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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
287.1.d.a \(3\) \(0.143\) \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-287}) \) None \(-1\) \(-1\) \(0\) \(3\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}-\beta _{1}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
287.1.d.b \(3\) \(0.143\) \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-287}) \) None \(-1\) \(1\) \(0\) \(-3\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}+\beta _{1}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
287.2.a.a \(2\) \(2.292\) \(\Q(\sqrt{5}) \) None None \(-1\) \(-3\) \(-1\) \(2\) \(+\) \(q-\beta q^{2}+(-1-\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
287.2.a.b \(2\) \(2.292\) \(\Q(\sqrt{5}) \) None None \(-1\) \(-1\) \(1\) \(-2\) \(+\) \(q-\beta q^{2}+(-1+\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
287.2.a.c \(3\) \(2.292\) 3.3.257.1 None None \(1\) \(-1\) \(6\) \(3\) \(-\) \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
287.2.a.d \(3\) \(2.292\) \(\Q(\zeta_{14})^+\) None None \(4\) \(5\) \(2\) \(-3\) \(-\) \(q+(1+\beta _{1})q^{2}+(2-\beta _{1})q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)
287.2.a.e \(5\) \(2.292\) 5.5.633117.1 None None \(-1\) \(4\) \(-5\) \(5\) \(-\) \(q-\beta _{1}q^{2}+(1-\beta _{1})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
287.2.a.f \(6\) \(2.292\) 6.6.185257757.1 None None \(-1\) \(-4\) \(-1\) \(-6\) \(-\) \(q-\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+(1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
287.2.c.a \(10\) \(2.292\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(4\) \(0\) \(-10\) \(0\) \(q+\beta _{2}q^{2}+(\beta _{1}-\beta _{7})q^{3}+(1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
287.2.c.b \(12\) \(2.292\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(-4\) \(0\) \(2\) \(0\) \(q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{8})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)
287.2.e.a \(4\) \(2.292\) \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(-1\) \(-2\) \(2\) \(-8\) \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots\)
287.2.e.b \(4\) \(2.292\) \(\Q(\sqrt{-3}, \sqrt{13})\) None None \(0\) \(-1\) \(1\) \(-2\) \(q-\beta _{1}q^{3}+(2+2\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
287.2.e.c \(10\) \(2.292\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(2\) \(2\) \(-2\) \(8\) \(q-\beta _{7}q^{2}+\beta _{8}q^{3}+(\beta _{1}-\beta _{2}-\beta _{6})q^{4}+\cdots\)
287.2.e.d \(34\) \(2.292\) None None \(-3\) \(-1\) \(1\) \(-2\)
287.2.f.a \(40\) \(2.292\) None None \(0\) \(4\) \(0\) \(0\)
287.2.h.a \(4\) \(2.292\) \(\Q(\zeta_{10})\) None None \(0\) \(0\) \(-1\) \(1\) \(q+(-1-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{3}+2\zeta_{10}^{3}q^{4}+\cdots\)
287.2.h.b \(4\) \(2.292\) \(\Q(\zeta_{10})\) None None \(1\) \(6\) \(-2\) \(-1\) \(q+(-1+2\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
287.2.h.c \(40\) \(2.292\) None None \(-3\) \(0\) \(-4\) \(-10\)
287.2.h.d \(40\) \(2.292\) None None \(-2\) \(-10\) \(-1\) \(10\)
287.2.j.a \(52\) \(2.292\) None None \(-2\) \(0\) \(-6\) \(0\)
287.2.l.a \(104\) \(2.292\) None None \(-8\) \(0\) \(0\) \(-4\)
287.2.n.a \(88\) \(2.292\) None None \(0\) \(0\) \(8\) \(0\)
287.2.r.a \(4\) \(2.292\) \(\Q(\zeta_{12})\) None None \(0\) \(-2\) \(-6\) \(10\) \(q+\zeta_{12}q^{2}+(-1+\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
287.2.r.b \(4\) \(2.292\) \(\Q(\zeta_{12})\) None None \(0\) \(4\) \(6\) \(0\) \(q+\zeta_{12}q^{2}+(1+\zeta_{12})q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
287.2.r.c \(96\) \(2.292\) None None \(0\) \(-4\) \(0\) \(-14\)
287.2.s.a \(208\) \(2.292\) None None \(-3\) \(-8\) \(-7\) \(-6\)
287.2.u.a \(160\) \(2.292\) None None \(0\) \(-4\) \(0\) \(0\)
287.2.w.a \(208\) \(2.292\) None None \(-4\) \(-12\) \(-12\) \(-8\)
287.2.z.a \(208\) \(2.292\) None None \(-3\) \(0\) \(1\) \(-10\)
287.2.bb.a \(416\) \(2.292\) None None \(-32\) \(0\) \(0\) \(-16\)
287.2.bc.a \(416\) \(2.292\) None None \(-10\) \(-8\) \(-10\) \(-16\)
287.2.be.a \(832\) \(2.292\) None None \(-16\) \(-48\) \(-48\) \(-32\)
287.3.b.a \(52\) \(7.820\) None None \(2\) \(0\) \(0\) \(12\)
287.3.d.a \(7\) \(7.820\) 7.7.\(\cdots\).1 \(\Q(\sqrt{-287}) \) None \(0\) \(0\) \(0\) \(-49\) \(q+\beta _{2}q^{2}+\beta _{4}q^{3}+(4+\beta _{3}+\beta _{4})q^{4}+\cdots\)
287.3.d.b \(7\) \(7.820\) 7.7.\(\cdots\).1 \(\Q(\sqrt{-287}) \) None \(0\) \(0\) \(0\) \(49\) \(q+\beta _{2}q^{2}-\beta _{4}q^{3}+(4+\beta _{3}+\beta _{4})q^{4}+\cdots\)
287.3.d.c \(8\) \(7.820\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(-8\) \(0\) \(0\) \(0\) \(q-q^{2}-\beta _{4}q^{3}-3q^{4}+\beta _{6}q^{5}+\beta _{4}q^{6}+\cdots\)
287.3.d.d \(32\) \(7.820\) None None \(4\) \(0\) \(0\) \(0\)
287.3.g.a \(108\) \(7.820\) None None \(0\) \(0\) \(0\) \(-2\)
287.3.i.a \(108\) \(7.820\) None None \(-2\) \(0\) \(-6\) \(0\)
287.3.k.a \(108\) \(7.820\) None None \(-2\) \(-6\) \(-6\) \(-4\)
287.3.m.a \(168\) \(7.820\) None None \(8\) \(-16\) \(0\) \(0\)
287.3.o.a \(216\) \(7.820\) None None \(-6\) \(0\) \(0\) \(-3\)
287.3.p.a \(216\) \(7.820\) None None \(-6\) \(0\) \(0\) \(-5\)
287.3.q.a \(216\) \(7.820\) None None \(0\) \(-6\) \(0\) \(-4\)
287.3.t.a \(432\) \(7.820\) None None \(-20\) \(0\) \(0\) \(-8\)
287.3.v.a \(432\) \(7.820\) None None \(-4\) \(-4\) \(-4\) \(-8\)
287.3.x.a \(432\) \(7.820\) None None \(-3\) \(0\) \(-9\) \(-10\)
287.3.y.a \(432\) \(7.820\) None None \(-3\) \(-24\) \(-9\) \(-6\)
287.3.ba.a \(672\) \(7.820\) None None \(-8\) \(16\) \(0\) \(0\)
287.3.bd.a \(864\) \(7.820\) None None \(-10\) \(-24\) \(-30\) \(-16\)
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