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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
405.1.h.a \(2\) \(0.202\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-15}) \) None \(-1\) \(0\) \(1\) \(0\) \(q-\zeta_{6}q^{2}-\zeta_{6}^{2}q^{5}-q^{8}-q^{10}+\zeta_{6}q^{16}+\cdots\)
405.1.h.b \(2\) \(0.202\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-15}) \) None \(1\) \(0\) \(-1\) \(0\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{5}+q^{8}-q^{10}+\zeta_{6}q^{16}+\cdots\)
405.2.a.a \(1\) \(3.234\) \(\Q\) None None \(-2\) \(0\) \(-1\) \(0\) \(+\) \(q-2q^{2}+2q^{4}-q^{5}+2q^{10}-5q^{11}+\cdots\)
405.2.a.b \(1\) \(3.234\) \(\Q\) None None \(-1\) \(0\) \(1\) \(-3\) \(+\) \(q-q^{2}-q^{4}+q^{5}-3q^{7}+3q^{8}-q^{10}+\cdots\)
405.2.a.c \(1\) \(3.234\) \(\Q\) None None \(0\) \(0\) \(-1\) \(2\) \(+\) \(q-2q^{4}-q^{5}+2q^{7}-3q^{11}-4q^{13}+\cdots\)
405.2.a.d \(1\) \(3.234\) \(\Q\) None None \(0\) \(0\) \(1\) \(2\) \(-\) \(q-2q^{4}+q^{5}+2q^{7}+3q^{11}-4q^{13}+\cdots\)
405.2.a.e \(1\) \(3.234\) \(\Q\) None None \(1\) \(0\) \(-1\) \(-3\) \(+\) \(q+q^{2}-q^{4}-q^{5}-3q^{7}-3q^{8}-q^{10}+\cdots\)
405.2.a.f \(1\) \(3.234\) \(\Q\) None None \(2\) \(0\) \(1\) \(0\) \(-\) \(q+2q^{2}+2q^{4}+q^{5}+2q^{10}+5q^{11}+\cdots\)
405.2.a.g \(2\) \(3.234\) \(\Q(\sqrt{3}) \) None None \(-2\) \(0\) \(2\) \(-6\) \(+\) \(q+(-1+\beta )q^{2}+(2-2\beta )q^{4}+q^{5}+(-3+\cdots)q^{7}+\cdots\)
405.2.a.h \(2\) \(3.234\) \(\Q(\sqrt{3}) \) None None \(2\) \(0\) \(-2\) \(-6\) \(-\) \(q+(1+\beta )q^{2}+(2+2\beta )q^{4}-q^{5}+(-3+\cdots)q^{7}+\cdots\)
405.2.a.i \(3\) \(3.234\) 3.3.564.1 None None \(-1\) \(0\) \(-3\) \(5\) \(-\) \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots\)
405.2.a.j \(3\) \(3.234\) 3.3.564.1 None None \(1\) \(0\) \(3\) \(5\) \(-\) \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots\)
405.2.b.a \(4\) \(3.234\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(0\) \(-3\) \(0\) \(q-\beta _{2}q^{2}+(-2+\beta _{1}+\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)
405.2.b.b \(4\) \(3.234\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(0\) \(3\) \(0\) \(q-\beta _{2}q^{2}+(-2+\beta _{1}+\beta _{3})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
405.2.b.c \(4\) \(3.234\) \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots\)
405.2.b.d \(4\) \(3.234\) \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots\)
405.2.b.e \(4\) \(3.234\) \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{5}+\beta _{3}q^{7}-2\beta _{1}q^{8}+\cdots\)
405.2.e.a \(2\) \(3.234\) \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(-1\) \(0\) \(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\)
405.2.e.b \(2\) \(3.234\) \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(-1\) \(3\) \(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\)
405.2.e.c \(2\) \(3.234\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(0\) \(1\) \(0\) \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+\zeta_{6}q^{5}-3q^{8}+\cdots\)
405.2.e.d \(2\) \(3.234\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(-2\) \(q+2\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+\cdots\)
405.2.e.e \(2\) \(3.234\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(1\) \(-2\) \(q+2\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+\cdots\)
405.2.e.f \(2\) \(3.234\) \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(-1\) \(0\) \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+3q^{8}+\cdots\)
405.2.e.g \(2\) \(3.234\) \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(1\) \(0\) \(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+\zeta_{6}q^{5}+2q^{10}+\cdots\)
405.2.e.h \(2\) \(3.234\) \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(1\) \(3\) \(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+\zeta_{6}q^{5}+(3+\cdots)q^{7}+\cdots\)
405.2.e.i \(4\) \(3.234\) \(\Q(\zeta_{12})\) None None \(-2\) \(0\) \(2\) \(6\) \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-2+2\zeta_{12}+\cdots)q^{4}+\cdots\)
405.2.e.j \(4\) \(3.234\) \(\Q(\sqrt{-3}, \sqrt{13})\) None None \(-1\) \(0\) \(2\) \(-2\) \(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
405.2.e.k \(4\) \(3.234\) \(\Q(\sqrt{-3}, \sqrt{13})\) None None \(1\) \(0\) \(-2\) \(-2\) \(q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
405.2.e.l \(4\) \(3.234\) \(\Q(\zeta_{12})\) None None \(2\) \(0\) \(-2\) \(6\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(-2+2\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
405.2.f.a \(16\) \(3.234\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(4\) \(q+\beta _{3}q^{2}+(\beta _{6}-\beta _{14})q^{4}-\beta _{4}q^{5}+\beta _{10}q^{7}+\cdots\)
405.2.f.b \(24\) \(3.234\) None None \(0\) \(0\) \(0\) \(0\)
405.2.j.a \(4\) \(3.234\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(-3\) \(0\) \(-6\) \(-12\) \(q+(-1-\beta _{3})q^{2}+(2-\beta _{1}-\beta _{2}+2\beta _{3})q^{4}+\cdots\)
405.2.j.b \(4\) \(3.234\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(-3\) \(0\) \(-3\) \(12\) \(q+(-1-\beta _{3})q^{2}+(2-\beta _{1}-\beta _{2}+2\beta _{3})q^{4}+\cdots\)
405.2.j.c \(4\) \(3.234\) \(\Q(\sqrt{-3}, \sqrt{-5})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+3\beta _{2}q^{4}+(\beta _{1}-\beta _{3})q^{5}+\beta _{3}q^{8}+\cdots\)
405.2.j.d \(4\) \(3.234\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(3\) \(0\) \(3\) \(12\) \(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
405.2.j.e \(4\) \(3.234\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(3\) \(0\) \(6\) \(-12\) \(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
405.2.j.f \(8\) \(3.234\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{6}q^{2}-\zeta_{24}^{4}q^{5}-\zeta_{24}q^{7}+(2\zeta_{24}^{5}+\cdots)q^{8}+\cdots\)
405.2.j.g \(8\) \(3.234\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{5}q^{2}+(\zeta_{24}^{2}+\zeta_{24}^{3})q^{5}+\zeta_{24}^{6}q^{7}+\cdots\)
405.2.j.h \(8\) \(3.234\) 8.0.12960000.1 \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(2-\beta _{3}+2\beta _{5}+\beta _{6})q^{4}+\cdots\)
405.2.k.a \(30\) \(3.234\) None None \(0\) \(0\) \(0\) \(0\)
405.2.k.b \(42\) \(3.234\) None None \(0\) \(0\) \(0\) \(0\)
405.2.m.a \(8\) \(3.234\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(8\) \(q+\zeta_{24}^{7}q^{2}+\zeta_{24}^{2}q^{4}+(-\zeta_{24}^{3}+2\zeta_{24}^{5}+\cdots)q^{5}+\cdots\)
405.2.m.b \(16\) \(3.234\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(-8\) \(q+(\beta _{9}-\beta _{10})q^{2}+(-2\beta _{1}-\beta _{13}-\beta _{14}+\cdots)q^{4}+\cdots\)
405.2.m.c \(16\) \(3.234\) 16.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(4\) \(q-\beta _{10}q^{2}+(-\beta _{9}-\beta _{15})q^{4}+(-\beta _{7}+\cdots)q^{5}+\cdots\)
405.2.m.d \(24\) \(3.234\) None None \(0\) \(0\) \(0\) \(-12\)
405.2.m.e \(24\) \(3.234\) None None \(0\) \(0\) \(0\) \(12\)
405.2.p.a \(96\) \(3.234\) None None \(0\) \(0\) \(9\) \(0\)
405.2.q.a \(306\) \(3.234\) None None \(0\) \(0\) \(0\) \(0\)
405.2.q.b \(342\) \(3.234\) None None \(0\) \(0\) \(0\) \(0\)
405.2.r.a \(192\) \(3.234\) None None \(12\) \(0\) \(12\) \(-12\)
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