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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
300.1.b.a \(2\) \(0.150\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-iq^{7}-q^{9}+iq^{13}+q^{19}+\cdots\)
300.1.g.a \(1\) \(0.150\) \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(1\) \(q-q^{3}+q^{7}+q^{9}+q^{13}-q^{19}-q^{21}+\cdots\)
300.1.g.b \(1\) \(0.150\) \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-1\) \(q+q^{3}-q^{7}+q^{9}-q^{13}-q^{19}-q^{21}+\cdots\)
300.1.l.a \(4\) \(0.150\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{3}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}-q^{6}+\cdots\)
300.2.a.a \(1\) \(2.396\) \(\Q\) None None \(0\) \(-1\) \(0\) \(-4\) \(+\) \(q-q^{3}-4q^{7}+q^{9}-4q^{11}-4q^{17}+\cdots\)
300.2.a.b \(1\) \(2.396\) \(\Q\) None None \(0\) \(-1\) \(0\) \(1\) \(-\) \(q-q^{3}+q^{7}+q^{9}+6q^{11}-5q^{13}+\cdots\)
300.2.a.c \(1\) \(2.396\) \(\Q\) None None \(0\) \(1\) \(0\) \(-1\) \(-\) \(q+q^{3}-q^{7}+q^{9}+6q^{11}+5q^{13}+\cdots\)
300.2.a.d \(1\) \(2.396\) \(\Q\) None None \(0\) \(1\) \(0\) \(4\) \(-\) \(q+q^{3}+4q^{7}+q^{9}-4q^{11}+4q^{17}+\cdots\)
300.2.d.a \(2\) \(2.396\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+iq^{7}-q^{9}+6q^{11}+5iq^{13}+\cdots\)
300.2.e.a \(4\) \(2.396\) \(\Q(\sqrt{3}, \sqrt{-5})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+\beta _{2}q^{4}+(2+\cdots)q^{6}+\cdots\)
300.2.e.b \(4\) \(2.396\) \(\Q(\sqrt{2}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+2q^{4}+(-1+\cdots)q^{6}+\cdots\)
300.2.e.c \(8\) \(2.396\) 8.0.342102016.5 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{2}+(-\beta _{6}+\beta _{7})q^{3}+(\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
300.2.e.d \(8\) \(2.396\) 8.0.4521217600.1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{2}-\beta _{2}q^{3}+(\beta _{1}-\beta _{2}-\beta _{3})q^{4}+\cdots\)
300.2.e.e \(8\) \(2.396\) 8.0.4521217600.1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{2}+\beta _{3}q^{3}+(\beta _{1}-\beta _{2}-\beta _{3})q^{4}+\cdots\)
300.2.h.a \(8\) \(2.396\) 8.0.342102016.5 None None \(-2\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
300.2.h.b \(8\) \(2.396\) 8.0.342102016.5 None None \(2\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(-\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
300.2.h.c \(16\) \(2.396\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{10}q^{3}-\beta _{4}q^{4}-\beta _{12}q^{6}+\cdots\)
300.2.i.a \(4\) \(2.396\) \(\Q(i, \sqrt{5})\) None None \(0\) \(-2\) \(0\) \(4\) \(q+(-1+\beta _{3})q^{3}+(1-\beta _{2})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
300.2.i.b \(4\) \(2.396\) \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+2\beta _{3}q^{7}+3\beta _{2}q^{9}+4\beta _{1}q^{13}+\cdots\)
300.2.i.c \(4\) \(2.396\) \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-3\beta _{3}q^{7}+3\beta _{2}q^{9}-\beta _{1}q^{13}+\cdots\)
300.2.j.a \(8\) \(2.396\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}-\zeta_{24}^{4}+\zeta_{24}^{5})q^{2}+\zeta_{24}q^{3}+\cdots\)
300.2.j.b \(8\) \(2.396\) 8.0.157351936.1 None None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{2}+\beta _{4})q^{2}+\beta _{6}q^{3}+(\beta _{3}+\beta _{5})q^{4}+\cdots\)
300.2.j.c \(8\) \(2.396\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}-\zeta_{24}^{7})q^{2}-\zeta_{24}^{5}q^{3}+(\zeta_{24}^{2}+\cdots)q^{4}+\cdots\)
300.2.j.d \(12\) \(2.396\) 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{9}q^{3}+(\beta _{2}+\beta _{8}+\beta _{9})q^{4}+\cdots\)
300.2.m.a \(8\) \(2.396\) \(\Q(\zeta_{15})\) None None \(0\) \(-2\) \(5\) \(-8\) \(q+\zeta_{15}^{5}q^{3}+(-1-2\zeta_{15}^{2}-\zeta_{15}^{3}+\cdots)q^{5}+\cdots\)
300.2.m.b \(8\) \(2.396\) 8.0.26265625.1 None None \(0\) \(2\) \(-5\) \(8\) \(q+\beta _{3}q^{3}+(-1+\beta _{6}-\beta _{7})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
300.2.n.a \(224\) \(2.396\) None None \(0\) \(0\) \(0\) \(0\)
300.2.o.a \(24\) \(2.396\) None None \(0\) \(0\) \(-2\) \(0\)
300.2.r.a \(224\) \(2.396\) None None \(0\) \(0\) \(0\) \(0\)
300.2.w.a \(240\) \(2.396\) None None \(0\) \(0\) \(0\) \(0\)
300.2.x.a \(80\) \(2.396\) None None \(0\) \(-2\) \(0\) \(4\)
300.3.b.a \(2\) \(8.174\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{3}+2iq^{7}-9q^{9}+22iq^{13}+\cdots\)
300.3.b.b \(2\) \(8.174\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{3}-13iq^{7}-9q^{9}-23iq^{13}+\cdots\)
300.3.b.c \(4\) \(8.174\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{3})q^{3}+\beta _{1}q^{7}+(1-2\beta _{2}+\cdots)q^{9}+\cdots\)
300.3.b.d \(4\) \(8.174\) \(\Q(i, \sqrt{35})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-8\beta _{2}q^{7}+(9+\beta _{3})q^{9}+(-3+\cdots)q^{11}+\cdots\)
300.3.c.a \(2\) \(8.174\) \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(0\) \(0\) \(q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
300.3.c.b \(2\) \(8.174\) \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(0\) \(0\) \(q+(1+\zeta_{6})q^{2}-\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
300.3.c.c \(2\) \(8.174\) \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(0\) \(0\) \(q+(1+\zeta_{6})q^{2}-\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
300.3.c.d \(8\) \(8.174\) 8.0.85100625.1 None None \(-4\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{2}+\beta _{6}q^{3}+(1-\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots\)
300.3.c.e \(8\) \(8.174\) 8.0.4069419264.1 None None \(-2\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{2}-\beta _{5}q^{3}+(-1+\beta _{7})q^{4}+(-1+\cdots)q^{6}+\cdots\)
300.3.c.f \(8\) \(8.174\) 8.0.6080256576.2 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{2}-\beta _{2}q^{3}+(1-\beta _{7})q^{4}+(-1+\cdots)q^{6}+\cdots\)
300.3.c.g \(8\) \(8.174\) 8.0.4069419264.1 None None \(2\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}+\beta _{5}q^{3}+(-1+\beta _{7})q^{4}+(-1+\cdots)q^{6}+\cdots\)
300.3.f.a \(4\) \(8.174\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+\zeta_{12}^{3}q^{3}+(2+2\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
300.3.f.b \(16\) \(8.174\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{12}q^{2}-\beta _{9}q^{3}+(-1+\beta _{4})q^{4}+\cdots\)
300.3.f.c \(16\) \(8.174\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}-\beta _{4}q^{3}+(1+\beta _{5})q^{4}+(-1+\cdots)q^{6}+\cdots\)
300.3.g.a \(1\) \(8.174\) \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(0\) \(-13\) \(q-3q^{3}-13q^{7}+9q^{9}+23q^{13}+11q^{19}+\cdots\)
300.3.g.b \(1\) \(8.174\) \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(0\) \(-2\) \(q+3q^{3}-2q^{7}+9q^{9}+22q^{13}+26q^{19}+\cdots\)
300.3.g.c \(1\) \(8.174\) \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(0\) \(13\) \(q+3q^{3}+13q^{7}+9q^{9}-23q^{13}+11q^{19}+\cdots\)
300.3.g.d \(2\) \(8.174\) \(\Q(\sqrt{-5}) \) None None \(0\) \(-4\) \(0\) \(-4\) \(q+(-2+\beta )q^{3}-2q^{7}+(-1-4\beta )q^{9}+\cdots\)
300.3.g.e \(2\) \(8.174\) \(\Q(\sqrt{-5}) \) None None \(0\) \(-4\) \(0\) \(16\) \(q+(-2+\beta )q^{3}+8q^{7}+(-1-4\beta )q^{9}+\cdots\)
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