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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
175.1.c.a \(2\) \(0.087\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{7}-iq^{8}-q^{9}-q^{11}+\cdots\)
175.1.d.a \(1\) \(0.087\) \(\Q\) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(1\) \(q-q^{2}+q^{7}+q^{8}+q^{9}-q^{11}-q^{14}+\cdots\)
175.1.d.b \(1\) \(0.087\) \(\Q\) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(-1\) \(q+q^{2}-q^{7}-q^{8}+q^{9}-q^{11}-q^{14}+\cdots\)
175.2.a.a \(1\) \(1.397\) \(\Q\) None None \(-2\) \(-1\) \(0\) \(1\) \(+\) \(q-2q^{2}-q^{3}+2q^{4}+2q^{6}+q^{7}-2q^{9}+\cdots\)
175.2.a.b \(1\) \(1.397\) \(\Q\) None None \(0\) \(-1\) \(0\) \(-1\) \(+\) \(q-q^{3}-2q^{4}-q^{7}-2q^{9}-3q^{11}+\cdots\)
175.2.a.c \(1\) \(1.397\) \(\Q\) None None \(2\) \(1\) \(0\) \(-1\) \(-\) \(q+2q^{2}+q^{3}+2q^{4}+2q^{6}-q^{7}-2q^{9}+\cdots\)
175.2.a.d \(2\) \(1.397\) \(\Q(\sqrt{5}) \) None None \(-1\) \(2\) \(0\) \(-2\) \(-\) \(q-\beta q^{2}+(2-2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
175.2.a.e \(2\) \(1.397\) \(\Q(\sqrt{5}) \) None None \(1\) \(-2\) \(0\) \(2\) \(-\) \(q+\beta q^{2}+(-2+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
175.2.a.f \(2\) \(1.397\) \(\Q(\sqrt{17}) \) None None \(1\) \(1\) \(0\) \(2\) \(-\) \(q+\beta q^{2}+(1-\beta )q^{3}+(2+\beta )q^{4}-4q^{6}+\cdots\)
175.2.b.a \(2\) \(1.397\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+2q^{4}-iq^{7}+2q^{9}-3q^{11}+\cdots\)
175.2.b.b \(4\) \(1.397\) \(\Q(i, \sqrt{17})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-3+\beta _{3})q^{4}+\cdots\)
175.2.b.c \(4\) \(1.397\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-2\beta _{1}-2\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
175.2.e.a \(2\) \(1.397\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(1\) \(0\) \(-1\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
175.2.e.b \(2\) \(1.397\) \(\Q(\sqrt{-3}) \) None None \(1\) \(-1\) \(0\) \(1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
175.2.e.c \(4\) \(1.397\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(2\) \(2\) \(0\) \(-2\) \(q+(1+\beta _{1}+\beta _{2})q^{2}+(\beta _{1}-\beta _{2}+\beta _{3})q^{3}+\cdots\)
175.2.e.d \(6\) \(1.397\) 6.0.1783323.2 None None \(-1\) \(3\) \(0\) \(2\) \(q-\beta _{1}q^{2}+(\beta _{3}+\beta _{4}-\beta _{5})q^{3}+(-\beta _{3}+\cdots)q^{4}+\cdots\)
175.2.e.e \(6\) \(1.397\) 6.0.1783323.2 None None \(1\) \(-3\) \(0\) \(-2\) \(q+\beta _{1}q^{2}+(-\beta _{3}-\beta _{4}+\beta _{5})q^{3}+(-\beta _{3}+\cdots)q^{4}+\cdots\)
175.2.f.a \(4\) \(1.397\) \(\Q(i, \sqrt{14})\) \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-2\beta _{2}q^{4}-\beta _{3}q^{7}+4\beta _{2}q^{9}+\cdots\)
175.2.f.b \(4\) \(1.397\) \(\Q(i, \sqrt{14})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+5\beta _{2}q^{4}-\beta _{1}q^{7}+3\beta _{3}q^{8}+\cdots\)
175.2.f.c \(4\) \(1.397\) \(\Q(i, \sqrt{10})\) None None \(4\) \(0\) \(0\) \(-4\) \(q+(1+\beta _{2})q^{2}+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{6}+\cdots\)
175.2.f.d \(8\) \(1.397\) 8.0.\(\cdots\).1 \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{4}+\beta _{6})q^{4}+(\beta _{1}+\beta _{3})q^{7}+\cdots\)
175.2.h.a \(4\) \(1.397\) \(\Q(\zeta_{10})\) None None \(-5\) \(-4\) \(-5\) \(-4\) \(q+(-1-\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
175.2.h.b \(28\) \(1.397\) None None \(6\) \(4\) \(8\) \(-28\)
175.2.h.c \(32\) \(1.397\) None None \(-3\) \(-4\) \(1\) \(32\)
175.2.k.a \(8\) \(1.397\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{3}q^{2}-\zeta_{24}^{4}q^{3}+(1-\zeta_{24}-\zeta_{24}^{6}+\cdots)q^{4}+\cdots\)
175.2.k.b \(12\) \(1.397\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{10}-\beta _{11})q^{3}+(1+\beta _{3}+\cdots)q^{4}+\cdots\)
175.2.n.a \(56\) \(1.397\) None None \(0\) \(0\) \(-6\) \(0\)
175.2.o.a \(4\) \(1.397\) \(\Q(\zeta_{12})\) None None \(-2\) \(4\) \(0\) \(10\) \(q+(-1+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(1+\zeta_{12}+\cdots)q^{3}+\cdots\)
175.2.o.b \(4\) \(1.397\) \(\Q(\zeta_{12})\) None None \(4\) \(2\) \(0\) \(0\) \(q+(1-\zeta_{12})q^{2}+(\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
175.2.o.c \(8\) \(1.397\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{7}q^{2}+(-2\zeta_{24}+\zeta_{24}^{5})q^{3}+\cdots\)
175.2.o.d \(24\) \(1.397\) None None \(0\) \(0\) \(0\) \(0\)
175.2.q.a \(144\) \(1.397\) None None \(-3\) \(-3\) \(-3\) \(-22\)
175.2.s.a \(144\) \(1.397\) None None \(-16\) \(0\) \(0\) \(-14\)
175.2.t.a \(144\) \(1.397\) None None \(-5\) \(-5\) \(-3\) \(0\)
175.2.x.a \(288\) \(1.397\) None None \(-8\) \(-24\) \(-30\) \(-10\)
175.3.c.a \(2\) \(4.768\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{2}-5q^{4}+7iq^{7}-3iq^{8}-9q^{9}+\cdots\)
175.3.c.b \(4\) \(4.768\) \(\Q(i, \sqrt{21})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{2})q^{2}+(-5+3\beta _{3})q^{4}+7\beta _{2}q^{7}+\cdots\)
175.3.c.c \(4\) \(4.768\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{6}+(-\beta _{1}+3\beta _{3})q^{7}+\cdots\)
175.3.c.d \(4\) \(4.768\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+3q^{4}+\beta _{2}q^{6}-7\beta _{1}q^{7}+\cdots\)
175.3.c.e \(8\) \(4.768\) 8.0.\(\cdots\).11 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}-\beta _{3}q^{3}+(-3+2\beta _{1})q^{4}+\cdots\)
175.3.d.a \(1\) \(4.768\) \(\Q\) \(\Q(\sqrt{-7}) \) None \(3\) \(0\) \(0\) \(7\) \(q+3q^{2}+5q^{4}+7q^{7}+3q^{8}+9q^{9}+\cdots\)
175.3.d.b \(2\) \(4.768\) \(\Q(\sqrt{-10}) \) None None \(-6\) \(0\) \(0\) \(6\) \(q-3q^{2}+\beta q^{3}+5q^{4}-3\beta q^{6}+(3+2\beta )q^{7}+\cdots\)
175.3.d.c \(2\) \(4.768\) \(\Q(\sqrt{-5}) \) None None \(-4\) \(0\) \(0\) \(4\) \(q-2q^{2}+\beta q^{3}-2\beta q^{6}+(2-3\beta )q^{7}+\cdots\)
175.3.d.d \(2\) \(4.768\) \(\Q(\sqrt{21}) \) \(\Q(\sqrt{-7}) \) None \(-3\) \(0\) \(0\) \(14\) \(q+(-1-\beta )q^{2}+(2+3\beta )q^{4}+7q^{7}+\cdots\)
175.3.d.e \(2\) \(4.768\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-4q^{4}-7iq^{7}+8q^{9}-13q^{11}+\cdots\)
175.3.d.f \(2\) \(4.768\) \(\Q(\sqrt{-5}) \) None None \(2\) \(0\) \(0\) \(-14\) \(q+q^{2}+\beta q^{3}-3q^{4}+\beta q^{6}-7q^{7}+\cdots\)
175.3.d.g \(2\) \(4.768\) \(\Q(\sqrt{21}) \) \(\Q(\sqrt{-7}) \) None \(3\) \(0\) \(0\) \(-14\) \(q+(1+\beta )q^{2}+(2+3\beta )q^{4}-7q^{7}+(13+\cdots)q^{8}+\cdots\)
175.3.d.h \(2\) \(4.768\) \(\Q(\sqrt{-10}) \) None None \(6\) \(0\) \(0\) \(-6\) \(q+3q^{2}+\beta q^{3}+5q^{4}+3\beta q^{6}+(-3+\cdots)q^{7}+\cdots\)
175.3.d.i \(4\) \(4.768\) 4.0.1163520.6 None None \(-4\) \(0\) \(0\) \(4\) \(q+(-1+\beta _{3})q^{2}-\beta _{1}q^{3}+(3-2\beta _{3})q^{4}+\cdots\)
175.3.d.j \(4\) \(4.768\) 4.0.1163520.6 None None \(4\) \(0\) \(0\) \(-4\) \(q+(1-\beta _{3})q^{2}-\beta _{1}q^{3}+(3-2\beta _{3})q^{4}+\cdots\)
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