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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1536.1.e.a \(4\) \(0.767\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{3}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots\)
1536.1.e.b \(4\) \(0.767\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{9}+(\zeta_{8}+\zeta_{8}^{3})q^{11}+\cdots\)
1536.1.h.a \(2\) \(0.767\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-6}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}-\beta q^{5}-\beta q^{7}+q^{9}+\beta q^{15}+\cdots\)
1536.1.h.b \(2\) \(0.767\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-6}) \) None \(0\) \(2\) \(0\) \(0\) \(q+q^{3}-\beta q^{5}+\beta q^{7}+q^{9}-\beta q^{15}+\cdots\)
1536.1.h.c \(4\) \(0.767\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{9}+(-\zeta_{8}+\zeta_{8}^{3})q^{11}+\cdots\)
1536.2.a.a \(2\) \(12.265\) \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(-4\) \(0\) \(+\) \(q-q^{3}+(-2+\beta )q^{5}+\beta q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)
1536.2.a.b \(2\) \(12.265\) \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(-4\) \(4\) \(-\) \(q-q^{3}+(-2+\beta )q^{5}+(2+\beta )q^{7}+q^{9}+\cdots\)
1536.2.a.c \(2\) \(12.265\) \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(0\) \(0\) \(+\) \(q-q^{3}+\beta q^{5}-\beta q^{7}+q^{9}-2q^{11}+\cdots\)
1536.2.a.d \(2\) \(12.265\) \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(0\) \(0\) \(-\) \(q-q^{3}+\beta q^{5}+3\beta q^{7}+q^{9}+6q^{11}+\cdots\)
1536.2.a.e \(2\) \(12.265\) \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(4\) \(-4\) \(+\) \(q-q^{3}+(2+\beta )q^{5}+(-2+\beta )q^{7}+q^{9}+\cdots\)
1536.2.a.f \(2\) \(12.265\) \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(4\) \(0\) \(-\) \(q-q^{3}+(2+\beta )q^{5}+\beta q^{7}+q^{9}+(2+2\beta )q^{11}+\cdots\)
1536.2.a.g \(2\) \(12.265\) \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(-4\) \(-4\) \(+\) \(q+q^{3}+(-2+\beta )q^{5}+(-2-\beta )q^{7}+\cdots\)
1536.2.a.h \(2\) \(12.265\) \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(-4\) \(0\) \(+\) \(q+q^{3}+(-2+\beta )q^{5}-\beta q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
1536.2.a.i \(2\) \(12.265\) \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(0\) \(0\) \(+\) \(q+q^{3}+\beta q^{5}-3\beta q^{7}+q^{9}-6q^{11}+\cdots\)
1536.2.a.j \(2\) \(12.265\) \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(0\) \(0\) \(-\) \(q+q^{3}+\beta q^{5}+\beta q^{7}+q^{9}+2q^{11}+\cdots\)
1536.2.a.k \(2\) \(12.265\) \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(4\) \(0\) \(-\) \(q+q^{3}+(2+\beta )q^{5}-\beta q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
1536.2.a.l \(2\) \(12.265\) \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(4\) \(4\) \(-\) \(q+q^{3}+(2+\beta )q^{5}+(2-\beta )q^{7}+q^{9}+\cdots\)
1536.2.a.m \(4\) \(12.265\) 4.4.4352.1 None None \(0\) \(-4\) \(0\) \(0\) \(-\) \(q-q^{3}+\beta _{1}q^{5}-\beta _{3}q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
1536.2.a.n \(4\) \(12.265\) 4.4.4352.1 None None \(0\) \(4\) \(0\) \(0\) \(-\) \(q+q^{3}+\beta _{1}q^{5}+\beta _{3}q^{7}+q^{9}+(2+\beta _{2}+\cdots)q^{11}+\cdots\)
1536.2.c.a \(2\) \(12.265\) \(\Q(\sqrt{-2}) \) None None \(0\) \(-2\) \(0\) \(0\) \(q+(-1+\beta )q^{3}+\beta q^{5}-3\beta q^{7}+(-1+\cdots)q^{9}+\cdots\)
1536.2.c.b \(2\) \(12.265\) \(\Q(\sqrt{-2}) \) None None \(0\) \(-2\) \(0\) \(0\) \(q+(-1-\beta )q^{3}+\beta q^{5}-3\beta q^{7}+(-1+\cdots)q^{9}+\cdots\)
1536.2.c.c \(2\) \(12.265\) \(\Q(\sqrt{-2}) \) None None \(0\) \(2\) \(0\) \(0\) \(q+(1-\beta )q^{3}+\beta q^{5}+3\beta q^{7}+(-1-2\beta )q^{9}+\cdots\)
1536.2.c.d \(2\) \(12.265\) \(\Q(\sqrt{-2}) \) None None \(0\) \(2\) \(0\) \(0\) \(q+(1+\beta )q^{3}+\beta q^{5}+3\beta q^{7}+(-1+2\beta )q^{9}+\cdots\)
1536.2.c.e \(4\) \(12.265\) \(\Q(\sqrt{-2}, \sqrt{7})\) None None \(0\) \(-4\) \(0\) \(0\) \(q+(-1-\beta _{1})q^{3}+\beta _{2}q^{5}+\beta _{2}q^{7}+(-1+\cdots)q^{9}+\cdots\)
1536.2.c.f \(4\) \(12.265\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) None \(0\) \(-4\) \(0\) \(0\) \(q+(-1-\zeta_{8}^{2})q^{3}+(-\zeta_{8}+2\zeta_{8}^{2}+\zeta_{8}^{3})q^{9}+\cdots\)
1536.2.c.g \(4\) \(12.265\) \(\Q(\sqrt{-2}, \sqrt{-5})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}-2\beta _{2}q^{5}+(2+\beta _{3})q^{9}+(2\beta _{1}+\cdots)q^{11}+\cdots\)
1536.2.c.h \(4\) \(12.265\) \(\Q(\sqrt{-2}, \sqrt{-5})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{2})q^{3}-2\beta _{2}q^{5}+(2-\beta _{3})q^{9}+\cdots\)
1536.2.c.i \(4\) \(12.265\) \(\Q(\sqrt{-2}, \sqrt{7})\) None None \(0\) \(4\) \(0\) \(0\) \(q+(1-\beta _{1})q^{3}+\beta _{2}q^{5}-\beta _{2}q^{7}+(-1+\cdots)q^{9}+\cdots\)
1536.2.c.j \(4\) \(12.265\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) None \(0\) \(4\) \(0\) \(0\) \(q+(1+\zeta_{8}^{2})q^{3}+(-\zeta_{8}+2\zeta_{8}^{2}+\zeta_{8}^{3})q^{9}+\cdots\)
1536.2.c.k \(8\) \(12.265\) 8.0.40960000.1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{3}-\beta _{1}q^{5}+(-2+\beta _{2})q^{9}-\beta _{3}q^{11}+\cdots\)
1536.2.c.l \(8\) \(12.265\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}q^{3}+\zeta_{24}^{3}q^{5}+\zeta_{24}^{2}q^{7}+3q^{9}+\cdots\)
1536.2.c.m \(16\) \(12.265\) 16.0.\(\cdots\).7 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{7}q^{3}+\beta _{2}q^{5}-\beta _{6}q^{7}+\beta _{13}q^{9}+\cdots\)
1536.2.d.a \(4\) \(12.265\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(-8\) \(q-\zeta_{8}q^{3}+(2\zeta_{8}-\zeta_{8}^{2})q^{5}+(-2-\zeta_{8}^{3})q^{7}+\cdots\)
1536.2.d.b \(4\) \(12.265\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{3}+(2\zeta_{8}-\zeta_{8}^{2})q^{5}+\zeta_{8}^{3}q^{7}+\cdots\)
1536.2.d.c \(4\) \(12.265\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}-3\zeta_{8}^{3}q^{7}-q^{9}+\cdots\)
1536.2.d.d \(4\) \(12.265\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}-\zeta_{8}^{3}q^{7}-q^{9}+\cdots\)
1536.2.d.e \(4\) \(12.265\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}+(2\zeta_{8}-\zeta_{8}^{2})q^{5}-\zeta_{8}^{3}q^{7}+\cdots\)
1536.2.d.f \(4\) \(12.265\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(8\) \(q+\zeta_{8}q^{3}+(2\zeta_{8}-\zeta_{8}^{2})q^{5}+(2+\zeta_{8}^{3})q^{7}+\cdots\)
1536.2.d.g \(8\) \(12.265\) 8.0.18939904.2 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{3}+\beta _{5}q^{5}-\beta _{2}q^{7}-q^{9}+(2\beta _{4}+\cdots)q^{11}+\cdots\)
1536.2.f.a \(4\) \(12.265\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) None \(0\) \(-4\) \(0\) \(0\) \(q+(-1-\zeta_{8}+\zeta_{8}^{2})q^{3}+(2\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{9}+\cdots\)
1536.2.f.b \(4\) \(12.265\) \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(-8\) \(0\) \(q-\beta _{2}q^{3}+(-2+\beta _{3})q^{5}+(-\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)
1536.2.f.c \(4\) \(12.265\) \(\Q(\sqrt{-2}, \sqrt{-5})\) None None \(0\) \(0\) \(-8\) \(0\) \(q+\beta _{1}q^{3}-2q^{5}+(2+\beta _{3})q^{9}+\beta _{2}q^{11}+\cdots\)
1536.2.f.d \(4\) \(12.265\) \(\Q(\sqrt{2}, \sqrt{-5})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}-2\beta _{2}q^{5}+(-2+\beta _{3})q^{9}+\cdots\)
1536.2.f.e \(4\) \(12.265\) \(\Q(\sqrt{2}, \sqrt{-5})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-2\beta _{2}q^{5}+(-2+\beta _{3})q^{9}+\cdots\)
1536.2.f.f \(4\) \(12.265\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}+\zeta_{8}^{3})q^{3}-\zeta_{8}^{3}q^{5}+3\zeta_{8}^{2}q^{7}+\cdots\)
1536.2.f.g \(4\) \(12.265\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{3}q^{5}+3\zeta_{8}^{2}q^{7}+\cdots\)
1536.2.f.h \(4\) \(12.265\) \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(8\) \(0\) \(q+\beta _{2}q^{3}+(2+\beta _{3})q^{5}+(\beta _{1}-2\beta _{2})q^{7}+\cdots\)
1536.2.f.i \(4\) \(12.265\) \(\Q(\sqrt{-2}, \sqrt{-5})\) None None \(0\) \(0\) \(8\) \(0\) \(q+\beta _{1}q^{3}+2q^{5}+(2+\beta _{3})q^{9}+\beta _{2}q^{11}+\cdots\)
1536.2.f.j \(4\) \(12.265\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) None \(0\) \(4\) \(0\) \(0\) \(q+(1+\zeta_{8}-\zeta_{8}^{2})q^{3}+(2\zeta_{8}-\zeta_{8}^{2}-2\zeta_{8}^{3})q^{9}+\cdots\)
1536.2.f.k \(8\) \(12.265\) 8.0.157351936.1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{3}+\beta _{7}q^{5}-\beta _{6}q^{7}+(1-\beta _{4}+\cdots)q^{9}+\cdots\)
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