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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
350.2.a.a \(1\) \(2.795\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
350.2.a.b \(1\) \(2.795\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}-3q^{9}+4q^{11}+\cdots\)
350.2.a.c \(1\) \(2.795\) \(\Q\) None \(-1\) \(3\) \(0\) \(1\) \(-\) \(q-q^{2}+3q^{3}+q^{4}-3q^{6}+q^{7}-q^{8}+\cdots\)
350.2.a.d \(1\) \(2.795\) \(\Q\) None \(1\) \(-3\) \(0\) \(-1\) \(+\) \(q+q^{2}-3q^{3}+q^{4}-3q^{6}-q^{7}+q^{8}+\cdots\)
350.2.a.e \(1\) \(2.795\) \(\Q\) None \(1\) \(1\) \(0\) \(1\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
350.2.a.f \(1\) \(2.795\) \(\Q\) None \(1\) \(2\) \(0\) \(-1\) \(-\) \(q+q^{2}+2q^{3}+q^{4}+2q^{6}-q^{7}+q^{8}+\cdots\)
350.2.a.g \(2\) \(2.795\) \(\Q(\sqrt{6}) \) None \(-2\) \(0\) \(0\) \(-2\) \(-\) \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{7}-q^{8}+\cdots\)
350.2.a.h \(2\) \(2.795\) \(\Q(\sqrt{6}) \) None \(2\) \(0\) \(0\) \(2\) \(-\) \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+q^{7}+q^{8}+\cdots\)
350.2.c.a \(2\) \(2.795\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+3iq^{3}-q^{4}-3q^{6}-iq^{7}+\cdots\)
350.2.c.b \(2\) \(2.795\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{7}-iq^{8}+3q^{9}+\cdots\)
350.2.c.c \(2\) \(2.795\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+iq^{7}-iq^{8}+\cdots\)
350.2.c.d \(2\) \(2.795\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-2iq^{3}-q^{4}+2q^{6}-iq^{7}+\cdots\)
350.2.e.a \(2\) \(2.795\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-2\) \(0\) \(-5\) \(q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
350.2.e.b \(2\) \(2.795\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-2\) \(0\) \(4\) \(q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
350.2.e.c \(2\) \(2.795\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(-4\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(-3+2\zeta_{6})q^{7}+\cdots\)
350.2.e.d \(2\) \(2.795\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(1\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(2-3\zeta_{6})q^{7}+\cdots\)
350.2.e.e \(2\) \(2.795\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(1\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
350.2.e.f \(2\) \(2.795\) \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(0\) \(5\) \(q-\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
350.2.e.g \(2\) \(2.795\) \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(0\) \(-5\) \(q+\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
350.2.e.h \(2\) \(2.795\) \(\Q(\sqrt{-3}) \) None \(1\) \(-2\) \(0\) \(4\) \(q+\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
350.2.e.i \(2\) \(2.795\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(-1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(-2+3\zeta_{6})q^{7}+\cdots\)
350.2.e.j \(2\) \(2.795\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(4\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(3-2\zeta_{6})q^{7}+\cdots\)
350.2.e.k \(2\) \(2.795\) \(\Q(\sqrt{-3}) \) None \(1\) \(2\) \(0\) \(5\) \(q+\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
350.2.e.l \(2\) \(2.795\) \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(0\) \(-1\) \(q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
350.2.g.a \(8\) \(2.795\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(8\) \(q+\zeta_{16}q^{2}+\zeta_{16}^{2}q^{3}+\zeta_{16}^{3}q^{4}+(\zeta_{16}^{4}+\cdots)q^{6}+\cdots\)
350.2.g.b \(16\) \(2.795\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+\beta _{3}q^{3}+\beta _{10}q^{4}+\beta _{15}q^{6}+\cdots\)
350.2.h.a \(8\) \(2.795\) \(\Q(\zeta_{15})\) None \(-2\) \(3\) \(0\) \(8\) \(q+\zeta_{15}^{4}q^{2}+(-\zeta_{15}^{3}-\zeta_{15}^{4}+\zeta_{15}^{6}+\cdots)q^{3}+\cdots\)
350.2.h.b \(12\) \(2.795\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(3\) \(1\) \(-5\) \(-12\) \(q+\beta _{5}q^{2}+(\beta _{1}-\beta _{3}+\beta _{7})q^{3}-\beta _{3}q^{4}+\cdots\)
350.2.h.c \(16\) \(2.795\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(-4\) \(1\) \(-4\) \(-16\) \(q+\beta _{6}q^{2}-\beta _{10}q^{3}-\beta _{1}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
350.2.h.d \(20\) \(2.795\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(5\) \(3\) \(-5\) \(20\) \(q+\beta _{14}q^{2}+\beta _{1}q^{3}+\beta _{6}q^{4}+(\beta _{10}+\beta _{13}+\cdots)q^{5}+\cdots\)
350.2.j.a \(4\) \(2.795\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(-2\zeta_{12}+2\zeta_{12}^{3})q^{3}+\cdots\)
350.2.j.b \(4\) \(2.795\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
350.2.j.c \(4\) \(2.795\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(3\zeta_{12}-2\zeta_{12}^{3})q^{7}+\cdots\)
350.2.j.d \(4\) \(2.795\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(2\zeta_{12}-2\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
350.2.j.e \(4\) \(2.795\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(2\zeta_{12}-2\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
350.2.j.f \(4\) \(2.795\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(3\zeta_{12}-3\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
350.2.m.a \(24\) \(2.795\) None \(0\) \(0\) \(10\) \(0\)
350.2.m.b \(40\) \(2.795\) None \(0\) \(0\) \(6\) \(0\)
350.2.o.a \(8\) \(2.795\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{7}q^{2}+(2\zeta_{24}-\zeta_{24}^{3}-\zeta_{24}^{5}+\cdots)q^{3}+\cdots\)
350.2.o.b \(8\) \(2.795\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{7}q^{2}+(2\zeta_{24}+\zeta_{24}^{3}-\zeta_{24}^{5}+\cdots)q^{3}+\cdots\)
350.2.o.c \(16\) \(2.795\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(-8\) \(q+\beta _{13}q^{2}+(\beta _{3}-\beta _{7}-\beta _{15})q^{3}+(\beta _{11}+\cdots)q^{4}+\cdots\)
350.2.o.d \(16\) \(2.795\) 16.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{5}+\beta _{7})q^{2}+(-\beta _{4}-\beta _{13}+\beta _{14}+\cdots)q^{3}+\cdots\)
350.2.q.a \(8\) \(2.795\) \(\Q(\zeta_{15})\) None \(-1\) \(-3\) \(0\) \(-4\) \(q-\zeta_{15}q^{2}+(1-\zeta_{15}^{2}+\zeta_{15}^{3}-\zeta_{15}^{4}+\cdots)q^{3}+\cdots\)
350.2.q.b \(72\) \(2.795\) None \(-9\) \(1\) \(0\) \(8\)
350.2.q.c \(80\) \(2.795\) None \(10\) \(2\) \(-2\) \(4\)
350.2.r.a \(160\) \(2.795\) None \(0\) \(0\) \(0\) \(8\)
350.2.u.a \(160\) \(2.795\) None \(0\) \(0\) \(-2\) \(0\)
350.2.x.a \(320\) \(2.795\) None \(0\) \(0\) \(12\) \(-8\)
350.3.b.a \(4\) \(9.537\) 4.0.7168.1 None \(0\) \(0\) \(0\) \(-12\) \(q+\beta _{3}q^{2}+\beta _{1}q^{3}+2q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{6}+\cdots\)
350.3.b.b \(4\) \(9.537\) 4.0.7168.1 None \(0\) \(0\) \(0\) \(12\) \(q-\beta _{3}q^{2}+\beta _{1}q^{3}+2q^{4}+(\beta _{1}-\beta _{2}+\cdots)q^{6}+\cdots\)
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