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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
289.2.a.a \(1\) \(2.308\) \(\Q\) None \(-1\) \(0\) \(2\) \(-4\) \(+\) \(q-q^{2}-q^{4}+2q^{5}-4q^{7}+3q^{8}-3q^{9}+\cdots\)
289.2.a.b \(2\) \(2.308\) \(\Q(\sqrt{13}) \) None \(-1\) \(-1\) \(-1\) \(-3\) \(+\) \(q-\beta q^{2}+(-1+\beta )q^{3}+(1+\beta )q^{4}-\beta q^{5}+\cdots\)
289.2.a.c \(2\) \(2.308\) \(\Q(\sqrt{13}) \) None \(-1\) \(1\) \(1\) \(3\) \(-\) \(q-\beta q^{2}+(1-\beta )q^{3}+(1+\beta )q^{4}+\beta q^{5}+\cdots\)
289.2.a.d \(3\) \(2.308\) \(\Q(\zeta_{18})^+\) None \(0\) \(-3\) \(-6\) \(0\) \(+\) \(q-\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+\beta _{2}q^{4}+(-2+\cdots)q^{5}+\cdots\)
289.2.a.e \(3\) \(2.308\) \(\Q(\zeta_{18})^+\) None \(0\) \(3\) \(6\) \(0\) \(-\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{3}+\beta _{2}q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\)
289.2.a.f \(4\) \(2.308\) \(\Q(\zeta_{16})^+\) None \(4\) \(0\) \(0\) \(0\) \(-\) \(q+(1+\beta _{2})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(1+2\beta _{2}+\cdots)q^{4}+\cdots\)
289.2.b.a \(2\) \(2.308\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}-q^{4}+iq^{5}+2iq^{7}-3q^{8}+\cdots\)
289.2.b.b \(4\) \(2.308\) 4.0.2048.2 None \(-4\) \(0\) \(0\) \(0\) \(q+(-1+\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(1-2\beta _{2}+\cdots)q^{4}+\cdots\)
289.2.b.c \(4\) \(2.308\) \(\Q(i, \sqrt{13})\) None \(2\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}+\beta _{1}q^{3}+(1+\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
289.2.b.d \(6\) \(2.308\) 6.0.419904.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(\beta _{2}-\beta _{4})q^{4}+\cdots\)
289.2.c.a \(4\) \(2.308\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}+q^{4}+\zeta_{8}q^{5}+2\zeta_{8}^{3}q^{7}+\cdots\)
289.2.c.b \(8\) \(2.308\) 8.0.1871773696.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{2}+\beta _{1}q^{3}+(-2-\beta _{4})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
289.2.c.c \(8\) \(2.308\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{16}^{2}-\zeta_{16}^{3})q^{2}+(-\zeta_{16}+\zeta_{16}^{7})q^{3}+\cdots\)
289.2.c.d \(12\) \(2.308\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{4}-\beta _{9})q^{2}+(-\beta _{8}-\beta _{10})q^{3}+\cdots\)
289.2.d.a \(4\) \(2.308\) \(\Q(\zeta_{8})\) None \(-4\) \(4\) \(0\) \(4\) \(q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
289.2.d.b \(4\) \(2.308\) \(\Q(\zeta_{8})\) None \(4\) \(-4\) \(-4\) \(-4\) \(q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
289.2.d.c \(4\) \(2.308\) \(\Q(\zeta_{8})\) None \(4\) \(4\) \(4\) \(4\) \(q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
289.2.d.d \(8\) \(2.308\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{2}q^{2}-\zeta_{16}^{4}q^{4}-\zeta_{16}^{7}q^{5}+\cdots\)
289.2.d.e \(16\) \(2.308\) 16.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{3}+\beta _{5})q^{2}+(-\beta _{6}-\beta _{7})q^{3}+(-2\beta _{8}+\cdots)q^{4}+\cdots\)
289.2.d.f \(24\) \(2.308\) None \(0\) \(0\) \(0\) \(0\)
289.2.f.a \(384\) \(2.308\) None \(-13\) \(-13\) \(-43\) \(-13\)
289.2.g.a \(384\) \(2.308\) None \(-17\) \(-17\) \(17\) \(-17\)
289.2.h.a \(768\) \(2.308\) None \(-34\) \(-34\) \(-34\) \(-34\)
289.2.i.a \(1600\) \(2.308\) None \(-64\) \(-64\) \(-68\) \(-64\)
289.3.e.a \(8\) \(7.875\) \(\Q(\zeta_{16})\) None \(-8\) \(-16\) \(-8\) \(-16\) \(q+(-1+\zeta_{16}^{6}+\zeta_{16}^{7})q^{2}+(-2-2\zeta_{16}+\cdots)q^{3}+\cdots\)
289.3.e.b \(8\) \(7.875\) \(\Q(\zeta_{16})\) None \(-8\) \(-8\) \(0\) \(-8\) \(q+(-1-\zeta_{16}-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
289.3.e.c \(8\) \(7.875\) \(\Q(\zeta_{16})\) None \(-8\) \(8\) \(-16\) \(-8\) \(q+(-1+\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
289.3.e.d \(8\) \(7.875\) \(\Q(\zeta_{16})\) None \(-8\) \(8\) \(0\) \(8\) \(q+(-1-\zeta_{16}-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
289.3.e.e \(8\) \(7.875\) \(\Q(\zeta_{16})\) None \(-8\) \(16\) \(8\) \(16\) \(q+(-1+\zeta_{16}^{6}+\zeta_{16}^{7})q^{2}+(2+2\zeta_{16}+\cdots)q^{3}+\cdots\)
289.3.e.f \(8\) \(7.875\) \(\Q(\zeta_{16})\) None \(0\) \(-8\) \(-8\) \(8\) \(q+(\zeta_{16}^{2}-\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(-1+\cdots)q^{3}+\cdots\)
289.3.e.g \(8\) \(7.875\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(24\) \(16\) \(q+(-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(-2\zeta_{16}^{2}+\cdots)q^{3}+\cdots\)
289.3.e.h \(8\) \(7.875\) \(\Q(\zeta_{16})\) None \(0\) \(8\) \(8\) \(-8\) \(q+(\zeta_{16}^{2}-\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(1+\zeta_{16}+\cdots)q^{3}+\cdots\)
289.3.e.i \(8\) \(7.875\) \(\Q(\zeta_{16})\) None \(8\) \(-8\) \(-16\) \(8\) \(q+(1+\zeta_{16}-\zeta_{16}^{2}+\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
289.3.e.j \(8\) \(7.875\) \(\Q(\zeta_{16})\) None \(8\) \(-8\) \(16\) \(-8\) \(q+(1-\zeta_{16}^{6}+\zeta_{16}^{7})q^{2}+(-1-\zeta_{16}+\cdots)q^{3}+\cdots\)
289.3.e.k \(8\) \(7.875\) \(\Q(\zeta_{16})\) None \(8\) \(0\) \(-16\) \(40\) \(q+(1-\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
289.3.e.l \(8\) \(7.875\) \(\Q(\zeta_{16})\) None \(8\) \(0\) \(16\) \(-40\) \(q+(1-\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
289.3.e.m \(8\) \(7.875\) \(\Q(\zeta_{16})\) None \(8\) \(8\) \(16\) \(-8\) \(q+(1+\zeta_{16}-\zeta_{16}^{2}+\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
289.3.e.n \(8\) \(7.875\) \(\Q(\zeta_{16})\) None \(8\) \(8\) \(-16\) \(8\) \(q+(1-\zeta_{16}^{6}+\zeta_{16}^{7})q^{2}+(1+\zeta_{16}+\cdots)q^{3}+\cdots\)
289.3.e.o \(16\) \(7.875\) 16.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{2}+\beta _{11}q^{3}+3\beta _{2}q^{4}-\beta _{7}q^{5}+\cdots\)
289.3.e.p \(32\) \(7.875\) None \(0\) \(0\) \(0\) \(0\)
289.3.e.q \(48\) \(7.875\) None \(0\) \(0\) \(0\) \(0\)
289.3.e.r \(96\) \(7.875\) None \(0\) \(0\) \(0\) \(0\)
289.3.j.a \(6400\) \(7.875\) None \(-128\) \(-128\) \(-128\) \(-128\)
289.4.a.a \(1\) \(17.052\) \(\Q\) None \(-3\) \(8\) \(-6\) \(28\) \(+\) \(q-3q^{2}+8q^{3}+q^{4}-6q^{5}-24q^{6}+\cdots\)
289.4.a.b \(3\) \(17.052\) 3.3.2636.1 None \(1\) \(-4\) \(8\) \(-22\) \(+\) \(q+(\beta _{1}-\beta _{2})q^{2}+(-2+\beta _{1}-2\beta _{2})q^{3}+\cdots\)
289.4.a.c \(4\) \(17.052\) 4.4.2555057.1 None \(1\) \(-2\) \(14\) \(36\) \(+\) \(q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(3+\beta _{1}+\cdots)q^{4}+\cdots\)
289.4.a.d \(4\) \(17.052\) 4.4.2555057.1 None \(1\) \(2\) \(-14\) \(-36\) \(-\) \(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(3+\beta _{1}+\cdots)q^{4}+\cdots\)
289.4.a.e \(4\) \(17.052\) 4.4.4669632.2 None \(2\) \(0\) \(0\) \(0\) \(+\) \(q+(1+\beta _{2})q^{2}-\beta _{1}q^{3}+(1+\beta _{2})q^{4}+\cdots\)
289.4.a.f \(8\) \(17.052\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(0\) \(0\) \(0\) \(+\) \(q+(1-\beta _{1})q^{2}-\beta _{3}q^{3}+(5-\beta _{1}+\beta _{6}+\cdots)q^{4}+\cdots\)
289.4.a.g \(12\) \(17.052\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-8\) \(0\) \(0\) \(0\) \(-\) \(q+(-1+\beta _{5})q^{2}+\beta _{7}q^{3}+(2+2\beta _{1}+\cdots)q^{4}+\cdots\)
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