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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
891.1.c.a \(1\) \(0.445\) \(\Q\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(-1\) \(0\) \(q+q^{4}-q^{5}+q^{11}+q^{16}-q^{20}+2q^{23}+\cdots\)
891.1.c.b \(1\) \(0.445\) \(\Q\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(1\) \(0\) \(q+q^{4}+q^{5}-q^{11}+q^{16}+q^{20}-2q^{23}+\cdots\)
891.1.q.a \(6\) \(0.445\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(3\) \(0\) \(q-\zeta_{18}^{5}q^{4}+(\zeta_{18}^{3}-\zeta_{18}^{4})q^{5}+\zeta_{18}q^{11}+\cdots\)
891.1.w.a \(18\) \(0.445\) \(\Q(\zeta_{54})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{54}^{13}q^{3}+\zeta_{54}^{10}q^{4}+(\zeta_{54}^{6}+\zeta_{54}^{8}+\cdots)q^{5}+\cdots\)
891.2.a.a \(1\) \(7.115\) \(\Q\) None None \(-2\) \(0\) \(-2\) \(4\) \(-\) \(q-2q^{2}+2q^{4}-2q^{5}+4q^{7}+4q^{10}+\cdots\)
891.2.a.b \(1\) \(7.115\) \(\Q\) None None \(-1\) \(0\) \(-1\) \(-2\) \(+\) \(q-q^{2}-q^{4}-q^{5}-2q^{7}+3q^{8}+q^{10}+\cdots\)
891.2.a.c \(1\) \(7.115\) \(\Q\) None None \(-1\) \(0\) \(-1\) \(4\) \(-\) \(q-q^{2}-q^{4}-q^{5}+4q^{7}+3q^{8}+q^{10}+\cdots\)
891.2.a.d \(1\) \(7.115\) \(\Q\) None None \(0\) \(0\) \(-3\) \(-4\) \(-\) \(q-2q^{4}-3q^{5}-4q^{7}+q^{11}+2q^{13}+\cdots\)
891.2.a.e \(1\) \(7.115\) \(\Q\) None None \(0\) \(0\) \(3\) \(-4\) \(-\) \(q-2q^{4}+3q^{5}-4q^{7}-q^{11}+2q^{13}+\cdots\)
891.2.a.f \(1\) \(7.115\) \(\Q\) None None \(1\) \(0\) \(1\) \(-2\) \(-\) \(q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots\)
891.2.a.g \(1\) \(7.115\) \(\Q\) None None \(1\) \(0\) \(1\) \(4\) \(-\) \(q+q^{2}-q^{4}+q^{5}+4q^{7}-3q^{8}+q^{10}+\cdots\)
891.2.a.h \(1\) \(7.115\) \(\Q\) None None \(2\) \(0\) \(2\) \(4\) \(-\) \(q+2q^{2}+2q^{4}+2q^{5}+4q^{7}+4q^{10}+\cdots\)
891.2.a.i \(2\) \(7.115\) \(\Q(\sqrt{13}) \) None None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(q-\beta q^{2}+(1+\beta )q^{4}-\beta q^{5}+(-1+2\beta )q^{7}+\cdots\)
891.2.a.j \(2\) \(7.115\) \(\Q(\sqrt{13}) \) None None \(1\) \(0\) \(1\) \(0\) \(-\) \(q+\beta q^{2}+(1+\beta )q^{4}+\beta q^{5}+(-1+2\beta )q^{7}+\cdots\)
891.2.a.k \(3\) \(7.115\) \(\Q(\zeta_{18})^+\) None None \(0\) \(0\) \(-3\) \(-3\) \(+\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-1-\beta _{1})q^{5}+(-1+\cdots)q^{7}+\cdots\)
891.2.a.l \(3\) \(7.115\) \(\Q(\zeta_{18})^+\) None None \(0\) \(0\) \(3\) \(-3\) \(+\) \(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(1+\beta _{1})q^{5}+(-1+\cdots)q^{7}+\cdots\)
891.2.a.m \(3\) \(7.115\) 3.3.837.1 None None \(0\) \(0\) \(-6\) \(0\) \(+\) \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-2+\beta _{1})q^{5}+\cdots\)
891.2.a.n \(3\) \(7.115\) 3.3.837.1 None None \(0\) \(0\) \(6\) \(0\) \(-\) \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(2-\beta _{1})q^{5}+\cdots\)
891.2.a.o \(4\) \(7.115\) 4.4.4752.1 None None \(-2\) \(0\) \(-8\) \(-2\) \(+\) \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-2-\beta _{1}+\cdots)q^{5}+\cdots\)
891.2.a.p \(4\) \(7.115\) 4.4.22545.1 None None \(-1\) \(0\) \(-4\) \(1\) \(-\) \(q-\beta _{2}q^{2}+(3+\beta _{3})q^{4}+(-1+\beta _{1}+\beta _{3})q^{5}+\cdots\)
891.2.a.q \(4\) \(7.115\) 4.4.22545.1 None None \(1\) \(0\) \(4\) \(1\) \(-\) \(q+\beta _{2}q^{2}+(3+\beta _{3})q^{4}+(1-\beta _{1}-\beta _{3})q^{5}+\cdots\)
891.2.a.r \(4\) \(7.115\) 4.4.4752.1 None None \(2\) \(0\) \(8\) \(-2\) \(-\) \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(2+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
891.2.d.a \(4\) \(7.115\) \(\Q(\sqrt{-3}, \sqrt{-11})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q-2q^{4}+\beta _{2}q^{5}+(\beta _{2}+\beta _{3})q^{11}+4q^{16}+\cdots\)
891.2.d.b \(16\) \(7.115\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(2-\beta _{3})q^{4}-\beta _{7}q^{5}+\beta _{6}q^{7}+\cdots\)
891.2.d.c \(24\) \(7.115\) None None \(0\) \(0\) \(0\) \(0\)
891.2.e.a \(2\) \(7.115\) \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(-2\) \(-1\) \(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots\)
891.2.e.b \(2\) \(7.115\) \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(1\) \(2\) \(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots\)
891.2.e.c \(2\) \(7.115\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(0\) \(-4\) \(2\) \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-4\zeta_{6}q^{5}+\cdots\)
891.2.e.d \(2\) \(7.115\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(0\) \(-1\) \(2\) \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
891.2.e.e \(2\) \(7.115\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(0\) \(2\) \(-4\) \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots\)
891.2.e.f \(2\) \(7.115\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(0\) \(2\) \(5\) \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots\)
891.2.e.g \(2\) \(7.115\) \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(-2\) \(-4\) \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-2\zeta_{6}q^{5}+(-4+\cdots)q^{7}+\cdots\)
891.2.e.h \(2\) \(7.115\) \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(-2\) \(5\) \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-2\zeta_{6}q^{5}+(5+\cdots)q^{7}+\cdots\)
891.2.e.i \(2\) \(7.115\) \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(1\) \(2\) \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+\cdots\)
891.2.e.j \(2\) \(7.115\) \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(4\) \(2\) \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+4\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
891.2.e.k \(2\) \(7.115\) \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(-1\) \(2\) \(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-\zeta_{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
891.2.e.l \(2\) \(7.115\) \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(2\) \(-1\) \(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots\)
891.2.e.m \(4\) \(7.115\) \(\Q(\zeta_{12})\) None None \(-2\) \(0\) \(-2\) \(4\) \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-2+2\zeta_{12}+\cdots)q^{4}+\cdots\)
891.2.e.n \(4\) \(7.115\) \(\Q(\sqrt{-3}, \sqrt{13})\) None None \(-1\) \(0\) \(-1\) \(0\) \(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
891.2.e.o \(4\) \(7.115\) \(\Q(\sqrt{-3}, \sqrt{13})\) None None \(1\) \(0\) \(1\) \(0\) \(q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
891.2.e.p \(4\) \(7.115\) \(\Q(\zeta_{12})\) None None \(2\) \(0\) \(2\) \(4\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(-2+2\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
891.2.e.q \(6\) \(7.115\) 6.0.954288.1 None None \(-1\) \(0\) \(2\) \(-7\) \(q+(\beta _{4}-\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+2\beta _{3}+\cdots)q^{4}+\cdots\)
891.2.e.r \(6\) \(7.115\) 6.0.2101707.2 None None \(0\) \(0\) \(-6\) \(0\) \(q+(-\beta _{2}+\beta _{4})q^{2}+(-\beta _{1}-2\beta _{3}-\beta _{5})q^{4}+\cdots\)
891.2.e.s \(6\) \(7.115\) 6.0.2101707.2 None None \(0\) \(0\) \(6\) \(0\) \(q+(\beta _{2}-\beta _{4})q^{2}+(-\beta _{1}-2\beta _{3}-\beta _{5})q^{4}+\cdots\)
891.2.e.t \(6\) \(7.115\) 6.0.954288.1 None None \(1\) \(0\) \(-2\) \(-7\) \(q+(-\beta _{4}+\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
891.2.e.u \(8\) \(7.115\) 8.0.22581504.2 None None \(-2\) \(0\) \(-8\) \(2\) \(q+(-1+\beta _{1}+\beta _{5})q^{2}+(1-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
891.2.e.v \(8\) \(7.115\) 8.0.22581504.2 None None \(2\) \(0\) \(8\) \(2\) \(q+(1-\beta _{1}-\beta _{5})q^{2}+(1-\beta _{1}-\beta _{2}-\beta _{5}+\cdots)q^{4}+\cdots\)
891.2.f.a \(4\) \(7.115\) \(\Q(\zeta_{10})\) None None \(-4\) \(0\) \(6\) \(1\) \(q+(-2+\zeta_{10}-\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots\)
891.2.f.b \(4\) \(7.115\) \(\Q(\zeta_{10})\) None None \(4\) \(0\) \(-6\) \(1\) \(q+(2-\zeta_{10}+\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}+(3+\cdots)q^{4}+\cdots\)
891.2.f.c \(24\) \(7.115\) None None \(-2\) \(0\) \(4\) \(7\)
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