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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
735.1.f.a \(1\) \(0.367\) \(\Q\) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-35}) \) \(\Q(\sqrt{21}) \) \(0\) \(-1\) \(-1\) \(0\) \(q-q^{3}-q^{4}-q^{5}+q^{9}+q^{12}+q^{15}+\cdots\)
735.1.f.b \(1\) \(0.367\) \(\Q\) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-35}) \) \(\Q(\sqrt{21}) \) \(0\) \(1\) \(1\) \(0\) \(q+q^{3}-q^{4}+q^{5}+q^{9}-q^{12}+q^{15}+\cdots\)
735.1.f.c \(2\) \(0.367\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-15}) \) None \(0\) \(-2\) \(2\) \(0\) \(q-\beta q^{2}-q^{3}+q^{4}+q^{5}+\beta q^{6}+q^{9}+\cdots\)
735.1.f.d \(2\) \(0.367\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-15}) \) None \(0\) \(2\) \(-2\) \(0\) \(q-\beta q^{2}+q^{3}+q^{4}-q^{5}-\beta q^{6}+q^{9}+\cdots\)
735.1.o.a \(2\) \(0.367\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-35}) \) \(\Q(\sqrt{21}) \) \(0\) \(-1\) \(-1\) \(0\) \(q-\zeta_{6}q^{3}+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}+\cdots\)
735.1.o.b \(2\) \(0.367\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-35}) \) \(\Q(\sqrt{21}) \) \(0\) \(1\) \(1\) \(0\) \(q+\zeta_{6}q^{3}+\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}+\cdots\)
735.1.o.c \(4\) \(0.367\) \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-15}) \) None \(0\) \(-2\) \(2\) \(0\) \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
735.1.o.d \(4\) \(0.367\) \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-15}) \) None \(0\) \(2\) \(-2\) \(0\) \(q-\beta _{1}q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
735.2.a.a \(1\) \(5.869\) \(\Q\) None None \(-2\) \(-1\) \(-1\) \(0\) \(-\) \(q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}+q^{9}+\cdots\)
735.2.a.b \(1\) \(5.869\) \(\Q\) None None \(-2\) \(1\) \(1\) \(0\) \(+\) \(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}+q^{9}+\cdots\)
735.2.a.c \(1\) \(5.869\) \(\Q\) None None \(-1\) \(1\) \(-1\) \(0\) \(+\) \(q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}+3q^{8}+\cdots\)
735.2.a.d \(1\) \(5.869\) \(\Q\) None None \(0\) \(-1\) \(1\) \(0\) \(+\) \(q-q^{3}-2q^{4}+q^{5}+q^{9}+2q^{12}+q^{13}+\cdots\)
735.2.a.e \(1\) \(5.869\) \(\Q\) None None \(0\) \(1\) \(-1\) \(0\) \(-\) \(q+q^{3}-2q^{4}-q^{5}+q^{9}-2q^{12}-q^{13}+\cdots\)
735.2.a.f \(1\) \(5.869\) \(\Q\) None None \(1\) \(-1\) \(-1\) \(0\) \(-\) \(q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}-3q^{8}+\cdots\)
735.2.a.g \(2\) \(5.869\) \(\Q(\sqrt{3}) \) None None \(-2\) \(-2\) \(2\) \(0\) \(-\) \(q+(-1+\beta )q^{2}-q^{3}+(2-2\beta )q^{4}+q^{5}+\cdots\)
735.2.a.h \(2\) \(5.869\) \(\Q(\sqrt{3}) \) None None \(-2\) \(2\) \(-2\) \(0\) \(+\) \(q+(-1+\beta )q^{2}+q^{3}+(2-2\beta )q^{4}-q^{5}+\cdots\)
735.2.a.i \(2\) \(5.869\) \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(-2\) \(0\) \(+\) \(q+\beta q^{2}-q^{3}-q^{5}-\beta q^{6}-2\beta q^{8}+\cdots\)
735.2.a.j \(2\) \(5.869\) \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(2\) \(0\) \(-\) \(q+\beta q^{2}+q^{3}+q^{5}+\beta q^{6}-2\beta q^{8}+\cdots\)
735.2.a.k \(2\) \(5.869\) \(\Q(\sqrt{5}) \) None None \(0\) \(2\) \(2\) \(0\) \(-\) \(q-\beta q^{2}+q^{3}+3q^{4}+q^{5}-\beta q^{6}-\beta q^{8}+\cdots\)
735.2.a.l \(2\) \(5.869\) \(\Q(\sqrt{2}) \) None None \(2\) \(-2\) \(-2\) \(0\) \(-\) \(q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}-q^{5}+\cdots\)
735.2.a.m \(2\) \(5.869\) \(\Q(\sqrt{2}) \) None None \(2\) \(2\) \(2\) \(0\) \(-\) \(q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}+q^{5}+\cdots\)
735.2.a.n \(4\) \(5.869\) 4.4.4352.1 None None \(4\) \(-4\) \(4\) \(0\) \(-\) \(q+(1+\beta _{1}-\beta _{3})q^{2}-q^{3}+(2+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
735.2.a.o \(4\) \(5.869\) 4.4.4352.1 None None \(4\) \(4\) \(-4\) \(0\) \(-\) \(q+(1+\beta _{1}-\beta _{3})q^{2}+q^{3}+(2+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
735.2.b.a \(2\) \(5.869\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(-2\) \(0\) \(q+(1-2\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-q^{4}+\cdots\)
735.2.b.b \(2\) \(5.869\) \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(2\) \(0\) \(q+(1-2\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-q^{4}+q^{5}+\cdots\)
735.2.b.c \(8\) \(5.869\) 8.0.856615824.2 None None \(0\) \(-1\) \(8\) \(0\) \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(-1+\beta _{2})q^{4}+q^{5}+\cdots\)
735.2.b.d \(8\) \(5.869\) 8.0.856615824.2 None None \(0\) \(1\) \(-8\) \(0\) \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(-1+\beta _{2})q^{4}-q^{5}+\cdots\)
735.2.b.e \(16\) \(5.869\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(-4\) \(16\) \(0\) \(q+\beta _{1}q^{2}+\beta _{7}q^{3}+(-\beta _{3}-\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)
735.2.b.f \(16\) \(5.869\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(4\) \(-16\) \(0\) \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(-\beta _{3}-\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)
735.2.d.a \(2\) \(5.869\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{2}-iq^{3}+q^{4}+(-1+2i)q^{5}+\cdots\)
735.2.d.b \(6\) \(5.869\) 6.0.350464.1 None None \(0\) \(0\) \(-2\) \(0\) \(q-\beta _{1}q^{2}-\beta _{4}q^{3}+(-1+\beta _{3}+\beta _{5})q^{4}+\cdots\)
735.2.d.c \(8\) \(5.869\) 8.0.309760000.3 None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{2}-\beta _{4}q^{3}+(-2+\beta _{6}-\beta _{7})q^{4}+\cdots\)
735.2.d.d \(8\) \(5.869\) 8.0.2058981376.2 None None \(0\) \(0\) \(-2\) \(0\) \(q+\beta _{6}q^{2}-\beta _{4}q^{3}+(-1+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
735.2.d.e \(8\) \(5.869\) 8.0.2058981376.2 None None \(0\) \(0\) \(2\) \(0\) \(q+\beta _{6}q^{2}+\beta _{4}q^{3}+(-1+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
735.2.d.f \(8\) \(5.869\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{4}q^{2}+\zeta_{24}q^{3}+\zeta_{24}^{3}q^{4}+(-\zeta_{24}^{2}+\cdots)q^{5}+\cdots\)
735.2.g.a \(16\) \(5.869\) 16.0.\(\cdots\).5 \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}+\beta _{5}q^{3}+(2-\beta _{8})q^{4}+\beta _{11}q^{5}+\cdots\)
735.2.g.b \(24\) \(5.869\) None None \(0\) \(0\) \(0\) \(0\)
735.2.g.c \(32\) \(5.869\) None None \(0\) \(0\) \(0\) \(0\)
735.2.i.a \(2\) \(5.869\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(-1\) \(-1\) \(0\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
735.2.i.b \(2\) \(5.869\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(1\) \(1\) \(0\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
735.2.i.c \(2\) \(5.869\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-1\) \(0\) \(q+(1-\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}-\zeta_{6}q^{5}+\cdots\)
735.2.i.d \(2\) \(5.869\) \(\Q(\sqrt{-3}) \) None None \(1\) \(-1\) \(1\) \(0\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
735.2.i.e \(2\) \(5.869\) \(\Q(\sqrt{-3}) \) None None \(1\) \(1\) \(-1\) \(0\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
735.2.i.f \(2\) \(5.869\) \(\Q(\sqrt{-3}) \) None None \(2\) \(1\) \(1\) \(0\) \(q+2\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
735.2.i.g \(4\) \(5.869\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(-2\) \(-2\) \(-2\) \(0\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}+\beta _{2}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
735.2.i.h \(4\) \(5.869\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(-2\) \(2\) \(2\) \(0\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}-\beta _{2}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
735.2.i.i \(4\) \(5.869\) \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(0\) \(-2\) \(-2\) \(0\) \(q-\beta _{2}q^{2}+\beta _{1}q^{3}+3\beta _{1}q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
735.2.i.j \(4\) \(5.869\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(-2\) \(-2\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-1-\beta _{2})q^{5}+\beta _{3}q^{6}+\cdots\)
735.2.i.k \(4\) \(5.869\) \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(0\) \(2\) \(2\) \(0\) \(q-\beta _{2}q^{2}-\beta _{1}q^{3}+3\beta _{1}q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
735.2.i.l \(4\) \(5.869\) \(\Q(\zeta_{12})\) None None \(2\) \(-2\) \(2\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(-1+\zeta_{12})q^{3}+\cdots\)
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