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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
225.1.g.a \(2\) \(0.112\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-15}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{4}-q^{16}-iq^{19}-q^{31}+iq^{49}+\cdots\)
225.2.a.a \(1\) \(1.797\) \(\Q\) None None \(-2\) \(0\) \(0\) \(-3\) \(+\) \(q-2q^{2}+2q^{4}-3q^{7}-2q^{11}+q^{13}+\cdots\)
225.2.a.b \(1\) \(1.797\) \(\Q\) None None \(-1\) \(0\) \(0\) \(0\) \(-\) \(q-q^{2}-q^{4}+3q^{8}+4q^{11}+2q^{13}+\cdots\)
225.2.a.c \(1\) \(1.797\) \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-5\) \(+\) \(q-2q^{4}-5q^{7}-5q^{13}+4q^{16}-q^{19}+\cdots\)
225.2.a.d \(1\) \(1.797\) \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(5\) \(-\) \(q-2q^{4}+5q^{7}+5q^{13}+4q^{16}-q^{19}+\cdots\)
225.2.a.e \(1\) \(1.797\) \(\Q\) None None \(2\) \(0\) \(0\) \(3\) \(-\) \(q+2q^{2}+2q^{4}+3q^{7}-2q^{11}-q^{13}+\cdots\)
225.2.a.f \(2\) \(1.797\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(q-\beta q^{2}+3q^{4}-\beta q^{8}-q^{16}+2\beta q^{17}+\cdots\)
225.2.b.a \(2\) \(1.797\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}-2q^{4}+3iq^{7}-2q^{11}+iq^{13}+\cdots\)
225.2.b.b \(2\) \(1.797\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+q^{4}+3iq^{8}+4q^{11}+2iq^{13}+\cdots\)
225.2.b.c \(2\) \(1.797\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2q^{4}+iq^{7}-iq^{13}+4q^{16}+q^{19}+\cdots\)
225.2.e.a \(2\) \(1.797\) \(\Q(\sqrt{-3}) \) None None \(1\) \(3\) \(0\) \(-3\) \(q+(1-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
225.2.e.b \(6\) \(1.797\) 6.0.954288.1 None None \(1\) \(-1\) \(0\) \(5\) \(q+(\beta _{1}-\beta _{2}+\beta _{4}+\beta _{5})q^{2}-\beta _{4}q^{3}+\cdots\)
225.2.e.c \(8\) \(1.797\) 8.0.1223810289.2 None None \(-2\) \(1\) \(0\) \(1\) \(q-\beta _{1}q^{2}+(-\beta _{4}+\beta _{7})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)
225.2.e.d \(8\) \(1.797\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}+(\zeta_{24}^{6}-\zeta_{24}^{7})q^{3}-\zeta_{24}^{2}q^{4}+\cdots\)
225.2.e.e \(8\) \(1.797\) 8.0.1223810289.2 None None \(2\) \(-1\) \(0\) \(-1\) \(q+\beta _{1}q^{2}+(\beta _{4}-\beta _{7})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)
225.2.f.a \(4\) \(1.797\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(8\) \(q+\zeta_{8}q^{2}-\zeta_{8}^{2}q^{4}+(2-2\zeta_{8}^{2})q^{7}+\cdots\)
225.2.f.b \(8\) \(1.797\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{6}q^{2}-4\zeta_{24}^{2}q^{4}+\zeta_{24}q^{7}+\cdots\)
225.2.h.a \(4\) \(1.797\) \(\Q(\zeta_{10})\) None None \(1\) \(0\) \(-5\) \(0\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{4}+\cdots\)
225.2.h.b \(4\) \(1.797\) \(\Q(\zeta_{10})\) None None \(2\) \(0\) \(5\) \(-2\) \(q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+(-1+\zeta_{10}+\zeta_{10}^{3})q^{4}+\cdots\)
225.2.h.c \(8\) \(1.797\) 8.0.26265625.1 None None \(1\) \(0\) \(5\) \(4\) \(q+(\beta _{3}+\beta _{7})q^{2}+(-1+2\beta _{1}+2\beta _{3}+\cdots)q^{4}+\cdots\)
225.2.h.d \(12\) \(1.797\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(6\) \(-12\) \(q+\beta _{2}q^{2}+(-1+\beta _{1}-\beta _{5}-2\beta _{8}+\beta _{9}+\cdots)q^{4}+\cdots\)
225.2.h.e \(16\) \(1.797\) 16.0.\(\cdots\).3 None None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{3}-\beta _{10}+\beta _{12}-\beta _{14})q^{2}+(-\beta _{8}+\cdots)q^{4}+\cdots\)
225.2.k.a \(4\) \(1.797\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
225.2.k.b \(12\) \(1.797\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{6}-\beta _{7})q^{2}+\beta _{6}q^{3}+(2+2\beta _{8}+\cdots)q^{4}+\cdots\)
225.2.k.c \(16\) \(1.797\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{10}+\beta _{14})q^{3}+(1-\beta _{3}+\cdots)q^{4}+\cdots\)
225.2.m.a \(8\) \(1.797\) 8.0.58140625.2 None None \(5\) \(0\) \(0\) \(0\) \(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
225.2.m.b \(16\) \(1.797\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{3}+\beta _{4}-\beta _{10}+\beta _{15})q^{2}+\cdots\)
225.2.m.c \(24\) \(1.797\) None None \(0\) \(0\) \(0\) \(0\)
225.2.p.a \(16\) \(1.797\) 16.0.\(\cdots\).9 None None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{6}-\beta _{13})q^{2}+\beta _{1}q^{3}+(-\beta _{9}+\cdots)q^{4}+\cdots\)
225.2.p.b \(16\) \(1.797\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(6\) \(6\) \(0\) \(2\) \(q+\beta _{5}q^{2}+(1-\beta _{9}+\beta _{11}+\beta _{12}+\beta _{13}+\cdots)q^{3}+\cdots\)
225.2.p.c \(32\) \(1.797\) None None \(0\) \(0\) \(0\) \(0\)
225.2.q.a \(224\) \(1.797\) None None \(-3\) \(-8\) \(-8\) \(-8\)
225.2.s.a \(80\) \(1.797\) None None \(0\) \(0\) \(0\) \(8\)
225.2.u.a \(224\) \(1.797\) None None \(-5\) \(-10\) \(0\) \(0\)
225.2.w.a \(448\) \(1.797\) None None \(-24\) \(-14\) \(-24\) \(-8\)
225.3.c.a \(2\) \(6.131\) \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(-18\) \(q+\beta q^{2}+2q^{4}-9q^{7}+6\beta q^{8}+13\beta q^{11}+\cdots\)
225.3.c.b \(2\) \(6.131\) \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(18\) \(q+\beta q^{2}+2q^{4}+9q^{7}+6\beta q^{8}-13\beta q^{11}+\cdots\)
225.3.c.c \(4\) \(6.131\) \(\Q(\sqrt{-2}, \sqrt{-5})\) None None \(0\) \(0\) \(0\) \(-16\) \(q+\beta _{2}q^{2}+(-3-2\beta _{1})q^{4}+(-4-\beta _{1}+\cdots)q^{7}+\cdots\)
225.3.c.d \(4\) \(6.131\) \(\Q(\sqrt{-2}, \sqrt{-7})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}-3q^{4}-\beta _{1}q^{7}-\beta _{2}q^{8}-\beta _{3}q^{11}+\cdots\)
225.3.d.a \(4\) \(6.131\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{2}-2q^{4}+9\zeta_{8}q^{7}-6\zeta_{8}^{3}q^{8}+\cdots\)
225.3.d.b \(8\) \(6.131\) 8.0.40960000.1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{2}+(3-\beta _{6})q^{4}+(2\beta _{1}-\beta _{3})q^{7}+\cdots\)
225.3.g.a \(4\) \(6.131\) \(\Q(i, \sqrt{6})\) None None \(-4\) \(0\) \(0\) \(-4\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}+(-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
225.3.g.b \(4\) \(6.131\) \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(0\) \(0\) \(q+2\beta _{1}q^{2}+8\beta _{2}q^{4}+5\beta _{1}q^{7}+8\beta _{3}q^{8}+\cdots\)
225.3.g.c \(4\) \(6.131\) \(\Q(i, \sqrt{30})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+11\beta _{2}q^{4}+7\beta _{3}q^{8}-61q^{16}+\cdots\)
225.3.g.d \(4\) \(6.131\) \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-4\beta _{2}q^{4}+\beta _{1}q^{7}-3\beta _{3}q^{13}-2^{4}q^{16}+\cdots\)
225.3.g.e \(4\) \(6.131\) \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{2}q^{4}+4\beta _{1}q^{7}-5\beta _{3}q^{8}+\cdots\)
225.3.g.f \(4\) \(6.131\) \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{2}q^{4}-6\beta _{1}q^{7}-5\beta _{3}q^{8}+\cdots\)
225.3.g.g \(4\) \(6.131\) \(\Q(i, \sqrt{10})\) None None \(0\) \(0\) \(0\) \(20\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(5+5\beta _{2})q^{7}-3\beta _{3}q^{8}+\cdots\)
225.3.i.a \(4\) \(6.131\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{2}+(-3\zeta_{12}+3\zeta_{12}^{3})q^{3}+\cdots\)
225.3.i.b \(32\) \(6.131\) None None \(0\) \(0\) \(0\) \(0\)
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