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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3484.1.q.a \(2\) \(1.739\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-13}) \) None \(-1\) \(0\) \(0\) \(1\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{7}+q^{8}+q^{9}+\cdots\)
3484.1.q.b \(2\) \(1.739\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-13}) \) None \(1\) \(0\) \(0\) \(-1\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{7}-q^{8}+q^{9}+\cdots\)
3484.1.bj.a \(4\) \(1.739\) \(\Q(\zeta_{12})\) None None \(4\) \(0\) \(0\) \(0\) \(q+q^{2}+\zeta_{12}^{5}q^{3}+q^{4}+\zeta_{12}^{5}q^{6}+\cdots\)
3484.1.bm.a \(4\) \(1.739\) \(\Q(\zeta_{12})\) None None \(-2\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{4}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
3484.1.co.a \(10\) \(1.739\) \(\Q(\zeta_{22})\) \(\Q(\sqrt{-13}) \) None \(-1\) \(0\) \(0\) \(-2\) \(q-\zeta_{22}^{3}q^{2}+\zeta_{22}^{6}q^{4}+(-\zeta_{22}-\zeta_{22}^{5}+\cdots)q^{7}+\cdots\)
3484.1.co.b \(10\) \(1.739\) \(\Q(\zeta_{22})\) \(\Q(\sqrt{-13}) \) None \(1\) \(0\) \(0\) \(2\) \(q+\zeta_{22}^{3}q^{2}+\zeta_{22}^{6}q^{4}+(\zeta_{22}+\zeta_{22}^{5}+\cdots)q^{7}+\cdots\)
3484.1.dz.a \(20\) \(1.739\) \(\Q(\zeta_{33})\) \(\Q(\sqrt{-13}) \) None \(-1\) \(0\) \(0\) \(1\) \(q+\zeta_{66}^{19}q^{2}-\zeta_{66}^{5}q^{4}+(\zeta_{66}^{21}-\zeta_{66}^{28}+\cdots)q^{7}+\cdots\)
3484.1.dz.b \(20\) \(1.739\) \(\Q(\zeta_{33})\) \(\Q(\sqrt{-13}) \) None \(1\) \(0\) \(0\) \(-1\) \(q-\zeta_{66}^{19}q^{2}-\zeta_{66}^{5}q^{4}+(-\zeta_{66}^{21}+\cdots)q^{7}+\cdots\)
3484.2.a.a \(1\) \(27.820\) \(\Q\) None None \(0\) \(0\) \(2\) \(4\) \(-\) \(q+2q^{5}+4q^{7}-3q^{9}-2q^{11}-q^{13}+\cdots\)
3484.2.a.b \(5\) \(27.820\) 5.5.2444177.1 None None \(0\) \(0\) \(-3\) \(-5\) \(-\) \(q+(-1+\beta _{3})q^{5}+(-1-\beta _{1}+\beta _{2})q^{7}+\cdots\)
3484.2.a.c \(10\) \(27.820\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(0\) \(4\) \(4\) \(-\) \(q-\beta _{5}q^{3}-\beta _{6}q^{5}+\beta _{1}q^{7}+(3-\beta _{4}+\cdots)q^{9}+\cdots\)
3484.2.a.d \(16\) \(27.820\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(-6\) \(-5\) \(-1\) \(+\) \(q-\beta _{1}q^{3}+\beta _{13}q^{5}-\beta _{6}q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
3484.2.a.e \(17\) \(27.820\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None None \(0\) \(0\) \(-7\) \(-3\) \(+\) \(q+\beta _{1}q^{3}-\beta _{9}q^{5}-\beta _{6}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
3484.2.a.f \(17\) \(27.820\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None None \(0\) \(6\) \(5\) \(5\) \(-\) \(q+\beta _{1}q^{3}+\beta _{14}q^{5}+\beta _{15}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
3484.2.f.a \(78\) \(27.820\) None None \(0\) \(0\) \(0\) \(0\)
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