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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
150.2.a.a \(1\) \(1.198\) \(\Q\) None \(-1\) \(-1\) \(0\) \(2\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots\)
150.2.a.b \(1\) \(1.198\) \(\Q\) None \(1\) \(-1\) \(0\) \(4\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+4q^{7}+q^{8}+\cdots\)
150.2.a.c \(1\) \(1.198\) \(\Q\) None \(1\) \(1\) \(0\) \(-2\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\)
150.2.c.a \(2\) \(1.198\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots\)
150.2.e.a \(4\) \(1.198\) \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(4\) \(q+\zeta_{8}q^{2}+(1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)
150.2.e.b \(8\) \(1.198\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}+\zeta_{24}^{5})q^{2}+(-2\zeta_{24}^{3}+\zeta_{24}^{7})q^{3}+\cdots\)
150.2.g.a \(4\) \(1.198\) \(\Q(\zeta_{10})\) None \(-1\) \(1\) \(5\) \(6\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
150.2.g.b \(4\) \(1.198\) \(\Q(\zeta_{10})\) None \(1\) \(1\) \(5\) \(8\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{3}+\cdots\)
150.2.g.c \(8\) \(1.198\) 8.0.1064390625.3 None \(2\) \(-2\) \(-4\) \(-2\) \(q-\beta _{2}q^{2}+\beta _{5}q^{3}+\beta _{5}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
150.2.h.a \(8\) \(1.198\) \(\Q(\zeta_{20})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}q^{2}-\zeta_{20}^{7}q^{3}+\zeta_{20}^{2}q^{4}+(\zeta_{20}+\cdots)q^{5}+\cdots\)
150.2.h.b \(16\) \(1.198\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(4\) \(0\) \(q+\beta _{8}q^{2}+\beta _{6}q^{3}-\beta _{10}q^{4}+(1+\beta _{3}+\cdots)q^{5}+\cdots\)
150.2.l.a \(80\) \(1.198\) None \(0\) \(4\) \(0\) \(4\)
150.3.b.a \(4\) \(4.087\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}+(-\zeta_{8}-2\zeta_{8}^{3})q^{3}+2q^{4}+\cdots\)
150.3.b.b \(8\) \(4.087\) 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}-\beta _{3}q^{3}+2q^{4}+(-1-\beta _{4}+\cdots)q^{6}+\cdots\)
150.3.d.a \(2\) \(4.087\) \(\Q(\sqrt{-2}) \) None \(0\) \(-2\) \(0\) \(-14\) \(q+\beta q^{2}+(-1-2\beta )q^{3}-2q^{4}+(4-\beta )q^{6}+\cdots\)
150.3.d.b \(2\) \(4.087\) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(14\) \(q+\beta q^{2}+(1-2\beta )q^{3}-2q^{4}+(4+\beta )q^{6}+\cdots\)
150.3.d.c \(4\) \(4.087\) \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(-4\) \(0\) \(-8\) \(q+\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}-2q^{4}+\cdots\)
150.3.d.d \(4\) \(4.087\) \(\Q(\sqrt{-2}, \sqrt{-17})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}-\beta _{1}q^{3}-2q^{4}+(-1+\beta _{3})q^{6}+\cdots\)
150.3.f.a \(4\) \(4.087\) \(\Q(i, \sqrt{6})\) None \(-4\) \(0\) \(0\) \(-24\) \(q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+\cdots\)
150.3.f.b \(4\) \(4.087\) \(\Q(i, \sqrt{6})\) None \(-4\) \(0\) \(0\) \(16\) \(q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+\cdots\)
150.3.f.c \(4\) \(4.087\) \(\Q(i, \sqrt{6})\) None \(4\) \(0\) \(0\) \(24\) \(q+(1-\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
150.3.i.a \(80\) \(4.087\) None \(0\) \(0\) \(0\) \(0\)
150.3.j.a \(80\) \(4.087\) None \(0\) \(-4\) \(0\) \(-8\)
150.3.k.a \(32\) \(4.087\) None \(8\) \(0\) \(0\) \(8\)
150.3.k.b \(48\) \(4.087\) None \(-12\) \(0\) \(0\) \(8\)
150.4.a.a \(1\) \(8.850\) \(\Q\) None \(-2\) \(-3\) \(0\) \(-1\) \(-\) \(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}-q^{7}+\cdots\)
150.4.a.b \(1\) \(8.850\) \(\Q\) None \(-2\) \(-3\) \(0\) \(4\) \(+\) \(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}+4q^{7}+\cdots\)
150.4.a.c \(1\) \(8.850\) \(\Q\) None \(-2\) \(3\) \(0\) \(-23\) \(-\) \(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}-23q^{7}+\cdots\)
150.4.a.d \(1\) \(8.850\) \(\Q\) None \(-2\) \(3\) \(0\) \(2\) \(+\) \(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+2q^{7}+\cdots\)
150.4.a.e \(1\) \(8.850\) \(\Q\) None \(2\) \(-3\) \(0\) \(-32\) \(-\) \(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}-2^{5}q^{7}+\cdots\)
150.4.a.f \(1\) \(8.850\) \(\Q\) None \(2\) \(-3\) \(0\) \(-2\) \(+\) \(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}-2q^{7}+\cdots\)
150.4.a.g \(1\) \(8.850\) \(\Q\) None \(2\) \(-3\) \(0\) \(23\) \(+\) \(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+23q^{7}+\cdots\)
150.4.a.h \(1\) \(8.850\) \(\Q\) None \(2\) \(3\) \(0\) \(1\) \(+\) \(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}+q^{7}+\cdots\)
150.4.a.i \(1\) \(8.850\) \(\Q\) None \(2\) \(3\) \(0\) \(16\) \(+\) \(q+2q^{2}+3q^{3}+4q^{4}+6q^{6}+2^{4}q^{7}+\cdots\)
150.4.c.a \(2\) \(8.850\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}+3iq^{3}-4q^{4}-6q^{6}-2^{5}iq^{7}+\cdots\)
150.4.c.b \(2\) \(8.850\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}+3iq^{3}-4q^{4}-6q^{6}+23iq^{7}+\cdots\)
150.4.c.c \(2\) \(8.850\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}-3iq^{3}-4q^{4}+6q^{6}-4iq^{7}+\cdots\)
150.4.c.d \(2\) \(8.850\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}-3iq^{3}-4q^{4}+6q^{6}+2^{4}iq^{7}+\cdots\)
150.4.c.e \(2\) \(8.850\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}-3iq^{3}-4q^{4}+6q^{6}+iq^{7}+\cdots\)
150.4.e.a \(4\) \(8.850\) \(\Q(\zeta_{8})\) None \(0\) \(-12\) \(0\) \(72\) \(q+2\zeta_{8}q^{2}+(-3-3\zeta_{8}^{2}+3\zeta_{8}^{3})q^{3}+\cdots\)
150.4.e.b \(4\) \(8.850\) \(\Q(\zeta_{8})\) None \(0\) \(12\) \(0\) \(-72\) \(q+2\zeta_{8}q^{2}+(3+3\zeta_{8}^{2}+3\zeta_{8}^{3})q^{3}+\cdots\)
150.4.e.c \(12\) \(8.850\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(-8\) \(0\) \(-12\) \(q-\beta _{1}q^{2}+(-1-\beta _{4}+\beta _{9})q^{3}+4\beta _{4}q^{4}+\cdots\)
150.4.e.d \(16\) \(8.850\) 16.0.\(\cdots\).10 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{13}q^{2}-\beta _{5}q^{3}+4\beta _{7}q^{4}+(2-2\beta _{2}+\cdots)q^{6}+\cdots\)
150.4.g.a \(12\) \(8.850\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-6\) \(9\) \(-10\) \(-44\) \(q-2\beta _{1}q^{2}+(3-3\beta _{1}+3\beta _{3}+3\beta _{5}+\cdots)q^{3}+\cdots\)
150.4.g.b \(16\) \(8.850\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-8\) \(-12\) \(15\) \(46\) \(q-2\beta _{6}q^{2}+(-3+3\beta _{4}+3\beta _{5}+3\beta _{6}+\cdots)q^{3}+\cdots\)
150.4.g.c \(16\) \(8.850\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(8\) \(-12\) \(5\) \(12\) \(q+(2-2\beta _{1}+2\beta _{2}-2\beta _{3})q^{2}-3\beta _{1}q^{3}+\cdots\)
150.4.g.d \(20\) \(8.850\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(10\) \(15\) \(-16\) \(-10\) \(q-2\beta _{3}q^{2}+3\beta _{5}q^{3}-4\beta _{5}q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
150.4.h.a \(24\) \(8.850\) None \(0\) \(0\) \(0\) \(0\)
150.4.h.b \(32\) \(8.850\) None \(0\) \(0\) \(-4\) \(0\)
150.4.l.a \(240\) \(8.850\) None \(0\) \(-8\) \(0\) \(-12\)
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