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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1287.1.g.a \(2\) \(0.642\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-143}) \) None \(-1\) \(0\) \(0\) \(1\) \(q-\beta q^{2}+\beta q^{4}+(1-\beta )q^{7}-q^{8}+q^{11}+\cdots\)
1287.1.g.b \(2\) \(0.642\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-143}) \) None \(1\) \(0\) \(0\) \(-1\) \(q+\beta q^{2}+\beta q^{4}+(-1+\beta )q^{7}+q^{8}+\cdots\)
1287.1.g.c \(4\) \(0.642\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+q^{4}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{5}+\cdots\)
1287.1.s.a \(4\) \(0.642\) \(\Q(\zeta_{12})\) None None \(0\) \(-4\) \(2\) \(0\) \(q-q^{3}+q^{4}+\zeta_{12}^{2}q^{5}+\zeta_{12}^{5}q^{7}+\cdots\)
1287.1.ba.a \(2\) \(0.642\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-143}) \) None \(-1\) \(-1\) \(0\) \(2\) \(q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{6}-\zeta_{6}^{2}q^{7}+\cdots\)
1287.1.ba.b \(2\) \(0.642\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-143}) \) None \(1\) \(-1\) \(0\) \(-2\) \(q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{6}+\zeta_{6}^{2}q^{7}+\cdots\)
1287.1.ba.c \(8\) \(0.642\) \(\Q(\zeta_{15})\) \(\Q(\sqrt{-143}) \) None \(-1\) \(1\) \(0\) \(2\) \(q+(\zeta_{30}^{4}+\zeta_{30}^{6})q^{2}-\zeta_{30}^{11}q^{3}+(\zeta_{30}^{8}+\cdots)q^{4}+\cdots\)
1287.1.ba.d \(8\) \(0.642\) \(\Q(\zeta_{15})\) \(\Q(\sqrt{-143}) \) None \(1\) \(1\) \(0\) \(-2\) \(q+(-\zeta_{30}^{4}-\zeta_{30}^{6})q^{2}-\zeta_{30}^{11}q^{3}+\cdots\)
1287.1.bg.a \(4\) \(0.642\) \(\Q(\zeta_{12})\) None None \(0\) \(2\) \(2\) \(0\) \(q-\zeta_{12}^{4}q^{3}-\zeta_{12}^{2}q^{4}-\zeta_{12}^{4}q^{5}+\cdots\)
1287.1.bu.a \(16\) \(0.642\) \(\Q(\zeta_{40})\) \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{40}^{9}+\zeta_{40}^{15})q^{2}+(-\zeta_{40}^{4}-\zeta_{40}^{10}+\cdots)q^{4}+\cdots\)
1287.2.a.a \(1\) \(10.277\) \(\Q\) None None \(-1\) \(0\) \(2\) \(-2\) \(+\) \(q-q^{2}-q^{4}+2q^{5}-2q^{7}+3q^{8}-2q^{10}+\cdots\)
1287.2.a.b \(1\) \(10.277\) \(\Q\) None None \(0\) \(0\) \(1\) \(-2\) \(+\) \(q-2q^{4}+q^{5}-2q^{7}+q^{11}-q^{13}+\cdots\)
1287.2.a.c \(1\) \(10.277\) \(\Q\) None None \(1\) \(0\) \(-2\) \(-2\) \(-\) \(q+q^{2}-q^{4}-2q^{5}-2q^{7}-3q^{8}-2q^{10}+\cdots\)
1287.2.a.d \(1\) \(10.277\) \(\Q\) None None \(1\) \(0\) \(0\) \(0\) \(+\) \(q+q^{2}-q^{4}-3q^{8}-q^{11}+q^{13}-q^{16}+\cdots\)
1287.2.a.e \(1\) \(10.277\) \(\Q\) None None \(1\) \(0\) \(2\) \(0\) \(-\) \(q+q^{2}-q^{4}+2q^{5}-3q^{8}+2q^{10}+\cdots\)
1287.2.a.f \(2\) \(10.277\) \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(2\) \(-4\) \(+\) \(q+\beta q^{2}+q^{4}+(1-\beta )q^{5}-2q^{7}-\beta q^{8}+\cdots\)
1287.2.a.g \(2\) \(10.277\) \(\Q(\sqrt{2}) \) None None \(2\) \(0\) \(4\) \(-4\) \(-\) \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(2+\beta )q^{5}+\cdots\)
1287.2.a.h \(3\) \(10.277\) 3.3.148.1 None None \(-3\) \(0\) \(-4\) \(-2\) \(+\) \(q+(-1-\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1287.2.a.i \(3\) \(10.277\) 3.3.148.1 None None \(-1\) \(0\) \(0\) \(-2\) \(+\) \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1287.2.a.j \(3\) \(10.277\) 3.3.564.1 None None \(1\) \(0\) \(2\) \(2\) \(-\) \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
1287.2.a.k \(4\) \(10.277\) 4.4.1957.1 None None \(-3\) \(0\) \(0\) \(6\) \(-\) \(q+(-1-\beta _{1}-\beta _{2})q^{2}+(1+2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1287.2.a.l \(4\) \(10.277\) 4.4.11344.1 None None \(-2\) \(0\) \(-6\) \(6\) \(+\) \(q+\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
1287.2.a.m \(4\) \(10.277\) 4.4.8468.1 None None \(2\) \(0\) \(0\) \(2\) \(-\) \(q-\beta _{2}q^{2}+(2-\beta _{1})q^{4}-\beta _{3}q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
1287.2.a.n \(4\) \(10.277\) 4.4.11344.1 None None \(2\) \(0\) \(6\) \(6\) \(-\) \(q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
1287.2.a.o \(5\) \(10.277\) 5.5.368464.1 None None \(-3\) \(0\) \(-4\) \(-4\) \(+\) \(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1287.2.a.p \(5\) \(10.277\) 5.5.368464.1 None None \(3\) \(0\) \(4\) \(-4\) \(-\) \(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
1287.2.a.q \(6\) \(10.277\) 6.6.194616205.1 None None \(0\) \(0\) \(-1\) \(4\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{5}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1287.2.b.a \(10\) \(10.277\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(-\beta _{5}+\beta _{7}+\cdots)q^{5}+\cdots\)
1287.2.b.b \(12\) \(10.277\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-1+\beta _{4}-\beta _{5})q^{4}+(-\beta _{6}+\cdots)q^{5}+\cdots\)
1287.2.b.c \(14\) \(10.277\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-1-\beta _{5}+\beta _{6})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
1287.2.b.d \(20\) \(10.277\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{12}q^{2}+(-1-\beta _{8})q^{4}+(\beta _{10}+\beta _{11}+\cdots)q^{5}+\cdots\)
1287.2.e.a \(4\) \(10.277\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(-8\) \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
1287.2.e.b \(4\) \(10.277\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(-8\) \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
1287.2.e.c \(4\) \(10.277\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(8\) \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
1287.2.e.d \(4\) \(10.277\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(8\) \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
1287.2.e.e \(40\) \(10.277\) None None \(0\) \(0\) \(0\) \(0\)
1287.2.f.a \(48\) \(10.277\) None None \(0\) \(0\) \(0\) \(0\)
1287.2.m.a \(4\) \(10.277\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{2}-\zeta_{8}^{2}q^{4}-3\zeta_{8}^{3}q^{8}-\zeta_{8}^{3}q^{11}+\cdots\)
1287.2.m.b \(40\) \(10.277\) None None \(0\) \(0\) \(0\) \(8\)
1287.2.m.c \(44\) \(10.277\) None None \(0\) \(0\) \(0\) \(8\)
1287.3.c.a \(80\) \(35.068\) None None \(0\) \(0\) \(0\) \(0\)
1287.3.h.a \(96\) \(35.068\) None None \(0\) \(0\) \(0\) \(0\)
1287.4.a.a \(1\) \(75.935\) \(\Q\) None None \(1\) \(0\) \(19\) \(19\) \(-\) \(q+q^{2}-7q^{4}+19q^{5}+19q^{7}-15q^{8}+\cdots\)
1287.4.a.b \(4\) \(75.935\) 4.4.297133.1 None None \(0\) \(0\) \(6\) \(-17\) \(-\) \(q-\beta _{1}q^{2}+(2+\beta _{1}+2\beta _{2})q^{4}+(2+3\beta _{1}+\cdots)q^{5}+\cdots\)
1287.4.a.c \(6\) \(75.935\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(-1\) \(0\) \(-13\) \(-25\) \(-\) \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-2-\beta _{4})q^{5}+\cdots\)
1287.4.a.d \(6\) \(75.935\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(0\) \(0\) \(-16\) \(-22\) \(-\) \(q+\beta _{1}q^{2}+(5+\beta _{1}+\beta _{2})q^{4}+(-2-\beta _{3}+\cdots)q^{5}+\cdots\)
1287.4.a.e \(6\) \(75.935\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(5\) \(0\) \(17\) \(-31\) \(+\) \(q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{3}+\beta _{4})q^{4}+\cdots\)
1287.4.a.f \(6\) \(75.935\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(6\) \(0\) \(8\) \(-53\) \(-\) \(q+(1-\beta _{1})q^{2}+(4-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
1287.4.a.g \(7\) \(75.935\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(3\) \(0\) \(33\) \(3\) \(+\) \(q+\beta _{1}q^{2}+(3+\beta _{1}+\beta _{2})q^{4}+(5-\beta _{5}+\cdots)q^{5}+\cdots\)
1287.4.a.h \(8\) \(75.935\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(-7\) \(0\) \(-7\) \(39\) \(-\) \(q+(-1+\beta _{1})q^{2}+(4-\beta _{1}+\beta _{2})q^{4}+\cdots\)
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