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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
91.2.a.a \(1\) \(0.727\) \(\Q\) None \(-2\) \(0\) \(-3\) \(-1\) \(+\) \(q-2q^{2}+2q^{4}-3q^{5}-q^{7}-3q^{9}+\cdots\)
91.2.a.b \(1\) \(0.727\) \(\Q\) None \(0\) \(-2\) \(-3\) \(1\) \(+\) \(q-2q^{3}-2q^{4}-3q^{5}+q^{7}+q^{9}+4q^{12}+\cdots\)
91.2.a.c \(2\) \(0.727\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(6\) \(2\) \(-\) \(q+\beta q^{2}-\beta q^{3}+(3+\beta )q^{5}-2q^{6}+q^{7}+\cdots\)
91.2.a.d \(3\) \(0.727\) 3.3.316.1 None \(1\) \(-2\) \(2\) \(-3\) \(-\) \(q+\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
91.2.c.a \(6\) \(0.727\) 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{3}+\beta _{4})q^{2}+\beta _{1}q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
91.2.e.a \(2\) \(0.727\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(1\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+(2-3\zeta_{6})q^{7}+\cdots\)
91.2.e.b \(4\) \(0.727\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(3\) \(0\) \(0\) \(-8\) \(q+(1+\beta _{1}+\beta _{3})q^{2}+(-2\beta _{1}-2\beta _{2}+\cdots)q^{3}+\cdots\)
91.2.e.c \(10\) \(0.727\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-4\) \(0\) \(-2\) \(1\) \(q+(\beta _{1}-\beta _{7})q^{2}+(-\beta _{4}+\beta _{9})q^{3}+(-2+\cdots)q^{4}+\cdots\)
91.2.f.a \(4\) \(0.727\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-3\) \(3\) \(6\) \(-2\) \(q+(-1-\beta _{1}-\beta _{3})q^{2}+(1+\beta _{1}+\beta _{3})q^{3}+\cdots\)
91.2.f.b \(4\) \(0.727\) \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(0\) \(-2\) \(q-\zeta_{12}^{2}q^{2}+(-\zeta_{12}-\zeta_{12}^{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
91.2.f.c \(8\) \(0.727\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(-1\) \(-14\) \(4\) \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
91.2.g.a \(2\) \(0.727\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-6\) \(-3\) \(-5\) \(q-\zeta_{6}q^{2}-3q^{3}+(1-\zeta_{6})q^{4}+(-3+\cdots)q^{5}+\cdots\)
91.2.g.b \(12\) \(0.727\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(2\) \(-2\) \(1\) \(9\) \(q+(-\beta _{1}-\beta _{5}+\beta _{11})q^{2}+(\beta _{3}-\beta _{11})q^{3}+\cdots\)
91.2.h.a \(2\) \(0.727\) \(\Q(\sqrt{-3}) \) None \(2\) \(3\) \(-3\) \(4\) \(q+q^{2}+3\zeta_{6}q^{3}-q^{4}-3\zeta_{6}q^{5}+3\zeta_{6}q^{6}+\cdots\)
91.2.h.b \(12\) \(0.727\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-4\) \(1\) \(1\) \(-3\) \(q+(\beta _{3}+\beta _{5}-\beta _{11})q^{2}+\beta _{11}q^{3}+(1+\cdots)q^{4}+\cdots\)
91.2.i.a \(12\) \(0.727\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-4\) \(0\) \(0\) \(-8\) \(q-\beta _{8}q^{2}+\beta _{10}q^{3}+(-\beta _{4}+\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)
91.2.k.a \(2\) \(0.727\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(3\) \(-4\) \(q+(1-2\zeta_{6})q^{2}+\zeta_{6}q^{3}-q^{4}+(2-\zeta_{6})q^{5}+\cdots\)
91.2.k.b \(12\) \(0.727\) 12.0.\(\cdots\).1 None \(0\) \(-3\) \(-3\) \(-3\) \(q+\beta _{9}q^{2}+(\beta _{1}+\beta _{4}+\beta _{6})q^{3}+(-1+\cdots)q^{4}+\cdots\)
91.2.q.a \(12\) \(0.727\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}-\beta _{4}-\beta _{6}+\beta _{10})q^{2}+(-\beta _{2}+\cdots)q^{3}+\cdots\)
91.2.r.a \(16\) \(0.727\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-4\) \(0\) \(0\) \(q+\beta _{11}q^{2}+(-1+\beta _{3}+\beta _{6})q^{3}+(1+\cdots)q^{4}+\cdots\)
91.2.u.a \(2\) \(0.727\) \(\Q(\sqrt{-3}) \) None \(-3\) \(-2\) \(-3\) \(-5\) \(q+(-2+\zeta_{6})q^{2}-q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
91.2.u.b \(12\) \(0.727\) 12.0.\(\cdots\).1 None \(0\) \(6\) \(3\) \(3\) \(q-\beta _{10}q^{2}+(1-\beta _{1}+\beta _{3}+\beta _{8})q^{3}+\cdots\)
91.2.w.a \(28\) \(0.727\) None \(-2\) \(0\) \(-6\) \(2\)
91.2.ba.a \(28\) \(0.727\) None \(-2\) \(-6\) \(-6\) \(-6\)
91.2.bb.a \(32\) \(0.727\) None \(-2\) \(-12\) \(-6\) \(-6\)
91.2.bc.a \(32\) \(0.727\) None \(-8\) \(0\) \(0\) \(0\)
91.3.b.a \(1\) \(2.480\) \(\Q\) \(\Q(\sqrt{-91}) \) \(0\) \(0\) \(-3\) \(7\) \(q+4q^{4}-3q^{5}+7q^{7}+9q^{9}-13q^{13}+\cdots\)
91.3.b.b \(1\) \(2.480\) \(\Q\) \(\Q(\sqrt{-91}) \) \(0\) \(0\) \(3\) \(-7\) \(q+4q^{4}+3q^{5}-7q^{7}+9q^{9}+13q^{13}+\cdots\)
91.3.b.c \(4\) \(2.480\) \(\Q(i, \sqrt{26})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}+3q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
91.3.b.d \(6\) \(2.480\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(-8\) \(7\) \(q+\beta _{1}q^{2}+\beta _{1}q^{3}+(-5+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
91.3.b.e \(6\) \(2.480\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(8\) \(-7\) \(q+\beta _{1}q^{2}-\beta _{1}q^{3}+(-5+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots\)
91.3.d.a \(16\) \(2.480\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(2\) \(0\) \(0\) \(2\) \(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(2+\beta _{4})q^{4}+\beta _{3}q^{5}+\cdots\)
91.3.j.a \(28\) \(2.480\) None \(4\) \(0\) \(-20\) \(0\)
91.3.l.a \(34\) \(2.480\) None \(0\) \(-6\) \(0\) \(-19\)
91.3.m.a \(34\) \(2.480\) None \(1\) \(0\) \(-6\) \(14\)
91.3.n.a \(4\) \(2.480\) \(\Q(\sqrt{-3}, \sqrt{-13})\) None \(-2\) \(0\) \(0\) \(-14\) \(q+(-1+\beta _{2})q^{2}-\beta _{1}q^{3}+3\beta _{2}q^{4}+\cdots\)
91.3.n.b \(28\) \(2.480\) None \(0\) \(0\) \(0\) \(12\)
91.3.o.a \(32\) \(2.480\) None \(-2\) \(0\) \(-6\) \(-2\)
91.3.p.a \(34\) \(2.480\) None \(-3\) \(0\) \(0\) \(-8\)
91.3.s.a \(32\) \(2.480\) None \(0\) \(-12\) \(0\) \(0\)
91.3.t.a \(32\) \(2.480\) None \(-6\) \(0\) \(0\) \(18\)
91.3.v.a \(34\) \(2.480\) None \(-2\) \(0\) \(-6\) \(-7\)
91.3.x.a \(68\) \(2.480\) None \(-2\) \(2\) \(-2\) \(-26\)
91.3.y.a \(56\) \(2.480\) None \(-4\) \(0\) \(20\) \(0\)
91.3.z.a \(64\) \(2.480\) None \(-2\) \(-4\) \(-2\) \(-2\)
91.3.bd.a \(68\) \(2.480\) None \(-2\) \(-4\) \(-2\) \(6\)
91.4.a.a \(3\) \(5.369\) 3.3.1384.1 None \(1\) \(1\) \(-22\) \(-21\) \(-\) \(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
91.4.a.b \(4\) \(5.369\) 4.4.5364412.1 None \(-4\) \(-5\) \(-36\) \(28\) \(-\) \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{1}-\beta _{2})q^{3}+\cdots\)
91.4.a.c \(5\) \(5.369\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(7\) \(-5\) \(16\) \(-35\) \(+\) \(q+(1+\beta _{4})q^{2}+(-1-\beta _{3})q^{3}+(10-\beta _{2}+\cdots)q^{4}+\cdots\)
91.4.a.d \(6\) \(5.369\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(2\) \(13\) \(26\) \(42\) \(+\) \(q+\beta _{1}q^{2}+(2-\beta _{4})q^{3}+(2+\beta _{2})q^{4}+\cdots\)
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