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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4608.2.a.a \(2\) \(36.795\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-4\) \(-4\) \(+\) \(q+(-2+\beta )q^{5}+(-2-\beta )q^{7}+2q^{11}+\cdots\)
4608.2.a.b \(2\) \(36.795\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-4\) \(0\) \(-\) \(q+(-2+\beta )q^{5}-\beta q^{7}+(-2+2\beta )q^{11}+\cdots\)
4608.2.a.c \(2\) \(36.795\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-4\) \(0\) \(-\) \(q-2q^{5}+2\beta q^{7}+3\beta q^{11}+6q^{13}+\cdots\)
4608.2.a.d \(2\) \(36.795\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-4\) \(0\) \(+\) \(q+(-2+\beta )q^{5}+\beta q^{7}+(2-2\beta )q^{11}+\cdots\)
4608.2.a.e \(2\) \(36.795\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-4\) \(4\) \(+\) \(q+(-2+\beta )q^{5}+(2+\beta )q^{7}-2q^{11}+\cdots\)
4608.2.a.f \(2\) \(36.795\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-8\) \(+\) \(q+2\beta q^{5}-4q^{7}-\beta q^{11}+2\beta q^{13}+\cdots\)
4608.2.a.g \(2\) \(36.795\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(q+\beta q^{5}-3\beta q^{7}-6q^{11}-4\beta q^{13}+\cdots\)
4608.2.a.h \(2\) \(36.795\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(+\) \(q+\beta q^{5}-\beta q^{7}-2q^{11}-2q^{17}+4q^{19}+\cdots\)
4608.2.a.i \(2\) \(36.795\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) \(-\) \(q+(-2+3\beta )q^{11}+4\beta q^{17}+(6-\beta )q^{19}+\cdots\)
4608.2.a.j \(2\) \(36.795\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(+\) \(q+\beta q^{5}+\beta q^{7}+2q^{11}-2q^{17}-4q^{19}+\cdots\)
4608.2.a.k \(2\) \(36.795\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) \(+\) \(q+(2-3\beta )q^{11}+4\beta q^{17}+(-6+\beta )q^{19}+\cdots\)
4608.2.a.l \(2\) \(36.795\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(q+\beta q^{5}+3\beta q^{7}+6q^{11}-4\beta q^{13}+\cdots\)
4608.2.a.m \(2\) \(36.795\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(8\) \(-\) \(q+2\beta q^{5}+4q^{7}+\beta q^{11}+2\beta q^{13}+\cdots\)
4608.2.a.n \(2\) \(36.795\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(4\) \(-4\) \(-\) \(q+(2+\beta )q^{5}+(-2+\beta )q^{7}-2q^{11}+\cdots\)
4608.2.a.o \(2\) \(36.795\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(4\) \(0\) \(+\) \(q+(2+\beta )q^{5}-\beta q^{7}+(-2-2\beta )q^{11}+\cdots\)
4608.2.a.p \(2\) \(36.795\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(4\) \(0\) \(+\) \(q+2q^{5}+2\beta q^{7}-3\beta q^{11}-6q^{13}+\cdots\)
4608.2.a.q \(2\) \(36.795\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(4\) \(0\) \(-\) \(q+(2+\beta )q^{5}+\beta q^{7}+(2+2\beta )q^{11}+(-2+\cdots)q^{13}+\cdots\)
4608.2.a.r \(2\) \(36.795\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(4\) \(4\) \(-\) \(q+(2+\beta )q^{5}+(2-\beta )q^{7}+2q^{11}+2\beta q^{13}+\cdots\)
4608.2.a.s \(4\) \(36.795\) \(\Q(\zeta_{24})^+\) \(\Q(\sqrt{-6}) \) \(0\) \(0\) \(-8\) \(0\) \(+\) \(q+(-2-\beta _{2})q^{5}+(\beta _{1}+\beta _{3})q^{7}-\beta _{3}q^{11}+\cdots\)
4608.2.a.t \(4\) \(36.795\) 4.4.4352.1 None \(0\) \(0\) \(0\) \(0\) \(+\) \(q+\beta _{1}q^{5}-\beta _{3}q^{7}+(-2-\beta _{2})q^{11}+\cdots\)
4608.2.a.u \(4\) \(36.795\) \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(q+\beta _{1}q^{5}-\beta _{1}q^{7}-2q^{11}-\beta _{2}q^{13}+\cdots\)
4608.2.a.v \(4\) \(36.795\) \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(q+\beta _{2}q^{5}+\beta _{1}q^{7}-\beta _{3}q^{11}-2\beta _{2}q^{13}+\cdots\)
4608.2.a.w \(4\) \(36.795\) \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(q+\beta _{2}q^{5}+\beta _{3}q^{7}+\beta _{1}q^{11}+\beta _{2}q^{13}+\cdots\)
4608.2.a.x \(4\) \(36.795\) \(\Q(\sqrt{2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(q+\beta _{1}q^{5}-\beta _{2}q^{7}+\beta _{3}q^{11}-\beta _{3}q^{13}+\cdots\)
4608.2.a.y \(4\) \(36.795\) \(\Q(\sqrt{2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(q+\beta _{1}q^{5}+\beta _{2}q^{7}-\beta _{3}q^{11}-\beta _{3}q^{13}+\cdots\)
4608.2.a.z \(4\) \(36.795\) \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(q+\beta _{2}q^{5}+\beta _{1}q^{7}-\beta _{3}q^{11}+2\beta _{2}q^{13}+\cdots\)
4608.2.a.ba \(4\) \(36.795\) 4.4.4352.1 None \(0\) \(0\) \(0\) \(0\) \(-\) \(q+\beta _{1}q^{5}+\beta _{3}q^{7}+(2+\beta _{2})q^{11}+(-\beta _{1}+\cdots)q^{13}+\cdots\)
4608.2.a.bb \(4\) \(36.795\) \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(q+\beta _{1}q^{5}+\beta _{1}q^{7}+2q^{11}-\beta _{2}q^{13}+\cdots\)
4608.2.a.bc \(4\) \(36.795\) \(\Q(\zeta_{24})^+\) \(\Q(\sqrt{-6}) \) \(0\) \(0\) \(8\) \(0\) \(-\) \(q+(2+\beta _{2})q^{5}+(\beta _{1}+\beta _{3})q^{7}+\beta _{3}q^{11}+\cdots\)
4608.2.c.a \(2\) \(36.795\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3\beta q^{7}-4q^{11}-6q^{13}+3\beta q^{17}+\cdots\)
4608.2.c.b \(2\) \(36.795\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-3\beta q^{7}-4q^{11}+6q^{13}+3\beta q^{17}+\cdots\)
4608.2.c.c \(2\) \(36.795\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2\beta q^{5}+\beta q^{7}-2q^{13}-\beta q^{17}-2\beta q^{19}+\cdots\)
4608.2.c.d \(2\) \(36.795\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2\beta q^{5}-\beta q^{7}-2q^{13}-\beta q^{17}+2\beta q^{19}+\cdots\)
4608.2.c.e \(2\) \(36.795\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2\beta q^{5}-\beta q^{7}+2q^{13}+\beta q^{17}-2\beta q^{19}+\cdots\)
4608.2.c.f \(2\) \(36.795\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2\beta q^{5}+\beta q^{7}+2q^{13}+\beta q^{17}+2\beta q^{19}+\cdots\)
4608.2.c.g \(2\) \(36.795\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3\beta q^{7}+4q^{11}-6q^{13}-3\beta q^{17}+\cdots\)
4608.2.c.h \(2\) \(36.795\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-3\beta q^{7}+4q^{11}+6q^{13}-3\beta q^{17}+\cdots\)
4608.2.c.i \(4\) \(36.795\) \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{2})q^{5}+\beta _{2}q^{7}+(-2+\beta _{3})q^{11}+\cdots\)
4608.2.c.j \(4\) \(36.795\) \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{2})q^{5}+\beta _{2}q^{7}+(-2+\beta _{3})q^{11}+\cdots\)
4608.2.c.k \(4\) \(36.795\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{5}+\zeta_{8}^{2}q^{7}+\zeta_{8}^{3}q^{11}+3\zeta_{8}^{2}q^{17}+\cdots\)
4608.2.c.l \(4\) \(36.795\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{5}-3\zeta_{8}^{2}q^{7}+\zeta_{8}^{3}q^{11}-2\zeta_{8}^{3}q^{13}+\cdots\)
4608.2.c.m \(4\) \(36.795\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{5}+3\zeta_{8}^{2}q^{7}-\zeta_{8}^{3}q^{11}-2\zeta_{8}^{3}q^{13}+\cdots\)
4608.2.c.n \(4\) \(36.795\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{5}-\zeta_{8}^{2}q^{7}-\zeta_{8}^{3}q^{11}+3\zeta_{8}^{2}q^{17}+\cdots\)
4608.2.c.o \(4\) \(36.795\) \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{2})q^{5}-\beta _{2}q^{7}+(2-\beta _{3})q^{11}+\cdots\)
4608.2.c.p \(4\) \(36.795\) \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{2})q^{5}-\beta _{2}q^{7}+(2-\beta _{3})q^{11}+\cdots\)
4608.2.c.q \(8\) \(36.795\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{2}q^{5}+(-\zeta_{16}-\zeta_{16}^{3})q^{7}-\zeta_{16}^{5}q^{11}+\cdots\)
4608.2.c.r \(8\) \(36.795\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{2}q^{5}+(-\zeta_{16}-\zeta_{16}^{3})q^{7}-\zeta_{16}^{5}q^{11}+\cdots\)
4608.2.d.a \(2\) \(36.795\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-8\) \(q+2\beta q^{5}-4q^{7}+\beta q^{11}-2\beta q^{13}+\cdots\)
4608.2.d.b \(2\) \(36.795\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(8\) \(q+2\beta q^{5}+4q^{7}-\beta q^{11}-2\beta q^{13}+\cdots\)
4608.2.d.c \(4\) \(36.795\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-8\) \(q+(\zeta_{8}-\zeta_{8}^{2})q^{5}+(-2-\zeta_{8}^{3})q^{7}+\zeta_{8}q^{11}+\cdots\)
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