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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
525.1.k.a \(4\) \(0.262\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-35}) \) \(\Q(\sqrt{105}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{9}+\cdots\)
525.1.p.a \(4\) \(0.262\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}-\zeta_{12}^{4}q^{4}+\zeta_{12}q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
525.1.u.a \(2\) \(0.262\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots\)
525.1.u.b \(2\) \(0.262\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(1\) \(q-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots\)
525.1.be.a \(8\) \(0.262\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{5}q^{3}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{11}q^{7}+\cdots\)
525.2.a.a \(1\) \(4.192\) \(\Q\) None None \(-1\) \(-1\) \(0\) \(-1\) \(+\) \(q-q^{2}-q^{3}-q^{4}+q^{6}-q^{7}+3q^{8}+\cdots\)
525.2.a.b \(1\) \(4.192\) \(\Q\) None None \(-1\) \(1\) \(0\) \(-1\) \(+\) \(q-q^{2}+q^{3}-q^{4}-q^{6}-q^{7}+3q^{8}+\cdots\)
525.2.a.c \(1\) \(4.192\) \(\Q\) None None \(1\) \(-1\) \(0\) \(1\) \(+\) \(q+q^{2}-q^{3}-q^{4}-q^{6}+q^{7}-3q^{8}+\cdots\)
525.2.a.d \(1\) \(4.192\) \(\Q\) None None \(1\) \(-1\) \(0\) \(1\) \(-\) \(q+q^{2}-q^{3}-q^{4}-q^{6}+q^{7}-3q^{8}+\cdots\)
525.2.a.e \(2\) \(4.192\) \(\Q(\sqrt{5}) \) None None \(-3\) \(-2\) \(0\) \(2\) \(+\) \(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+(1+\beta )q^{6}+\cdots\)
525.2.a.f \(2\) \(4.192\) \(\Q(\sqrt{13}) \) None None \(-1\) \(-2\) \(0\) \(-2\) \(+\) \(q-\beta q^{2}-q^{3}+(1+\beta )q^{4}+\beta q^{6}-q^{7}+\cdots\)
525.2.a.g \(2\) \(4.192\) \(\Q(\sqrt{5}) \) None None \(0\) \(2\) \(0\) \(-2\) \(-\) \(q-\beta q^{2}+q^{3}+3q^{4}-\beta q^{6}-q^{7}-\beta q^{8}+\cdots\)
525.2.a.h \(2\) \(4.192\) \(\Q(\sqrt{13}) \) None None \(1\) \(2\) \(0\) \(2\) \(-\) \(q+\beta q^{2}+q^{3}+(1+\beta )q^{4}+\beta q^{6}+q^{7}+\cdots\)
525.2.a.i \(2\) \(4.192\) \(\Q(\sqrt{5}) \) None None \(3\) \(2\) \(0\) \(-2\) \(-\) \(q+(1+\beta )q^{2}+q^{3}+3\beta q^{4}+(1+\beta )q^{6}+\cdots\)
525.2.a.j \(3\) \(4.192\) 3.3.148.1 None None \(-1\) \(3\) \(0\) \(3\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
525.2.a.k \(3\) \(4.192\) 3.3.148.1 None None \(1\) \(-3\) \(0\) \(-3\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
525.2.b.a \(2\) \(4.192\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{6}q^{2}-\zeta_{6}q^{3}-q^{4}-3q^{6}+(-2+\cdots)q^{7}+\cdots\)
525.2.b.b \(2\) \(4.192\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{6}q^{2}+\zeta_{6}q^{3}-q^{4}+3q^{6}+(-2+\cdots)q^{7}+\cdots\)
525.2.b.c \(2\) \(4.192\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-5\) \(q+(1-2\zeta_{6})q^{3}+2q^{4}+(-2-\zeta_{6})q^{7}+\cdots\)
525.2.b.d \(2\) \(4.192\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(5\) \(q+(1-2\zeta_{6})q^{3}+2q^{4}+(3-\zeta_{6})q^{7}+\cdots\)
525.2.b.e \(4\) \(4.192\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(-1\) \(0\) \(8\) \(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+\beta _{3}q^{3}+(-1+\cdots)q^{4}+\cdots\)
525.2.b.f \(4\) \(4.192\) \(\Q(\sqrt{5}, \sqrt{-7})\) \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}+2q^{4}+(\beta _{1}-\beta _{3})q^{7}+(-1+\cdots)q^{9}+\cdots\)
525.2.b.g \(4\) \(4.192\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(1\) \(0\) \(8\) \(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}-\beta _{3}q^{3}+(-1+\cdots)q^{4}+\cdots\)
525.2.b.h \(8\) \(4.192\) 8.0.\(\cdots\).7 None None \(0\) \(0\) \(0\) \(-8\) \(q+\beta _{2}q^{2}-\beta _{7}q^{3}+(-2+\beta _{4})q^{4}+\beta _{3}q^{6}+\cdots\)
525.2.b.i \(8\) \(4.192\) 8.0.\(\cdots\).7 None None \(0\) \(0\) \(0\) \(8\) \(q+\beta _{3}q^{2}+\beta _{1}q^{3}+(-2+\beta _{4})q^{4}-\beta _{5}q^{6}+\cdots\)
525.2.b.j \(8\) \(4.192\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}q^{2}-\zeta_{24}^{3}q^{3}-q^{4}+(\zeta_{24}^{2}+\cdots)q^{6}+\cdots\)
525.2.d.a \(2\) \(4.192\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}+q^{4}-q^{6}+iq^{7}+3iq^{8}+\cdots\)
525.2.d.b \(2\) \(4.192\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}+q^{4}+q^{6}+iq^{7}+3iq^{8}+\cdots\)
525.2.d.c \(4\) \(4.192\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}-\beta _{1}q^{3}-3q^{4}+\beta _{3}q^{6}-\beta _{1}q^{7}+\cdots\)
525.2.d.d \(4\) \(4.192\) \(\Q(i, \sqrt{13})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-2+\beta _{3})q^{4}+(1+\cdots)q^{6}+\cdots\)
525.2.d.e \(4\) \(4.192\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{3})q^{2}+\beta _{3}q^{3}+3\beta _{2}q^{4}+(1+\cdots)q^{6}+\cdots\)
525.2.g.a \(4\) \(4.192\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}-2q^{4}+(\zeta_{12}-\zeta_{12}^{2})q^{7}+\cdots\)
525.2.g.b \(4\) \(4.192\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}-\zeta_{12}q^{3}+q^{4}-3q^{6}+(-\zeta_{12}+\cdots)q^{7}+\cdots\)
525.2.g.c \(4\) \(4.192\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}-\zeta_{12}q^{3}+q^{4}+3q^{6}+(-\zeta_{12}+\cdots)q^{7}+\cdots\)
525.2.g.d \(8\) \(4.192\) 8.0.303595776.1 None None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{4}-\beta _{5})q^{2}-\beta _{1}q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)
525.2.g.e \(8\) \(4.192\) 8.0.303595776.1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{2}+(-\beta _{2}-\beta _{4}-\beta _{6})q^{3}+(1+\cdots)q^{4}+\cdots\)
525.2.g.f \(16\) \(4.192\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+\beta _{4}q^{3}+(1-\beta _{5})q^{4}-\beta _{8}q^{6}+\cdots\)
525.2.i.a \(2\) \(4.192\) \(\Q(\sqrt{-3}) \) None None \(-2\) \(1\) \(0\) \(1\) \(q-2\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
525.2.i.b \(2\) \(4.192\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(-1\) \(0\) \(-1\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
525.2.i.c \(2\) \(4.192\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(0\) \(-5\) \(q+(1-\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+(-2-\zeta_{6})q^{7}+\cdots\)
525.2.i.d \(2\) \(4.192\) \(\Q(\sqrt{-3}) \) None None \(1\) \(1\) \(0\) \(1\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
525.2.i.e \(2\) \(4.192\) \(\Q(\sqrt{-3}) \) None None \(2\) \(1\) \(0\) \(5\) \(q+2\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
525.2.i.f \(4\) \(4.192\) \(\Q(\zeta_{12})\) None None \(-2\) \(-2\) \(0\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-1+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
525.2.i.g \(4\) \(4.192\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(-2\) \(0\) \(2\) \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{3}q^{6}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
525.2.i.h \(8\) \(4.192\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(-2\) \(4\) \(0\) \(2\) \(q+(-1-\beta _{1}-\beta _{3}+\beta _{4})q^{2}+\beta _{4}q^{3}+\cdots\)
525.2.i.i \(8\) \(4.192\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(-1\) \(4\) \(0\) \(1\) \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(\beta _{2}-\beta _{3}+2\beta _{5}+\cdots)q^{4}+\cdots\)
525.2.i.j \(8\) \(4.192\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(1\) \(-4\) \(0\) \(-1\) \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(\beta _{2}-\beta _{3}+2\beta _{5}+\cdots)q^{4}+\cdots\)
525.2.i.k \(8\) \(4.192\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(2\) \(-4\) \(0\) \(-2\) \(q+(1+\beta _{1}+\beta _{3}-\beta _{4})q^{2}-\beta _{4}q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
525.2.j.a \(16\) \(4.192\) 16.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{10}+\beta _{13}-\beta _{15})q^{2}+\beta _{7}q^{3}+\cdots\)
525.2.j.b \(24\) \(4.192\) None None \(0\) \(4\) \(0\) \(0\)
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