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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
276.1.h.a \(1\) \(0.138\) \(\Q\) \(\Q(\sqrt{-23}) \), \(\Q(\sqrt{-69}) \) \(\Q(\sqrt{3}) \) \(-1\) \(1\) \(0\) \(0\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
276.1.h.b \(1\) \(0.138\) \(\Q\) \(\Q(\sqrt{-23}) \), \(\Q(\sqrt{-69}) \) \(\Q(\sqrt{3}) \) \(1\) \(-1\) \(0\) \(0\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
276.1.h.c \(2\) \(0.138\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-23}) \) None \(-1\) \(1\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots\)
276.1.h.d \(2\) \(0.138\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-23}) \) None \(1\) \(-1\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-q^{6}-q^{8}+\cdots\)
276.2.a.a \(2\) \(2.204\) \(\Q(\sqrt{10}) \) None None \(0\) \(-2\) \(0\) \(4\) \(-\) \(q-q^{3}+\beta q^{5}+(2-\beta )q^{7}+q^{9}+4q^{13}+\cdots\)
276.2.a.b \(2\) \(2.204\) \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(4\) \(0\) \(-\) \(q+q^{3}+(2+\beta )q^{5}+\beta q^{7}+q^{9}-4\beta q^{11}+\cdots\)
276.2.c.a \(22\) \(2.204\) None None \(0\) \(0\) \(0\) \(0\)
276.2.c.b \(22\) \(2.204\) None None \(0\) \(0\) \(0\) \(0\)
276.2.e.a \(24\) \(2.204\) None None \(4\) \(0\) \(0\) \(0\)
276.2.g.a \(8\) \(2.204\) 8.0.\(\cdots\).7 None None \(0\) \(2\) \(0\) \(0\) \(q+\beta _{4}q^{3}+\beta _{5}q^{5}-\beta _{7}q^{7}+(-1-\beta _{3}+\cdots)q^{9}+\cdots\)
276.2.i.a \(20\) \(2.204\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(-2\) \(-4\) \(0\) \(q+\beta _{17}q^{3}+(\beta _{3}+\beta _{4}-\beta _{9}-\beta _{10}+\beta _{15}+\cdots)q^{5}+\cdots\)
276.2.i.b \(20\) \(2.204\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(2\) \(0\) \(-4\) \(q-\beta _{5}q^{3}+(1-\beta _{3}+\beta _{5}+\beta _{7}+\beta _{10}+\cdots)q^{5}+\cdots\)
276.2.k.a \(80\) \(2.204\) None None \(0\) \(-2\) \(0\) \(0\)
276.2.m.a \(240\) \(2.204\) None None \(-4\) \(0\) \(0\) \(0\)
276.2.o.a \(440\) \(2.204\) None None \(0\) \(0\) \(0\) \(0\)
276.3.b.a \(8\) \(7.520\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}-\beta _{2}q^{5}+(\beta _{2}+\beta _{7})q^{7}+3q^{9}+\cdots\)
276.3.d.a \(14\) \(7.520\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(0\) \(4\) \(0\) \(-4\) \(q+\beta _{1}q^{3}-\beta _{5}q^{5}-\beta _{2}q^{7}+(1+\beta _{3}+\cdots)q^{9}+\cdots\)
276.3.f.a \(4\) \(7.520\) \(\Q(\sqrt{-3}, \sqrt{-23})\) None None \(-4\) \(0\) \(4\) \(0\) \(q+(-1-\beta _{1})q^{2}+\beta _{1}q^{3}+(-2+2\beta _{1}+\cdots)q^{4}+\cdots\)
276.3.f.b \(40\) \(7.520\) None None \(4\) \(0\) \(4\) \(0\)
276.3.h.a \(2\) \(7.520\) \(\Q(\sqrt{6}) \) \(\Q(\sqrt{-69}) \) None \(-4\) \(-6\) \(0\) \(0\) \(q-2q^{2}-3q^{3}+4q^{4}+3\beta q^{5}+6q^{6}+\cdots\)
276.3.h.b \(2\) \(7.520\) \(\Q(\sqrt{46}) \) \(\Q(\sqrt{-69}) \) None \(-4\) \(6\) \(0\) \(0\) \(q-2q^{2}+3q^{3}+4q^{4}+\beta q^{5}-6q^{6}+\cdots\)
276.3.h.c \(2\) \(7.520\) \(\Q(\sqrt{46}) \) \(\Q(\sqrt{-69}) \) None \(4\) \(-6\) \(0\) \(0\) \(q+2q^{2}-3q^{3}+4q^{4}+\beta q^{5}-6q^{6}+\cdots\)
276.3.h.d \(2\) \(7.520\) \(\Q(\sqrt{6}) \) \(\Q(\sqrt{-69}) \) None \(4\) \(6\) \(0\) \(0\) \(q+2q^{2}+3q^{3}+4q^{4}+3\beta q^{5}+6q^{6}+\cdots\)
276.3.h.e \(6\) \(7.520\) 6.0.8869743.1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{2}+\beta _{5})q^{2}+(\beta _{2}+2\beta _{5})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
276.3.h.f \(6\) \(7.520\) 6.0.8869743.1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{4})q^{2}+(-\beta _{2}-2\beta _{5})q^{3}+\cdots\)
276.3.h.g \(72\) \(7.520\) None None \(0\) \(0\) \(0\) \(0\)
276.3.j.a \(920\) \(7.520\) None None \(0\) \(0\) \(0\) \(0\)
276.3.l.a \(480\) \(7.520\) None None \(4\) \(0\) \(0\) \(0\)
276.3.n.a \(160\) \(7.520\) None None \(0\) \(2\) \(0\) \(0\)
276.3.p.a \(80\) \(7.520\) None None \(0\) \(0\) \(0\) \(0\)
276.4.a.a \(1\) \(16.285\) \(\Q\) None None \(0\) \(3\) \(2\) \(-22\) \(-\) \(q+3q^{3}+2q^{5}-22q^{7}+9q^{9}-14q^{11}+\cdots\)
276.4.a.b \(1\) \(16.285\) \(\Q\) None None \(0\) \(3\) \(8\) \(34\) \(+\) \(q+3q^{3}+8q^{5}+34q^{7}+9q^{9}+6^{2}q^{11}+\cdots\)
276.4.a.c \(2\) \(16.285\) \(\Q(\sqrt{13}) \) None None \(0\) \(-6\) \(-2\) \(4\) \(-\) \(q-3q^{3}+(-1-\beta )q^{5}+2q^{7}+9q^{9}+\cdots\)
276.4.a.d \(2\) \(16.285\) \(\Q(\sqrt{13}) \) None None \(0\) \(6\) \(14\) \(-10\) \(+\) \(q+3q^{3}+(7+3\beta )q^{5}+(-5+\beta )q^{7}+\cdots\)
276.4.a.e \(4\) \(16.285\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None None \(0\) \(-12\) \(-2\) \(-14\) \(+\) \(q-3q^{3}+\beta _{3}q^{5}+(-3+\beta _{1})q^{7}+9q^{9}+\cdots\)
276.4.e.a \(72\) \(16.285\) None None \(-4\) \(0\) \(0\) \(0\)
276.4.g.a \(24\) \(16.285\) None None \(0\) \(-4\) \(0\) \(0\)
276.5.b.a \(16\) \(28.530\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+\beta _{1}q^{5}+\beta _{7}q^{7}+3^{3}q^{9}+\cdots\)
276.5.d.a \(30\) \(28.530\) None None \(0\) \(-8\) \(0\) \(188\)
276.5.f.a \(88\) \(28.530\) None None \(0\) \(0\) \(-48\) \(0\)
276.6.a.a \(4\) \(44.266\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None None \(0\) \(-36\) \(22\) \(-154\) \(+\) \(q-9q^{3}+(6+\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(-39+\cdots)q^{7}+\cdots\)
276.6.a.b \(4\) \(44.266\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None None \(0\) \(36\) \(-50\) \(-62\) \(+\) \(q+9q^{3}+(-13-\beta _{1}-\beta _{2})q^{5}+(-15+\cdots)q^{7}+\cdots\)
276.6.a.c \(6\) \(44.266\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(0\) \(-54\) \(22\) \(134\) \(-\) \(q-9q^{3}+(4-\beta _{1})q^{5}+(22+\beta _{4})q^{7}+\cdots\)
276.6.a.d \(6\) \(44.266\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(0\) \(54\) \(50\) \(-154\) \(-\) \(q+9q^{3}+(8-\beta _{2})q^{5}+(-26-\beta _{4})q^{7}+\cdots\)
276.6.g.a \(40\) \(44.266\) None None \(0\) \(2\) \(0\) \(0\)
276.7.b.a \(24\) \(63.495\) None None \(0\) \(0\) \(0\) \(0\)
276.7.d.a \(44\) \(63.495\) None None \(0\) \(-20\) \(0\) \(-968\)
276.8.a.a \(5\) \(86.218\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(0\) \(-135\) \(252\) \(414\) \(-\) \(q-3^{3}q^{3}+(50+\beta _{3})q^{5}+(3^{4}+2\beta _{1}+\cdots)q^{7}+\cdots\)
276.8.a.b \(5\) \(86.218\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(0\) \(135\) \(-392\) \(-986\) \(-\) \(q+3^{3}q^{3}+(-78-\beta _{3})q^{5}+(-198+\cdots)q^{7}+\cdots\)
276.8.a.c \(7\) \(86.218\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(0\) \(-189\) \(252\) \(958\) \(+\) \(q-3^{3}q^{3}+(6^{2}+\beta _{1})q^{5}+(137-\beta _{1}+\cdots)q^{7}+\cdots\)
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