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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
450.2.a.a \(1\) \(3.593\) \(\Q\) None \(-1\) \(0\) \(0\) \(-2\) \(+\) \(q-q^{2}+q^{4}-2q^{7}-q^{8}-6q^{11}+4q^{13}+\cdots\)
450.2.a.b \(1\) \(3.593\) \(\Q\) None \(-1\) \(0\) \(0\) \(-2\) \(+\) \(q-q^{2}+q^{4}-2q^{7}-q^{8}-2q^{11}-6q^{13}+\cdots\)
450.2.a.c \(1\) \(3.593\) \(\Q\) None \(-1\) \(0\) \(0\) \(-2\) \(-\) \(q-q^{2}+q^{4}-2q^{7}-q^{8}+3q^{11}+4q^{13}+\cdots\)
450.2.a.d \(1\) \(3.593\) \(\Q\) None \(-1\) \(0\) \(0\) \(4\) \(-\) \(q-q^{2}+q^{4}+4q^{7}-q^{8}-2q^{13}-4q^{14}+\cdots\)
450.2.a.e \(1\) \(3.593\) \(\Q\) None \(1\) \(0\) \(0\) \(-2\) \(-\) \(q+q^{2}+q^{4}-2q^{7}+q^{8}+6q^{11}+4q^{13}+\cdots\)
450.2.a.f \(1\) \(3.593\) \(\Q\) None \(1\) \(0\) \(0\) \(2\) \(-\) \(q+q^{2}+q^{4}+2q^{7}+q^{8}-2q^{11}+6q^{13}+\cdots\)
450.2.a.g \(1\) \(3.593\) \(\Q\) None \(1\) \(0\) \(0\) \(2\) \(-\) \(q+q^{2}+q^{4}+2q^{7}+q^{8}+3q^{11}-4q^{13}+\cdots\)
450.2.c.a \(2\) \(3.593\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}-6q^{11}+\cdots\)
450.2.c.b \(2\) \(3.593\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-4iq^{7}-iq^{8}-2iq^{13}+\cdots\)
450.2.c.c \(2\) \(3.593\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}+3q^{11}+\cdots\)
450.2.c.d \(2\) \(3.593\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-2iq^{7}-iq^{8}+6q^{11}+\cdots\)
450.2.e.a \(2\) \(3.593\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(0\) \(-4\) \(q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
450.2.e.b \(2\) \(3.593\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(0\) \(1\) \(q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
450.2.e.c \(2\) \(3.593\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(-2\) \(q+(-1+\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
450.2.e.d \(2\) \(3.593\) \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(0\) \(-4\) \(q+(-1+\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
450.2.e.e \(2\) \(3.593\) \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(0\) \(-1\) \(q+(1-\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
450.2.e.f \(2\) \(3.593\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(2\) \(q+(1-\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
450.2.e.g \(2\) \(3.593\) \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(0\) \(-1\) \(q+(1-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
450.2.e.h \(2\) \(3.593\) \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(0\) \(4\) \(q+(1-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
450.2.e.i \(2\) \(3.593\) \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(0\) \(2\) \(q+(1-\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
450.2.e.j \(4\) \(3.593\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-2\) \(-2\) \(0\) \(1\) \(q+(-1+\beta _{2})q^{2}+(-\beta _{1}+\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots\)
450.2.e.k \(4\) \(3.593\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-2\) \(2\) \(0\) \(4\) \(q-\beta _{2}q^{2}+(-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
450.2.e.l \(4\) \(3.593\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-2\) \(4\) \(0\) \(4\) \(q+(-1+\beta _{2})q^{2}+(1-\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots\)
450.2.e.m \(4\) \(3.593\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(2\) \(-4\) \(0\) \(-4\) \(q+(1-\beta _{2})q^{2}+(-1+\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots\)
450.2.e.n \(4\) \(3.593\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(2\) \(-2\) \(0\) \(-4\) \(q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
450.2.f.a \(4\) \(3.593\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-12\) \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-3+3\zeta_{8}^{2})q^{7}+\cdots\)
450.2.f.b \(4\) \(3.593\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-8\) \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-2+2\zeta_{8}^{2})q^{7}+\cdots\)
450.2.f.c \(4\) \(3.593\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(12\) \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(3-3\zeta_{8}^{2})q^{7}+\cdots\)
450.2.h.a \(4\) \(3.593\) \(\Q(\zeta_{10})\) None \(-1\) \(0\) \(-5\) \(-12\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
450.2.h.b \(4\) \(3.593\) \(\Q(\zeta_{10})\) None \(-1\) \(0\) \(-5\) \(8\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
450.2.h.c \(4\) \(3.593\) \(\Q(\zeta_{10})\) None \(1\) \(0\) \(-5\) \(6\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{4}+\cdots\)
450.2.h.d \(8\) \(3.593\) 8.0.1064390625.3 None \(-2\) \(0\) \(4\) \(-2\) \(q-\beta _{3}q^{2}+(-1-\beta _{2}+\beta _{3}-\beta _{5})q^{4}+\cdots\)
450.2.h.e \(8\) \(3.593\) 8.0.58140625.2 None \(2\) \(0\) \(0\) \(4\) \(q+\beta _{6}q^{2}-\beta _{3}q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
450.2.h.f \(12\) \(3.593\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-3\) \(0\) \(1\) \(-2\) \(q-\beta _{7}q^{2}+(-1+\beta _{4}-\beta _{6}+\beta _{7})q^{4}+\cdots\)
450.2.h.g \(12\) \(3.593\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(3\) \(0\) \(-1\) \(-2\) \(q+\beta _{7}q^{2}+(-1+\beta _{4}-\beta _{6}+\beta _{7})q^{4}+\cdots\)
450.2.j.a \(4\) \(3.593\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(-\zeta_{12}+2\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
450.2.j.b \(4\) \(3.593\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(-2\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
450.2.j.c \(4\) \(3.593\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
450.2.j.d \(4\) \(3.593\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
450.2.j.e \(4\) \(3.593\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(\zeta_{12}-2\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
450.2.j.f \(8\) \(3.593\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}+\zeta_{24}^{3})q^{2}+(\zeta_{24}^{3}+\zeta_{24}^{7})q^{3}+\cdots\)
450.2.j.g \(8\) \(3.593\) 8.0.303595776.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}+(\beta _{1}-\beta _{3}-\beta _{5}-\beta _{7})q^{3}+\cdots\)
450.2.l.a \(8\) \(3.593\) \(\Q(\zeta_{20})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}q^{2}+\zeta_{20}^{2}q^{4}+(\zeta_{20}+\zeta_{20}^{2}+\cdots)q^{5}+\cdots\)
450.2.l.b \(8\) \(3.593\) \(\Q(\zeta_{20})\) None \(0\) \(0\) \(10\) \(0\) \(q+\zeta_{20}q^{2}+\zeta_{20}^{2}q^{4}+(1-\zeta_{20}-\zeta_{20}^{3}+\cdots)q^{5}+\cdots\)
450.2.l.c \(16\) \(3.593\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-4\) \(0\) \(q-\beta _{8}q^{2}-\beta _{10}q^{4}+(-1-\beta _{3}+\beta _{5}+\cdots)q^{5}+\cdots\)
450.2.l.d \(16\) \(3.593\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{11}q^{2}+(1+\beta _{3}+\beta _{4}+\beta _{5})q^{4}+\cdots\)
450.2.p.a \(8\) \(3.593\) \(\Q(\zeta_{24})\) None \(0\) \(-4\) \(0\) \(8\) \(q+\zeta_{24}^{7}q^{2}+(-1-\zeta_{24}^{2}+\zeta_{24}^{4}+\cdots)q^{3}+\cdots\)
450.2.p.b \(8\) \(3.593\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{7}q^{2}+(2\zeta_{24}-\zeta_{24}^{5})q^{3}-\zeta_{24}^{2}q^{4}+\cdots\)
450.2.p.c \(8\) \(3.593\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{7}q^{2}+(\zeta_{24}^{3}-2\zeta_{24}^{7})q^{3}-\zeta_{24}^{2}q^{4}+\cdots\)
450.2.p.d \(8\) \(3.593\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{7}q^{2}+(-2\zeta_{24}+\zeta_{24}^{5})q^{3}+\cdots\)
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