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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
480.1.c.a \(4\) \(0.240\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}+(\zeta_{8}+\zeta_{8}^{3})q^{7}+\cdots\)
480.1.i.a \(2\) \(0.240\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{10}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-iq^{5}-q^{9}-q^{15}-q^{25}+\cdots\)
480.1.bu.a \(8\) \(0.240\) \(\Q(\zeta_{16})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{3}q^{2}-\zeta_{16}^{7}q^{3}+\zeta_{16}^{6}q^{4}+\cdots\)
480.2.a.a \(1\) \(3.833\) \(\Q\) None None \(0\) \(-1\) \(-1\) \(-4\) \(-\) \(q-q^{3}-q^{5}-4q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
480.2.a.b \(1\) \(3.833\) \(\Q\) None None \(0\) \(-1\) \(-1\) \(0\) \(+\) \(q-q^{3}-q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
480.2.a.c \(1\) \(3.833\) \(\Q\) None None \(0\) \(-1\) \(1\) \(-4\) \(+\) \(q-q^{3}+q^{5}-4q^{7}+q^{9}-2q^{13}-q^{15}+\cdots\)
480.2.a.d \(1\) \(3.833\) \(\Q\) None None \(0\) \(-1\) \(1\) \(0\) \(-\) \(q-q^{3}+q^{5}+q^{9}+2q^{13}-q^{15}+6q^{17}+\cdots\)
480.2.a.e \(1\) \(3.833\) \(\Q\) None None \(0\) \(1\) \(-1\) \(0\) \(-\) \(q+q^{3}-q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
480.2.a.f \(1\) \(3.833\) \(\Q\) None None \(0\) \(1\) \(-1\) \(4\) \(-\) \(q+q^{3}-q^{5}+4q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
480.2.a.g \(1\) \(3.833\) \(\Q\) None None \(0\) \(1\) \(1\) \(0\) \(-\) \(q+q^{3}+q^{5}+q^{9}+2q^{13}+q^{15}+6q^{17}+\cdots\)
480.2.a.h \(1\) \(3.833\) \(\Q\) None None \(0\) \(1\) \(1\) \(4\) \(-\) \(q+q^{3}+q^{5}+4q^{7}+q^{9}-2q^{13}+q^{15}+\cdots\)
480.2.b.a \(8\) \(3.833\) 8.0.1649659456.5 None None \(0\) \(0\) \(-8\) \(0\) \(q-\beta _{1}q^{3}-q^{5}-\beta _{2}q^{7}+(-\beta _{3}-\beta _{5}+\cdots)q^{9}+\cdots\)
480.2.b.b \(8\) \(3.833\) 8.0.1649659456.5 None None \(0\) \(0\) \(8\) \(0\) \(q-\beta _{1}q^{3}+q^{5}+\beta _{2}q^{7}+(-\beta _{3}-\beta _{5}+\cdots)q^{9}+\cdots\)
480.2.d.a \(6\) \(3.833\) 6.0.839056.1 None None \(0\) \(-6\) \(0\) \(0\) \(q-q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}+q^{9}+(\beta _{1}+\beta _{5})q^{11}+\cdots\)
480.2.d.b \(6\) \(3.833\) 6.0.839056.1 None None \(0\) \(6\) \(0\) \(0\) \(q+q^{3}+\beta _{4}q^{5}+\beta _{1}q^{7}+q^{9}+(\beta _{1}+\beta _{5})q^{11}+\cdots\)
480.2.f.a \(2\) \(3.833\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-4\) \(0\) \(q+iq^{3}+(-2+i)q^{5}-2iq^{7}-q^{9}+\cdots\)
480.2.f.b \(2\) \(3.833\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-4\) \(0\) \(q+iq^{3}+(-2-i)q^{5}-2iq^{7}-q^{9}+\cdots\)
480.2.f.c \(2\) \(3.833\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(0\) \(q+iq^{3}+(1+2i)q^{5}+4iq^{7}-q^{9}+\cdots\)
480.2.f.d \(2\) \(3.833\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(0\) \(q+iq^{3}+(1-2i)q^{5}+4iq^{7}-q^{9}+\cdots\)
480.2.f.e \(4\) \(3.833\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{2}q^{5}-2\beta _{1}q^{7}-q^{9}-2\beta _{3}q^{11}+\cdots\)
480.2.h.a \(4\) \(3.833\) \(\Q(\zeta_{8})\) None None \(0\) \(-4\) \(0\) \(0\) \(q+(-1-\zeta_{8}^{2})q^{3}+\zeta_{8}q^{5}+(-2\zeta_{8}+\cdots)q^{7}+\cdots\)
480.2.h.b \(4\) \(3.833\) \(\Q(\zeta_{8})\) None None \(0\) \(-4\) \(0\) \(0\) \(q+(-1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{5}+\cdots\)
480.2.h.c \(4\) \(3.833\) \(\Q(\zeta_{8})\) None None \(0\) \(4\) \(0\) \(0\) \(q+(1+\zeta_{8}^{2})q^{3}+\zeta_{8}q^{5}+(2\zeta_{8}-2\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
480.2.h.d \(4\) \(3.833\) \(\Q(\zeta_{8})\) None None \(0\) \(4\) \(0\) \(0\) \(q+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots\)
480.2.k.a \(2\) \(3.833\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-4\) \(q+iq^{3}+iq^{5}-2q^{7}-q^{9}+4iq^{11}+\cdots\)
480.2.k.b \(6\) \(3.833\) 6.0.399424.1 None None \(0\) \(0\) \(0\) \(-4\) \(q-\beta _{2}q^{3}+\beta _{2}q^{5}+(-1+\beta _{3})q^{7}-q^{9}+\cdots\)
480.2.m.a \(4\) \(3.833\) \(\Q(\sqrt{3}, \sqrt{-5})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{3}-\beta _{1}q^{5}+3q^{9}+\beta _{2}q^{15}+\cdots\)
480.2.m.b \(16\) \(3.833\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{14}q^{3}+(\beta _{1}+\beta _{10})q^{5}-\beta _{4}q^{7}+\cdots\)
480.2.o.a \(24\) \(3.833\) None None \(0\) \(0\) \(0\) \(0\)
480.2.v.a \(4\) \(3.833\) \(\Q(\zeta_{8})\) None None \(0\) \(-4\) \(0\) \(-12\) \(q+(-1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\)
480.2.v.b \(4\) \(3.833\) \(\Q(\zeta_{8})\) None None \(0\) \(4\) \(0\) \(12\) \(q+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots\)
480.2.v.c \(16\) \(3.833\) 16.0.\(\cdots\).9 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{3}+\beta _{13}q^{5}+(\beta _{5}+\beta _{11})q^{7}+\cdots\)
480.2.v.d \(24\) \(3.833\) None None \(0\) \(0\) \(0\) \(0\)
480.2.w.a \(4\) \(3.833\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(-4\) \(q+\zeta_{8}q^{3}+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+(-1+\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
480.2.w.b \(4\) \(3.833\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(4\) \(q+\zeta_{8}q^{3}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+(1-\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
480.2.w.c \(8\) \(3.833\) 8.0.1698758656.6 None None \(0\) \(0\) \(0\) \(-4\) \(q-\beta _{1}q^{3}+(-\beta _{2}-\beta _{3}-\beta _{5})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
480.2.w.d \(8\) \(3.833\) 8.0.1698758656.6 None None \(0\) \(0\) \(0\) \(4\) \(q+\beta _{1}q^{3}+(-\beta _{2}-\beta _{3}-\beta _{5})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
480.2.bh.a \(24\) \(3.833\) None None \(0\) \(0\) \(0\) \(0\)
480.2.bi.a \(4\) \(3.833\) \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(-4\) \(4\) \(q+\beta _{1}q^{3}+(-1-\beta _{2}+\beta _{3})q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots\)
480.2.bi.b \(4\) \(3.833\) \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(4\) \(4\) \(q+\beta _{1}q^{3}+(1+\beta _{2}+\beta _{3})q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots\)
480.2.bi.c \(32\) \(3.833\) None None \(0\) \(0\) \(0\) \(0\)
480.2.bo.a \(192\) \(3.833\) None None \(0\) \(0\) \(0\) \(0\)
480.2.br.a \(368\) \(3.833\) None None \(0\) \(-4\) \(0\) \(0\)
480.2.bs.a \(16\) \(3.833\) 16.0.\(\cdots\).3 \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{9}-\beta _{12})q^{3}+\beta _{2}q^{4}+\cdots\)
480.2.bs.b \(352\) \(3.833\) None None \(0\) \(0\) \(0\) \(0\)
480.2.bv.a \(56\) \(3.833\) None None \(0\) \(0\) \(0\) \(0\)
480.2.bv.b \(72\) \(3.833\) None None \(0\) \(0\) \(0\) \(0\)
480.2.bx.a \(256\) \(3.833\) None None \(0\) \(0\) \(0\) \(0\)
480.2.by.a \(192\) \(3.833\) None None \(0\) \(0\) \(0\) \(0\)
480.2.cb.a \(368\) \(3.833\) None None \(0\) \(-4\) \(0\) \(-16\)
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