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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
285.1.n.a \(2\) \(0.142\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-15}) \) None \(-1\) \(1\) \(1\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{6}+\cdots\)
285.1.n.b \(2\) \(0.142\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-15}) \) None \(1\) \(-1\) \(-1\) \(0\) \(q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{6}+\cdots\)
285.1.bd.a \(6\) \(0.142\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-15}) \) None \(-3\) \(0\) \(0\) \(0\) \(q+(\zeta_{18}^{4}+\zeta_{18}^{6})q^{2}+\zeta_{18}^{2}q^{3}+(-\zeta_{18}+\cdots)q^{4}+\cdots\)
285.1.bd.b \(6\) \(0.142\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-15}) \) None \(3\) \(0\) \(0\) \(0\) \(q+(-\zeta_{18}^{4}-\zeta_{18}^{6})q^{2}-\zeta_{18}^{2}q^{3}+\cdots\)
285.2.a.a \(1\) \(2.276\) \(\Q\) None None \(-1\) \(1\) \(-1\) \(-2\) \(+\) \(q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}-2q^{7}+\cdots\)
285.2.a.b \(1\) \(2.276\) \(\Q\) None None \(1\) \(-1\) \(-1\) \(-2\) \(+\) \(q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}-2q^{7}+\cdots\)
285.2.a.c \(1\) \(2.276\) \(\Q\) None None \(1\) \(-1\) \(1\) \(4\) \(-\) \(q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}+4q^{7}+\cdots\)
285.2.a.d \(2\) \(2.276\) \(\Q(\sqrt{7}) \) None None \(0\) \(-2\) \(2\) \(-2\) \(-\) \(q+\beta q^{2}-q^{3}+5q^{4}+q^{5}-\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
285.2.a.e \(2\) \(2.276\) \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(2\) \(-2\) \(-\) \(q+\beta q^{2}+q^{3}+q^{4}+q^{5}+\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
285.2.a.f \(2\) \(2.276\) \(\Q(\sqrt{2}) \) None None \(2\) \(-2\) \(-2\) \(4\) \(-\) \(q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}-q^{5}+\cdots\)
285.2.a.g \(2\) \(2.276\) \(\Q(\sqrt{2}) \) None None \(2\) \(2\) \(-2\) \(0\) \(-\) \(q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}-q^{5}+\cdots\)
285.2.b.a \(4\) \(2.276\) \(\Q(\sqrt{-3}, \sqrt{5})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+\beta _{2}q^{3}-q^{4}-\beta _{1}q^{5}-3q^{6}+\cdots\)
285.2.b.b \(16\) \(2.276\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{9}q^{2}-\beta _{3}q^{3}+(-2+\beta _{7})q^{4}-\beta _{2}q^{5}+\cdots\)
285.2.b.c \(16\) \(2.276\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{11}q^{2}-\beta _{12}q^{3}-\beta _{4}q^{4}+(-\beta _{5}+\cdots)q^{5}+\cdots\)
285.2.c.a \(6\) \(2.276\) 6.0.350464.1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}-\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{4}+\cdots\)
285.2.c.b \(14\) \(2.276\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None None \(0\) \(0\) \(2\) \(0\) \(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(-2+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots\)
285.2.h.a \(28\) \(2.276\) None None \(0\) \(0\) \(0\) \(-16\)
285.2.i.a \(2\) \(2.276\) \(\Q(\sqrt{-3}) \) None None \(-2\) \(-1\) \(1\) \(-4\) \(q+(-2+2\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots\)
285.2.i.b \(2\) \(2.276\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-1\) \(4\) \(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
285.2.i.c \(2\) \(2.276\) \(\Q(\sqrt{-3}) \) None None \(2\) \(1\) \(1\) \(-4\) \(q+(2-2\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots\)
285.2.i.d \(4\) \(2.276\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(-2\) \(2\) \(2\) \(-4\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}+(1+\beta _{2})q^{3}+\cdots\)
285.2.i.e \(4\) \(2.276\) \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(1\) \(-2\) \(2\) \(12\) \(q+\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
285.2.i.f \(10\) \(2.276\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(1\) \(5\) \(-5\) \(4\) \(q+(-\beta _{1}-\beta _{2})q^{2}-\beta _{4}q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots\)
285.2.k.a \(4\) \(2.276\) \(\Q(\zeta_{12})\) None None \(-4\) \(0\) \(-4\) \(-6\) \(q+(-1+\zeta_{12}^{3})q^{2}+(1-2\zeta_{12}^{2})q^{3}+\cdots\)
285.2.k.b \(4\) \(2.276\) \(\Q(\zeta_{12})\) None None \(4\) \(0\) \(4\) \(-6\) \(q+(1+\zeta_{12}^{3})q^{2}+(2\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
285.2.k.c \(28\) \(2.276\) None None \(0\) \(-2\) \(0\) \(0\)
285.2.k.d \(36\) \(2.276\) None None \(0\) \(-2\) \(0\) \(4\)
285.2.m.a \(4\) \(2.276\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(-4\) \(4\) \(q+\zeta_{8}q^{2}-\zeta_{8}^{3}q^{3}-\zeta_{8}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
285.2.m.b \(36\) \(2.276\) None None \(0\) \(0\) \(0\) \(0\)
285.2.p.a \(4\) \(2.276\) \(\Q(\zeta_{12})\) None None \(0\) \(6\) \(0\) \(4\) \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{2}+(2-\zeta_{12}^{2})q^{3}+\cdots\)
285.2.p.b \(52\) \(2.276\) None None \(0\) \(-12\) \(0\) \(12\)
285.2.q.a \(4\) \(2.276\) \(\Q(\sqrt{-3}, \sqrt{5})\) \(\Q(\sqrt{-15}) \) None \(-3\) \(6\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{2})q^{2}+(2+\beta _{3})q^{3}+(1+3\beta _{1}+\cdots)q^{4}+\cdots\)
285.2.q.b \(4\) \(2.276\) \(\Q(\sqrt{-3}, \sqrt{5})\) \(\Q(\sqrt{-15}) \) None \(3\) \(-6\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{2})q^{2}+(-2-\beta _{3})q^{3}+(1+3\beta _{1}+\cdots)q^{4}+\cdots\)
285.2.q.c \(8\) \(2.276\) 8.0.3317760000.3 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(-2+2\beta _{3})q^{4}-\beta _{2}q^{5}+\cdots\)
285.2.q.d \(56\) \(2.276\) None None \(0\) \(0\) \(0\) \(0\)
285.2.r.a \(40\) \(2.276\) None None \(0\) \(0\) \(-2\) \(0\)
285.2.u.a \(12\) \(2.276\) 12.0.\(\cdots\).1 None None \(3\) \(0\) \(0\) \(6\) \(q+(1-\beta _{5}-\beta _{8}+\beta _{9}-\beta _{11})q^{2}+\beta _{10}q^{3}+\cdots\)
285.2.u.b \(18\) \(2.276\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(-3\) \(0\) \(0\) \(6\) \(q-\beta _{4}q^{2}+\beta _{5}q^{3}+(-\beta _{2}-\beta _{5}-\beta _{8}+\cdots)q^{4}+\cdots\)
285.2.u.c \(24\) \(2.276\) None None \(0\) \(0\) \(0\) \(-6\)
285.2.u.d \(30\) \(2.276\) None None \(0\) \(0\) \(0\) \(-6\)
285.2.v.a \(144\) \(2.276\) None None \(0\) \(-2\) \(0\) \(-16\)
285.2.x.a \(80\) \(2.276\) None None \(0\) \(0\) \(4\) \(8\)
285.2.z.a \(156\) \(2.276\) None None \(0\) \(6\) \(0\) \(0\)
285.2.be.a \(120\) \(2.276\) None None \(0\) \(0\) \(0\) \(0\)
285.2.bf.a \(12\) \(2.276\) 12.0.\(\cdots\).1 \(\Q(\sqrt{-15}) \) None \(-9\) \(0\) \(0\) \(0\) \(q+(-1+\beta _{4}-\beta _{5}-\beta _{6}+\beta _{11})q^{2}+\cdots\)
285.2.bf.b \(12\) \(2.276\) 12.0.\(\cdots\).1 \(\Q(\sqrt{-15}) \) None \(9\) \(0\) \(0\) \(0\) \(q+(1-\beta _{4}-\beta _{5}-\beta _{6}-\beta _{8}-\beta _{10}+\beta _{11})q^{2}+\cdots\)
285.2.bf.c \(192\) \(2.276\) None None \(0\) \(0\) \(0\) \(0\)
285.2.bh.a \(240\) \(2.276\) None None \(0\) \(0\) \(0\) \(-12\)
285.2.bi.a \(432\) \(2.276\) None None \(0\) \(-12\) \(0\) \(-12\)
285.3.d.a \(48\) \(7.766\) None None \(0\) \(0\) \(0\) \(0\)
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