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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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