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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3528.1.d.a \(2\) \(1.761\) \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{5}-\beta q^{11}-q^{13}-q^{19}-q^{25}+\cdots\)
3528.1.d.b \(2\) \(1.761\) \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{5}-\beta q^{11}+q^{13}+q^{19}-q^{25}+\cdots\)
3528.1.g.a \(1\) \(1.761\) \(\Q\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{14}) \) \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+2q^{11}+q^{16}-2q^{22}+\cdots\)
3528.1.g.b \(2\) \(1.761\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-42}) \) \(\Q(\sqrt{6}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{8}+q^{16}-iq^{23}+\cdots\)
3528.1.g.c \(2\) \(1.761\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-2}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}+q^{16}-\beta q^{17}+\beta q^{19}+\cdots\)
3528.1.l.a \(4\) \(1.761\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{3}q^{2}-q^{4}+(-\zeta_{12}+\zeta_{12}^{5}+\cdots)q^{5}+\cdots\)
3528.1.n.a \(4\) \(1.761\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{8}+(-\zeta_{8}+\cdots)q^{11}+\cdots\)
3528.1.u.a \(16\) \(1.761\) \(\Q(\zeta_{48})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{48}^{4}q^{2}-\zeta_{48}^{9}q^{3}+\zeta_{48}^{8}q^{4}+\cdots\)
3528.1.ba.a \(2\) \(1.761\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(-1\) \(-2\) \(0\) \(0\) \(q-\zeta_{6}q^{2}-q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{6}+q^{8}+\cdots\)
3528.1.ba.b \(2\) \(1.761\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(-1\) \(2\) \(0\) \(0\) \(q-\zeta_{6}q^{2}+q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{6}+q^{8}+\cdots\)
3528.1.ba.c \(4\) \(1.761\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-2}) \) None \(-2\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{4}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
3528.1.ba.d \(4\) \(1.761\) \(\Q(\zeta_{12})\) None None \(0\) \(-2\) \(0\) \(0\) \(q-\zeta_{12}q^{2}-\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}+\cdots\)
3528.1.ba.e \(8\) \(1.761\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-2}) \) None \(4\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{8}q^{2}+\zeta_{24}^{9}q^{3}-\zeta_{24}^{4}q^{4}+\cdots\)
3528.1.bd.a \(8\) \(1.761\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{9}q^{8}+\cdots\)
3528.1.bg.a \(8\) \(1.761\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{10}q^{2}+\zeta_{24}^{9}q^{3}-\zeta_{24}^{8}q^{4}+\cdots\)
3528.1.bi.a \(8\) \(1.761\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{6}q^{2}-\zeta_{24}^{7}q^{3}-q^{4}+(-\zeta_{24}^{3}+\cdots)q^{5}+\cdots\)
3528.1.bp.a \(2\) \(1.761\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-14}) \) None \(2\) \(-1\) \(1\) \(0\) \(q+q^{2}-\zeta_{6}q^{3}+q^{4}+\zeta_{6}q^{5}-\zeta_{6}q^{6}+\cdots\)
3528.1.bp.b \(2\) \(1.761\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-14}) \) None \(2\) \(1\) \(-1\) \(0\) \(q+q^{2}+\zeta_{6}q^{3}+q^{4}-\zeta_{6}q^{5}+\zeta_{6}q^{6}+\cdots\)
3528.1.bp.c \(4\) \(1.761\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-14}) \) None \(-4\) \(0\) \(0\) \(0\) \(q-q^{2}-\zeta_{12}q^{3}+q^{4}+(\zeta_{12}^{3}+\zeta_{12}^{5}+\cdots)q^{5}+\cdots\)
3528.1.bw.a \(2\) \(1.761\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \) \(\Q(\sqrt{2}) \) \(-1\) \(0\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{8}+\zeta_{6}^{2}q^{16}+\cdots\)
3528.1.bw.b \(4\) \(1.761\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{42}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{3}q^{8}+\cdots\)
3528.1.bw.c \(4\) \(1.761\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+(-\zeta_{12}-\zeta_{12}^{3}+\cdots)q^{5}+\cdots\)
3528.1.bx.a \(2\) \(1.761\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{14}) \) \(1\) \(0\) \(0\) \(0\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{8}+\zeta_{6}^{2}q^{11}+\cdots\)
3528.1.bx.b \(4\) \(1.761\) \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) None \(-2\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+q^{8}+\beta _{2}q^{16}+\cdots\)
3528.1.bx.c \(4\) \(1.761\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-42}) \) \(\Q(\sqrt{6}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{8}+\zeta_{12}^{4}q^{16}+\cdots\)
3528.1.ce.a \(2\) \(1.761\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(2\) \(-1\) \(0\) \(0\) \(q+q^{2}+\zeta_{6}^{2}q^{3}+q^{4}+\zeta_{6}^{2}q^{6}+q^{8}+\cdots\)
3528.1.ce.b \(2\) \(1.761\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(2\) \(1\) \(0\) \(0\) \(q+q^{2}-\zeta_{6}^{2}q^{3}+q^{4}-\zeta_{6}^{2}q^{6}+q^{8}+\cdots\)
3528.1.ce.c \(4\) \(1.761\) \(\Q(\zeta_{12})\) None None \(0\) \(4\) \(0\) \(0\) \(q-\zeta_{12}^{3}q^{2}+q^{3}-q^{4}-\zeta_{12}q^{5}-\zeta_{12}^{3}q^{6}+\cdots\)
3528.1.ce.d \(4\) \(1.761\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-2}) \) None \(4\) \(0\) \(0\) \(0\) \(q+q^{2}+\zeta_{12}^{5}q^{3}+q^{4}+\zeta_{12}^{5}q^{6}+\cdots\)
3528.1.ce.e \(8\) \(1.761\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-2}) \) None \(-8\) \(0\) \(0\) \(0\) \(q-q^{2}-\zeta_{24}^{7}q^{3}+q^{4}+\zeta_{24}^{7}q^{6}+\cdots\)
3528.1.cg.a \(2\) \(1.761\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(-1\) \(1\) \(0\) \(0\) \(q-\zeta_{6}q^{2}+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{6}+\cdots\)
3528.1.cg.b \(4\) \(1.761\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-2}) \) None \(-2\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{4}q^{2}-\zeta_{12}q^{3}-\zeta_{12}^{2}q^{4}-\zeta_{12}^{5}q^{6}+\cdots\)
3528.1.cg.c \(4\) \(1.761\) \(\Q(\zeta_{12})\) None None \(0\) \(-2\) \(0\) \(0\) \(q-\zeta_{12}q^{2}-\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{5}+\cdots\)
3528.1.cg.d \(4\) \(1.761\) \(\Q(\zeta_{12})\) None None \(0\) \(2\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{5}q^{5}+\cdots\)
3528.1.cg.e \(8\) \(1.761\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-2}) \) None \(4\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{8}q^{2}-\zeta_{24}^{5}q^{3}-\zeta_{24}^{4}q^{4}+\cdots\)
3528.1.cm.a \(16\) \(1.761\) \(\Q(\zeta_{48})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{48}^{12}q^{2}+\zeta_{48}^{5}q^{3}-q^{4}+\zeta_{48}^{17}q^{6}+\cdots\)
3528.1.co.a \(16\) \(1.761\) \(\Q(\zeta_{48})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{48}^{20}q^{2}+\zeta_{48}^{5}q^{3}-\zeta_{48}^{16}q^{4}+\cdots\)
3528.1.ct.a \(8\) \(1.761\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{9}q^{8}+\cdots\)
3528.1.cu.a \(4\) \(1.761\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{3})q^{5}-\beta _{1}q^{11}+q^{13}+\cdots\)
3528.1.cw.a \(2\) \(1.761\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-14}) \) None \(-1\) \(-1\) \(-2\) \(0\) \(q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-q^{5}+\cdots\)
3528.1.cw.b \(2\) \(1.761\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-14}) \) None \(-1\) \(1\) \(2\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+q^{5}+\cdots\)
3528.1.cw.c \(4\) \(1.761\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-14}) \) None \(2\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{5}q^{3}+\zeta_{12}^{4}q^{4}+\cdots\)
3528.1.db.a \(8\) \(1.761\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{2}q^{2}-\zeta_{24}^{5}q^{3}+\zeta_{24}^{4}q^{4}+\cdots\)
3528.1.dh.a \(12\) \(1.761\) \(\Q(\zeta_{28})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+\zeta_{28}q^{2}+\zeta_{28}^{2}q^{4}+(\zeta_{28}^{9}+\zeta_{28}^{11}+\cdots)q^{5}+\cdots\)
3528.1.fb.a \(24\) \(1.761\) \(\Q(\zeta_{84})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(2\) \(q-\zeta_{84}^{31}q^{2}-\zeta_{84}^{20}q^{4}+(-\zeta_{84}^{33}+\cdots)q^{5}+\cdots\)
3528.2.a.a \(1\) \(28.171\) \(\Q\) None None \(0\) \(0\) \(-4\) \(0\) \(+\) \(q-4q^{5}-3q^{13}+4q^{17}+7q^{19}-4q^{23}+\cdots\)
3528.2.a.b \(1\) \(28.171\) \(\Q\) None None \(0\) \(0\) \(-4\) \(0\) \(-\) \(q-4q^{5}-2q^{17}+2q^{19}-8q^{23}+11q^{25}+\cdots\)
3528.2.a.c \(1\) \(28.171\) \(\Q\) None None \(0\) \(0\) \(-4\) \(0\) \(+\) \(q-4q^{5}+3q^{13}+4q^{17}-7q^{19}+4q^{23}+\cdots\)
3528.2.a.d \(1\) \(28.171\) \(\Q\) None None \(0\) \(0\) \(-2\) \(0\) \(+\) \(q-2q^{5}-4q^{11}+2q^{13}+2q^{17}+4q^{19}+\cdots\)
3528.2.a.e \(1\) \(28.171\) \(\Q\) None None \(0\) \(0\) \(-2\) \(0\) \(+\) \(q-2q^{5}+2q^{11}-2q^{13}-6q^{17}+4q^{19}+\cdots\)
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