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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1024.1.c.a \(2\) \(0.511\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{5}+q^{9}+\beta q^{13}+q^{25}+\beta q^{29}+\cdots\)
1024.1.d.a \(2\) \(0.511\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{5}-q^{9}-\beta q^{13}-q^{25}-\beta q^{29}+\cdots\)
1024.1.f.a \(2\) \(0.511\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+(-1-i)q^{3}+iq^{9}+(1-i)q^{11}+\cdots\)
1024.1.f.b \(2\) \(0.511\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{9}+q^{17}-iq^{25}+iq^{41}-q^{49}+\cdots\)
1024.1.f.c \(2\) \(0.511\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(0\) \(q+(1+i)q^{3}+iq^{9}+(-1+i)q^{11}+\cdots\)
1024.2.a.a \(2\) \(8.177\) \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(-8\) \(-\) \(q+2\beta q^{3}+\beta q^{5}-4q^{7}+5q^{9}+2\beta q^{11}+\cdots\)
1024.2.a.b \(2\) \(8.177\) \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(-4\) \(+\) \(q+\beta q^{3}-\beta q^{5}-2q^{7}-q^{9}-\beta q^{11}+\cdots\)
1024.2.a.c \(2\) \(8.177\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(+\) \(q+\beta q^{5}-3q^{9}-5\beta q^{13}-8q^{17}-3q^{25}+\cdots\)
1024.2.a.d \(2\) \(8.177\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(q+3\beta q^{5}-3q^{9}+\beta q^{13}+8q^{17}+13q^{25}+\cdots\)
1024.2.a.e \(2\) \(8.177\) \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(4\) \(-\) \(q+\beta q^{3}+\beta q^{5}+2q^{7}-q^{9}-\beta q^{11}+\cdots\)
1024.2.a.f \(2\) \(8.177\) \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(8\) \(-\) \(q+2\beta q^{3}-\beta q^{5}+4q^{7}+5q^{9}+2\beta q^{11}+\cdots\)
1024.2.a.g \(4\) \(8.177\) \(\Q(\zeta_{24})^+\) None None \(0\) \(-4\) \(0\) \(0\) \(+\) \(q+(-1+\beta _{1})q^{3}-\beta _{3}q^{5}+(\beta _{2}+\beta _{3})q^{7}+\cdots\)
1024.2.a.h \(4\) \(8.177\) \(\Q(\zeta_{16})^+\) None None \(0\) \(0\) \(-8\) \(0\) \(+\) \(q+\beta _{1}q^{3}+(-2-\beta _{2})q^{5}+(-\beta _{1}+\beta _{3})q^{7}+\cdots\)
1024.2.a.i \(4\) \(8.177\) \(\Q(\zeta_{16})^+\) None None \(0\) \(0\) \(8\) \(0\) \(-\) \(q+\beta _{1}q^{3}+(2+\beta _{2})q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots\)
1024.2.a.j \(4\) \(8.177\) \(\Q(\zeta_{24})^+\) None None \(0\) \(4\) \(0\) \(0\) \(-\) \(q+(1-\beta _{1})q^{3}+\beta _{3}q^{5}+(\beta _{2}+\beta _{3})q^{7}+\cdots\)
1024.2.b.a \(2\) \(8.177\) \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(-8\) \(q+2\beta q^{3}+\beta q^{5}-4q^{7}-5q^{9}-2\beta q^{11}+\cdots\)
1024.2.b.b \(2\) \(8.177\) \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(-4\) \(q+\beta q^{3}-\beta q^{5}-2q^{7}+q^{9}+\beta q^{11}+\cdots\)
1024.2.b.c \(2\) \(8.177\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{5}+3q^{9}-5\beta q^{13}-8q^{17}+3q^{25}+\cdots\)
1024.2.b.d \(2\) \(8.177\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-3\beta q^{5}+3q^{9}+\beta q^{13}+8q^{17}-13q^{25}+\cdots\)
1024.2.b.e \(2\) \(8.177\) \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(4\) \(q+\beta q^{3}+\beta q^{5}+2q^{7}+q^{9}+\beta q^{11}+\cdots\)
1024.2.b.f \(2\) \(8.177\) \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(8\) \(q+2\beta q^{3}-\beta q^{5}+4q^{7}-5q^{9}-2\beta q^{11}+\cdots\)
1024.2.b.g \(8\) \(8.177\) \(\Q(\zeta_{16})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{2}q^{3}+\zeta_{16}q^{5}-\zeta_{16}^{3}q^{7}+(-1+\cdots)q^{9}+\cdots\)
1024.2.b.h \(8\) \(8.177\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}q^{3}+\zeta_{24}^{5}q^{5}+\zeta_{24}^{4}q^{7}+(-1+\cdots)q^{9}+\cdots\)
1024.2.e.a \(2\) \(8.177\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(-4\) \(0\) \(0\) \(q+(-2+2i)q^{3}-5iq^{9}+(2+2i)q^{11}+\cdots\)
1024.2.e.b \(2\) \(8.177\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(-4\) \(0\) \(q+(-1+i)q^{3}+(-2-2i)q^{5}-4iq^{7}+\cdots\)
1024.2.e.c \(2\) \(8.177\) \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(4\) \(0\) \(q+(-1+i)q^{3}+(2+2i)q^{5}+4iq^{7}+\cdots\)
1024.2.e.d \(2\) \(8.177\) \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(-4\) \(0\) \(q+(1-i)q^{3}+(-2-2i)q^{5}+4iq^{7}+\cdots\)
1024.2.e.e \(2\) \(8.177\) \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(4\) \(0\) \(q+(1-i)q^{3}+(2+2i)q^{5}-4iq^{7}+iq^{9}+\cdots\)
1024.2.e.f \(2\) \(8.177\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(4\) \(0\) \(0\) \(q+(2-2i)q^{3}-5iq^{9}+(-2-2i)q^{11}+\cdots\)
1024.2.e.g \(4\) \(8.177\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) None \(0\) \(-4\) \(0\) \(0\) \(q+(-1+\zeta_{8}-\zeta_{8}^{2})q^{3}+(-2\zeta_{8}+3\zeta_{8}^{2}+\cdots)q^{9}+\cdots\)
1024.2.e.h \(4\) \(8.177\) \(\Q(\zeta_{8})\) None None \(0\) \(-4\) \(0\) \(0\) \(q+(-1+\zeta_{8}^{2})q^{3}-\zeta_{8}q^{5}+(-\zeta_{8}-\zeta_{8}^{3})q^{7}+\cdots\)
1024.2.e.i \(4\) \(8.177\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{3}+\zeta_{8}^{3}q^{5}+4\zeta_{8}^{2}q^{7}+\zeta_{8}^{2}q^{9}+\cdots\)
1024.2.e.j \(4\) \(8.177\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{5}+3\zeta_{8}^{2}q^{9}-3\zeta_{8}^{3}q^{13}-2q^{17}+\cdots\)
1024.2.e.k \(4\) \(8.177\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{5}+3\zeta_{8}^{2}q^{9}-\zeta_{8}^{3}q^{13}+2q^{17}+\cdots\)
1024.2.e.l \(4\) \(8.177\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{3}+\zeta_{8}^{2}q^{9}-3\zeta_{8}^{3}q^{11}+6q^{17}+\cdots\)
1024.2.e.m \(4\) \(8.177\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{3}-\zeta_{8}^{3}q^{5}-4\zeta_{8}^{2}q^{7}+\zeta_{8}^{2}q^{9}+\cdots\)
1024.2.e.n \(4\) \(8.177\) \(\Q(\zeta_{8})\) None None \(0\) \(4\) \(0\) \(0\) \(q+(1-\zeta_{8}^{2})q^{3}-\zeta_{8}q^{5}+(\zeta_{8}+\zeta_{8}^{3})q^{7}+\cdots\)
1024.2.e.o \(4\) \(8.177\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) None \(0\) \(4\) \(0\) \(0\) \(q+(1+\zeta_{8}+\zeta_{8}^{2})q^{3}+(2\zeta_{8}+3\zeta_{8}^{2}+\cdots)q^{9}+\cdots\)
1024.2.e.p \(8\) \(8.177\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{7}q^{3}+\zeta_{24}q^{5}-\zeta_{24}^{6}q^{7}-3\zeta_{24}^{2}q^{9}+\cdots\)
1024.2.g.a \(16\) \(8.177\) \(\Q(\zeta_{48})\) None None \(0\) \(0\) \(-8\) \(0\) \(q+\zeta_{48}^{15}q^{3}+(-1+\zeta_{48}^{3}-\zeta_{48}^{8}+\cdots)q^{5}+\cdots\)
1024.2.g.b \(16\) \(8.177\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(-8\) \(0\) \(q+\beta _{2}q^{3}+(\beta _{3}+\beta _{10})q^{5}+(-\beta _{4}-\beta _{9}+\cdots)q^{7}+\cdots\)
1024.2.g.c \(16\) \(8.177\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(-8\) \(0\) \(q+\beta _{13}q^{3}+(-1-\beta _{3}+\beta _{5}+\beta _{8})q^{5}+\cdots\)
1024.2.g.d \(16\) \(8.177\) \(\Q(\zeta_{48})\) None None \(0\) \(0\) \(-8\) \(0\) \(q+(\zeta_{48}^{11}+\zeta_{48}^{14})q^{3}+(-\zeta_{48}-\zeta_{48}^{2}+\cdots)q^{5}+\cdots\)
1024.2.g.e \(16\) \(8.177\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(8\) \(0\) \(q+\beta _{2}q^{3}+(-\beta _{3}-\beta _{10})q^{5}+(\beta _{4}+\beta _{9}+\cdots)q^{7}+\cdots\)
1024.2.g.f \(16\) \(8.177\) \(\Q(\zeta_{48})\) None None \(0\) \(0\) \(8\) \(0\) \(q+\zeta_{48}^{15}q^{3}+(1+\zeta_{48}^{8}+\zeta_{48}^{13}+\cdots)q^{5}+\cdots\)
1024.2.g.g \(16\) \(8.177\) \(\Q(\zeta_{48})\) None None \(0\) \(0\) \(8\) \(0\) \(q+(\zeta_{48}^{11}+\zeta_{48}^{14})q^{3}+(\zeta_{48}+\zeta_{48}^{2}+\cdots)q^{5}+\cdots\)
1024.2.g.h \(16\) \(8.177\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(8\) \(0\) \(q+\beta _{13}q^{3}+(1+\beta _{3}-\beta _{5}-\beta _{8})q^{5}+\cdots\)
1024.3.c.a \(2\) \(27.902\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-7\beta q^{5}+9q^{9}-17\beta q^{13}-2^{4}q^{17}+\cdots\)
1024.3.c.b \(2\) \(27.902\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{5}+9q^{9}+7\beta q^{13}+2^{4}q^{17}+\cdots\)
1024.3.c.c \(4\) \(27.902\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}-5\beta _{1}q^{5}-\beta _{3}q^{7}-15q^{9}+\cdots\)
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