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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
900.1.c.a \(1\) \(0.449\) \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-15}) \) \(\Q(\sqrt{15}) \) \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+q^{16}+2q^{17}-q^{32}+\cdots\)
900.1.c.b \(1\) \(0.449\) \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-15}) \) \(\Q(\sqrt{15}) \) \(1\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}+q^{16}-2q^{17}+q^{32}+\cdots\)
900.1.l.a \(4\) \(0.449\) \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{7}-\beta _{3}q^{13}-\beta _{2}q^{19}+q^{31}+\cdots\)
900.1.m.a \(4\) \(0.449\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{8}+(1-\zeta_{8}^{2}+\cdots)q^{13}+\cdots\)
900.1.t.a \(4\) \(0.449\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}q^{3}-\zeta_{12}^{4}q^{4}+q^{6}+\cdots\)
900.1.x.a \(4\) \(0.449\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-1}) \) None \(1\) \(0\) \(1\) \(0\) \(q-\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}-\zeta_{10}^{2}q^{5}+\cdots\)
900.1.bb.a \(8\) \(0.449\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}^{3}q^{2}+\zeta_{20}^{6}q^{4}+\zeta_{20}^{9}q^{5}+\cdots\)
900.1.bd.a \(8\) \(0.449\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{11}q^{2}-\zeta_{24}q^{3}-\zeta_{24}^{10}q^{4}+\cdots\)
900.1.bh.a \(16\) \(0.449\) \(\Q(\zeta_{40})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{40}^{11}q^{2}-\zeta_{40}^{2}q^{4}+\zeta_{40}^{3}q^{5}+\cdots\)
900.2.a.a \(1\) \(7.187\) \(\Q\) None None \(0\) \(0\) \(0\) \(-4\) \(-\) \(q-4q^{7}+4q^{11}+4q^{17}+4q^{23}+6q^{29}+\cdots\)
900.2.a.b \(1\) \(7.187\) \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) \(+\) \(q-2q^{7}-2q^{13}-6q^{17}-4q^{19}+6q^{23}+\cdots\)
900.2.a.c \(1\) \(7.187\) \(\Q\) None None \(0\) \(0\) \(0\) \(-1\) \(-\) \(q-q^{7}-6q^{11}+5q^{13}+6q^{17}+5q^{19}+\cdots\)
900.2.a.d \(1\) \(7.187\) \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(+\) \(q-q^{7}-7q^{13}-7q^{19}+11q^{31}-10q^{37}+\cdots\)
900.2.a.e \(1\) \(7.187\) \(\Q\) None None \(0\) \(0\) \(0\) \(1\) \(+\) \(q+q^{7}-6q^{11}-5q^{13}-6q^{17}+5q^{19}+\cdots\)
900.2.a.f \(1\) \(7.187\) \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(-\) \(q+q^{7}+7q^{13}-7q^{19}+11q^{31}+10q^{37}+\cdots\)
900.2.a.g \(1\) \(7.187\) \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(4\) \(-\) \(q+4q^{7}-2q^{13}+8q^{19}-4q^{31}+10q^{37}+\cdots\)
900.2.a.h \(1\) \(7.187\) \(\Q\) None None \(0\) \(0\) \(0\) \(4\) \(-\) \(q+4q^{7}+4q^{11}-4q^{17}-4q^{23}+6q^{29}+\cdots\)
900.2.d.a \(2\) \(7.187\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}-6q^{11}+5iq^{13}-6iq^{17}+\cdots\)
900.2.d.b \(2\) \(7.187\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}+iq^{13}-8q^{19}-4q^{31}+\cdots\)
900.2.d.c \(2\) \(7.187\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}-iq^{13}+3iq^{17}+4q^{19}+\cdots\)
900.2.d.d \(2\) \(7.187\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{7}-7iq^{13}+7q^{19}+11q^{31}+\cdots\)
900.2.e.a \(2\) \(7.187\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{2}-2q^{4}+2\beta q^{8}-6q^{13}+4q^{16}+\cdots\)
900.2.e.b \(2\) \(7.187\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{2}-2q^{4}-2\beta q^{8}+4q^{13}+4q^{16}+\cdots\)
900.2.e.c \(2\) \(7.187\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{2}-2q^{4}+2\beta q^{8}+6q^{13}+4q^{16}+\cdots\)
900.2.e.d \(8\) \(7.187\) 8.0.18939904.2 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{2}+(1-\beta _{3}-\beta _{4}-\beta _{7})q^{4}+(-2+\cdots)q^{7}+\cdots\)
900.2.e.e \(8\) \(7.187\) 8.0.64000000.1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{2}-\beta _{2}q^{4}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
900.2.e.f \(8\) \(7.187\) 8.0.207360000.2 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(1-\beta _{5})q^{4}+(\beta _{2}+\beta _{7})q^{7}+\cdots\)
900.2.e.g \(8\) \(7.187\) 8.0.64000000.1 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{4}q^{4}+(-\beta _{4}+\beta _{7})q^{7}+\cdots\)
900.2.h.a \(4\) \(7.187\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}+2q^{4}-2\zeta_{8}^{3}q^{8}+2\zeta_{8}q^{13}+\cdots\)
900.2.h.b \(8\) \(7.187\) 8.0.18939904.2 None None \(-4\) \(0\) \(0\) \(0\) \(q+(-1-\beta _{3})q^{2}+(\beta _{3}+\beta _{5})q^{4}+(-2\beta _{4}+\cdots)q^{7}+\cdots\)
900.2.h.c \(8\) \(7.187\) 8.0.18939904.2 None None \(4\) \(0\) \(0\) \(0\) \(q+(1+\beta _{3})q^{2}+(\beta _{3}+\beta _{5})q^{4}+(-2\beta _{4}+\cdots)q^{7}+\cdots\)
900.2.h.d \(16\) \(7.187\) \(\Q(\zeta_{40})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{40}^{9}q^{2}+\zeta_{40}^{3}q^{4}+(\zeta_{40}^{5}+\zeta_{40}^{10}+\cdots)q^{7}+\cdots\)
900.2.i.a \(2\) \(7.187\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(0\) \(-1\) \(q+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{7}+(3+\cdots)q^{9}+\cdots\)
900.2.i.b \(2\) \(7.187\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(-1\) \(q+(1-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{7}-3q^{9}+\cdots\)
900.2.i.c \(6\) \(7.187\) 6.0.954288.1 None None \(0\) \(1\) \(0\) \(3\) \(q-\beta _{4}q^{3}+(-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{5})q^{7}+\cdots\)
900.2.i.d \(8\) \(7.187\) 8.0.142635249.1 None None \(0\) \(-1\) \(0\) \(1\) \(q+\beta _{3}q^{3}+(-\beta _{3}+\beta _{4}+\beta _{5}+\beta _{7})q^{7}+\cdots\)
900.2.i.e \(8\) \(7.187\) 8.0.142635249.1 None None \(0\) \(1\) \(0\) \(-1\) \(q-\beta _{2}q^{3}+(2\beta _{2}+\beta _{5}-\beta _{6}-\beta _{7})q^{7}+\cdots\)
900.2.i.f \(12\) \(7.187\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(\beta _{5}+\beta _{11})q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)
900.2.j.a \(4\) \(7.187\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(-8\) \(q+(-2+2\zeta_{8})q^{7}+2\zeta_{8}^{2}q^{11}+(-3+\cdots)q^{13}+\cdots\)
900.2.j.b \(8\) \(7.187\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{3}q^{7}-\zeta_{24}^{5}q^{11}-\zeta_{24}q^{13}+\cdots\)
900.2.k.a \(2\) \(7.187\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) None \(-2\) \(0\) \(0\) \(-6\) \(q+(-1+i)q^{2}-2iq^{4}+(-3+3i)q^{7}+\cdots\)
900.2.k.b \(2\) \(7.187\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(0\) \(q+(-1-i)q^{2}+2iq^{4}+(2-2i)q^{8}+\cdots\)
900.2.k.c \(2\) \(7.187\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(0\) \(q+(-1-i)q^{2}+2iq^{4}+(2-2i)q^{8}+\cdots\)
900.2.k.d \(2\) \(7.187\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) \(q+(1+i)q^{2}+2iq^{4}+(-2+2i)q^{8}+\cdots\)
900.2.k.e \(2\) \(7.187\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) None \(2\) \(0\) \(0\) \(6\) \(q+(1-i)q^{2}-2iq^{4}+(3-3i)q^{7}+(-2+\cdots)q^{8}+\cdots\)
900.2.k.f \(8\) \(7.187\) \(\Q(\zeta_{24})\) None None \(-4\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}+\zeta_{24}^{3})q^{2}+(\zeta_{24}+\zeta_{24}^{4}+\cdots)q^{4}+\cdots\)
900.2.k.g \(8\) \(7.187\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{4}q^{2}+(-2+\zeta_{24}^{2}-\zeta_{24}^{6}+\cdots)q^{4}+\cdots\)
900.2.k.h \(8\) \(7.187\) 8.0.157351936.1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{4}+\beta _{6})q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
900.2.k.i \(8\) \(7.187\) 8.0.3317760000.5 \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{2}+(\beta _{2}-\beta _{4})q^{4}+(\beta _{1}-\beta _{3})q^{8}+\cdots\)
900.2.k.j \(8\) \(7.187\) 8.0.3317760000.5 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{2}+(-\beta _{2}+\beta _{3})q^{4}+(\beta _{4}+2\beta _{6}+\cdots)q^{8}+\cdots\)
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