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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
786.2.a.a \(1\) \(6.276\) \(\Q\) None \(-1\) \(-1\) \(-2\) \(2\) \(+\) \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+2q^{7}+\cdots\)
786.2.a.b \(1\) \(6.276\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(-3\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-3q^{7}+\cdots\)
786.2.a.c \(1\) \(6.276\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(-1\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
786.2.a.d \(1\) \(6.276\) \(\Q\) None \(-1\) \(-1\) \(2\) \(0\) \(-\) \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots\)
786.2.a.e \(1\) \(6.276\) \(\Q\) None \(-1\) \(-1\) \(4\) \(-1\) \(+\) \(q-q^{2}-q^{3}+q^{4}+4q^{5}+q^{6}-q^{7}+\cdots\)
786.2.a.f \(1\) \(6.276\) \(\Q\) None \(-1\) \(1\) \(-3\) \(5\) \(-\) \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}+5q^{7}+\cdots\)
786.2.a.g \(1\) \(6.276\) \(\Q\) None \(-1\) \(1\) \(-2\) \(-2\) \(+\) \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots\)
786.2.a.h \(1\) \(6.276\) \(\Q\) None \(-1\) \(1\) \(1\) \(-5\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-5q^{7}+\cdots\)
786.2.a.i \(1\) \(6.276\) \(\Q\) None \(1\) \(-1\) \(-4\) \(3\) \(+\) \(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}+3q^{7}+\cdots\)
786.2.a.j \(1\) \(6.276\) \(\Q\) None \(1\) \(-1\) \(-1\) \(-3\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-3q^{7}+\cdots\)
786.2.a.k \(1\) \(6.276\) \(\Q\) None \(1\) \(-1\) \(4\) \(-4\) \(-\) \(q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}-4q^{7}+\cdots\)
786.2.a.l \(1\) \(6.276\) \(\Q\) None \(1\) \(1\) \(-3\) \(-3\) \(+\) \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-3q^{7}+\cdots\)
786.2.a.m \(1\) \(6.276\) \(\Q\) None \(1\) \(1\) \(1\) \(3\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+3q^{7}+\cdots\)
786.2.a.n \(3\) \(6.276\) 3.3.316.1 None \(-3\) \(3\) \(2\) \(3\) \(-\) \(q-q^{2}+q^{3}+q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
786.2.a.o \(3\) \(6.276\) 3.3.961.1 None \(3\) \(-3\) \(1\) \(1\) \(-\) \(q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}+\beta _{1}q^{7}+\cdots\)
786.2.a.p \(4\) \(6.276\) 4.4.64268.1 None \(4\) \(4\) \(0\) \(1\) \(-\) \(q+q^{2}+q^{3}+q^{4}-\beta _{3}q^{5}+q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
786.2.c.a \(22\) \(6.276\) None \(-22\) \(1\) \(0\) \(-2\)
786.2.c.b \(22\) \(6.276\) None \(22\) \(1\) \(0\) \(-2\)
786.2.e.a \(4\) \(6.276\) \(\Q(\zeta_{10})\) None \(1\) \(-1\) \(-2\) \(0\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{3}+\cdots\)
786.2.e.b \(4\) \(6.276\) \(\Q(\zeta_{10})\) None \(1\) \(-1\) \(4\) \(0\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{3}+\cdots\)
786.2.e.c \(4\) \(6.276\) \(\Q(\zeta_{10})\) None \(1\) \(1\) \(-4\) \(-4\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{3}+\cdots\)
786.2.e.d \(4\) \(6.276\) \(\Q(\zeta_{10})\) None \(1\) \(1\) \(6\) \(-2\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{3}+\cdots\)
786.2.e.e \(8\) \(6.276\) 8.0.\(\cdots\).1 None \(-2\) \(2\) \(-8\) \(-3\) \(q+\beta _{4}q^{2}-\beta _{6}q^{3}+\beta _{6}q^{4}+(-1+\beta _{4}+\cdots)q^{5}+\cdots\)
786.2.e.f \(12\) \(6.276\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(3\) \(3\) \(-4\) \(9\) \(q+\beta _{8}q^{2}+\beta _{9}q^{3}-\beta _{9}q^{4}+\beta _{5}q^{5}+\cdots\)
786.2.e.g \(16\) \(6.276\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-4\) \(4\) \(8\) \(-4\) \(q+\beta _{7}q^{2}+(1+\beta _{3}+\beta _{4}+\beta _{7})q^{3}+(-1+\cdots)q^{4}+\cdots\)
786.2.e.h \(16\) \(6.276\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(4\) \(-4\) \(0\) \(-1\) \(q+\beta _{10}q^{2}-\beta _{12}q^{3}-\beta _{12}q^{4}+(\beta _{9}+\cdots)q^{5}+\cdots\)
786.2.e.i \(20\) \(6.276\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-5\) \(-5\) \(8\) \(-3\) \(q+\beta _{6}q^{2}+(-1-\beta _{4}-\beta _{5}-\beta _{6})q^{3}+\cdots\)
786.2.g.a \(88\) \(6.276\) None \(-22\) \(-1\) \(0\) \(2\)
786.2.g.b \(88\) \(6.276\) None \(22\) \(-1\) \(0\) \(2\)
786.2.i.a \(60\) \(6.276\) None \(-5\) \(-5\) \(8\) \(7\)
786.2.i.b \(60\) \(6.276\) None \(5\) \(5\) \(-2\) \(3\)
786.2.i.c \(72\) \(6.276\) None \(-6\) \(6\) \(0\) \(3\)
786.2.i.d \(72\) \(6.276\) None \(6\) \(-6\) \(2\) \(-1\)
786.2.k.a \(264\) \(6.276\) None \(-22\) \(-1\) \(0\) \(2\)
786.2.k.b \(264\) \(6.276\) None \(22\) \(-1\) \(0\) \(2\)
786.2.m.a \(240\) \(6.276\) None \(-5\) \(-5\) \(2\) \(-3\)
786.2.m.b \(240\) \(6.276\) None \(5\) \(5\) \(-8\) \(3\)
786.2.m.c \(288\) \(6.276\) None \(-6\) \(6\) \(-2\) \(1\)
786.2.m.d \(288\) \(6.276\) None \(6\) \(-6\) \(0\) \(7\)
786.2.o.a \(1056\) \(6.276\) None \(-22\) \(1\) \(0\) \(-2\)
786.2.o.b \(1056\) \(6.276\) None \(22\) \(1\) \(0\) \(-2\)
786.3.b.a \(88\) \(21.417\) None \(0\) \(-4\) \(0\) \(8\)
786.3.d.a \(44\) \(21.417\) None \(0\) \(0\) \(8\) \(-16\)
786.4.a.a \(1\) \(46.376\) \(\Q\) None \(-2\) \(-3\) \(2\) \(-22\) \(+\) \(q-2q^{2}-3q^{3}+4q^{4}+2q^{5}+6q^{6}+\cdots\)
786.4.a.b \(1\) \(46.376\) \(\Q\) None \(2\) \(3\) \(-7\) \(-15\) \(-\) \(q+2q^{2}+3q^{3}+4q^{4}-7q^{5}+6q^{6}+\cdots\)
786.4.a.c \(5\) \(46.376\) 5.5.98582301.1 None \(10\) \(15\) \(-12\) \(-44\) \(-\) \(q+2q^{2}+3q^{3}+4q^{4}+(-2-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
786.4.a.d \(6\) \(46.376\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-12\) \(-18\) \(-1\) \(23\) \(+\) \(q-2q^{2}-3q^{3}+4q^{4}+(-1-\beta _{4}-\beta _{5})q^{5}+\cdots\)
786.4.a.e \(7\) \(46.376\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-14\) \(21\) \(-1\) \(-47\) \(-\) \(q-2q^{2}+3q^{3}+4q^{4}+(-1-\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
786.4.a.f \(7\) \(46.376\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(14\) \(-21\) \(-21\) \(14\) \(-\) \(q+2q^{2}-3q^{3}+4q^{4}+(-3+\beta _{3})q^{5}+\cdots\)
786.4.a.g \(8\) \(46.376\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-16\) \(-24\) \(1\) \(22\) \(-\) \(q-2q^{2}-3q^{3}+4q^{4}-\beta _{3}q^{5}+6q^{6}+\cdots\)
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