+q^{8}+2q^{10}+\cdots\)
2394.2.a.o \(1\) \(19.116\) \(\Q\) None \(1\) \(0\) \(4\) \(1\) \(-\) \(q+q^{2}+q^{4}+4q^{5}+q^{7}+q^{8}+4q^{10}+\cdots\)
2394.2.a.p \(2\) \(19.116\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-2\) \(2\) \(+\) \(q-q^{2}+q^{4}+(-1-\beta )q^{5}+q^{7}-q^{8}+\cdots\)
2394.2.a.q \(2\) \(19.116\) \(\Q(\sqrt{13}) \) None \(-2\) \(0\) \(-1\) \(2\) \(-\) \(q-q^{2}+q^{4}-\beta q^{5}+q^{7}-q^{8}+\beta q^{10}+\cdots\)
2394.2.a.r \(2\) \(19.116\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(2\) \(-\) \(q-q^{2}+q^{4}+\beta q^{5}+q^{7}-q^{8}-\beta q^{10}+\cdots\)
2394.2.a.s \(2\) \(19.116\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(2\) \(-2\) \(-\) \(q-q^{2}+q^{4}+(1+\beta )q^{5}-q^{7}-q^{8}+\cdots\)
2394.2.a.t \(2\) \(19.116\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(4\) \(2\) \(-\) \(q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-2q^{10}+\cdots\)
2394.2.a.u \(2\) \(19.116\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-4\) \(2\) \(+\) \(q+q^{2}+q^{4}-2q^{5}+q^{7}+q^{8}-2q^{10}+\cdots\)
2394.2.a.v \(2\) \(19.116\) \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(-2\) \(-2\) \(+\) \(q+q^{2}+q^{4}+(-1-\beta )q^{5}-q^{7}+q^{8}+\cdots\)
2394.2.a.w \(2\) \(19.116\) \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(-1\) \(2\) \(-\) \(q+q^{2}+q^{4}+(1-3\beta )q^{5}+q^{7}+q^{8}+\cdots\)
2394.2.a.x \(2\) \(19.116\) \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(0\) \(-2\) \(-\) \(q+q^{2}+q^{4}+\beta q^{5}-q^{7}+q^{8}+\beta q^{10}+\cdots\)
2394.2.a.y \(2\) \(19.116\) \(\Q(\sqrt{29}) \) None \(2\) \(0\) \(1\) \(-2\) \(-\) \(q+q^{2}+q^{4}+\beta q^{5}-q^{7}+q^{8}+\beta q^{10}+\cdots\)
2394.2.a.z \(2\) \(19.116\) \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(2\) \(2\) \(-\) \(q+q^{2}+q^{4}+(1+\beta )q^{5}+q^{7}+q^{8}+\cdots\)
2394.2.a.ba \(3\) \(19.116\) 3.3.469.1 None \(-3\) \(0\) \(-5\) \(-3\) \(-\) \(q-q^{2}+q^{4}+(-2+\beta _{1})q^{5}-q^{7}-q^{8}+\cdots\)
2394.2.a.bb \(3\) \(19.116\) 3.3.148.1 None \(-3\) \(0\) \(-2\) \(-3\) \(+\) \(q-q^{2}+q^{4}+(-1-\beta _{1})q^{5}-q^{7}-q^{8}+\cdots\)
2394.2.a.bc \(3\) \(19.116\) 3.3.148.1 None \(3\) \(0\) \(2\) \(-3\) \(-\) \(q+q^{2}+q^{4}+(1+\beta _{1})q^{5}-q^{7}+q^{8}+\cdots\)
2394.2.b.a \(2\) \(19.116\) \(\Q(\sqrt{-2}) \) None \(-2\) \(0\) \(0\) \(-2\) \(q-q^{2}+q^{4}-q^{7}-q^{8}-\beta q^{13}+q^{14}+\cdots\)
2394.2.b.b \(2\) \(19.116\) \(\Q(\sqrt{-2}) \) None \(-2\) \(0\) \(0\) \(2\) \(q-q^{2}+q^{4}+2\beta q^{5}+q^{7}-q^{8}-2\beta q^{10}+\cdots\)
2394.2.b.c \(2\) \(19.116\) \(\Q(\sqrt{-2}) \) None \(-2\) \(0\) \(0\) \(2\) \(q-q^{2}+q^{4}+\beta q^{5}+q^{7}-q^{8}-\beta q^{10}+\cdots\)
2394.2.b.d \(2\) \(19.116\) \(\Q(\sqrt{-2}) \) None \(2\) \(0\) \(0\) \(-2\) \(q+q^{2}+q^{4}-q^{7}+q^{8}-\beta q^{13}-q^{14}+\cdots\)
2394.2.b.e \(2\) \(19.116\) \(\Q(\sqrt{-2}) \) None \(2\) \(0\) \(0\) \(2\) \(q+q^{2}+q^{4}+2\beta q^{5}+q^{7}+q^{8}+2\beta q^{10}+\cdots\)
2394.2.b.f \(2\) \(19.116\) \(\Q(\sqrt{-2}) \) None \(2\) \(0\) \(0\) \(2\) \(q+q^{2}+q^{4}+\beta q^{5}+q^{7}+q^{8}+\beta q^{10}+\cdots\)
2394.2.b.g \(6\) \(19.116\) 6.0.2803712.1 None \(-6\) \(0\) \(0\) \(6\) \(q-q^{2}+q^{4}-\beta _{1}q^{5}+q^{7}-q^{8}+\beta _{1}q^{10}+\cdots\)
2394.2.b.h \(6\) \(19.116\) 6.0.2803712.1 None \(6\) \(0\) \(0\) \(6\) \(q+q^{2}+q^{4}-\beta _{1}q^{5}+q^{7}+q^{8}-\beta _{1}q^{10}+\cdots\)
2394.2.b.i \(8\) \(19.116\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(-8\) \(0\) \(0\) \(-8\) \(q-q^{2}+q^{4}+\beta _{3}q^{5}-q^{7}-q^{8}-\beta _{3}q^{10}+\cdots\)
2394.2.b.j \(8\) \(19.116\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(8\) \(0\) \(0\) \(-8\) \(q+q^{2}+q^{4}+\beta _{3}q^{5}-q^{7}+q^{8}+\beta _{3}q^{10}+\cdots\)
2394.2.e.a \(12\) \(19.116\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{2}-q^{4}-\beta _{2}q^{5}+\beta _{7}q^{7}-\beta _{4}q^{8}+\cdots\)
2394.2.e.b \(12\) \(19.116\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}-q^{4}-\beta _{2}q^{5}+\beta _{7}q^{7}+\beta _{4}q^{8}+\cdots\)
2394.2.e.c \(16\) \(19.116\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(6\) \(q-\beta _{11}q^{2}-q^{4}-\beta _{7}q^{5}+\beta _{12}q^{7}+\cdots\)
2394.2.e.d \(24\) \(19.116\) None \(0\) \(0\) \(0\) \(-8\)
2394.2.f.a \(24\) \(19.116\) None \(0\) \(0\) \(0\) \(4\)
2394.2.f.b \(24\) \(19.116\) None \(0\) \(0\) \(0\) \(4\)
2394.2.o.a \(2\) \(19.116\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-3\) \(-2\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-3+3\zeta_{6})q^{5}+\cdots\)
2394.2.o.b \(2\) \(19.116\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-3\) \(2\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-3+3\zeta_{6})q^{5}+\cdots\)
2394.2.o.c \(2\) \(19.116\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(-2\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
2394.2.o.d \(2\) \(19.116\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(-2\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
2394.2.o.e \(2\) \(19.116\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(2\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
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