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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1340.1.t.a \(2\) \(0.669\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-5}) \) None \(-1\) \(-2\) \(2\) \(1\) \(q-\zeta_{6}q^{2}-q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+\zeta_{6}q^{6}+\cdots\)
1340.1.t.b \(2\) \(0.669\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-5}) \) None \(1\) \(2\) \(2\) \(-1\) \(q+\zeta_{6}q^{2}+q^{3}+\zeta_{6}^{2}q^{4}+q^{5}+\zeta_{6}q^{6}+\cdots\)
1340.1.bb.a \(10\) \(0.669\) \(\Q(\zeta_{22})\) \(\Q(\sqrt{-5}) \) None \(-1\) \(-2\) \(-1\) \(-2\) \(q-\zeta_{22}q^{2}+(\zeta_{22}^{4}+\zeta_{22}^{8})q^{3}+\zeta_{22}^{2}q^{4}+\cdots\)
1340.1.bb.b \(10\) \(0.669\) \(\Q(\zeta_{22})\) \(\Q(\sqrt{-5}) \) None \(1\) \(2\) \(-1\) \(2\) \(q+\zeta_{22}q^{2}+(-\zeta_{22}^{4}-\zeta_{22}^{8})q^{3}+\zeta_{22}^{2}q^{4}+\cdots\)
1340.1.bl.a \(20\) \(0.669\) \(\Q(\zeta_{33})\) \(\Q(\sqrt{-5}) \) None \(-1\) \(-2\) \(-2\) \(1\) \(q+\zeta_{66}^{31}q^{2}+(\zeta_{66}^{17}+\zeta_{66}^{25})q^{3}+\cdots\)
1340.1.bl.b \(20\) \(0.669\) \(\Q(\zeta_{33})\) \(\Q(\sqrt{-5}) \) None \(1\) \(2\) \(-2\) \(-1\) \(q-\zeta_{66}^{31}q^{2}+(-\zeta_{66}^{17}-\zeta_{66}^{25}+\cdots)q^{3}+\cdots\)
1340.2.a.a \(1\) \(10.700\) \(\Q\) None None \(0\) \(-2\) \(-1\) \(2\) \(-\) \(q-2q^{3}-q^{5}+2q^{7}+q^{9}+2q^{13}+\cdots\)
1340.2.a.b \(1\) \(10.700\) \(\Q\) None None \(0\) \(1\) \(-1\) \(1\) \(+\) \(q+q^{3}-q^{5}+q^{7}-2q^{9}-6q^{11}+2q^{13}+\cdots\)
1340.2.a.c \(1\) \(10.700\) \(\Q\) None None \(0\) \(1\) \(-1\) \(5\) \(-\) \(q+q^{3}-q^{5}+5q^{7}-2q^{9}+2q^{13}+\cdots\)
1340.2.a.d \(2\) \(10.700\) \(\Q(\sqrt{17}) \) None None \(0\) \(-1\) \(2\) \(-3\) \(+\) \(q-\beta q^{3}+q^{5}+(-2+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
1340.2.a.e \(2\) \(10.700\) \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(2\) \(4\) \(-\) \(q+(1+\beta )q^{3}+q^{5}+2q^{7}+(1+2\beta )q^{9}+\cdots\)
1340.2.a.f \(3\) \(10.700\) \(\Q(\zeta_{14})^+\) None None \(0\) \(-2\) \(3\) \(-2\) \(+\) \(q+(-1-\beta _{2})q^{3}+q^{5}+(1-3\beta _{1}+2\beta _{2})q^{7}+\cdots\)
1340.2.a.g \(3\) \(10.700\) 3.3.257.1 None None \(0\) \(4\) \(-3\) \(-2\) \(-\) \(q+(1+\beta _{1})q^{3}-q^{5}+(-1+\beta _{1}+\beta _{2})q^{7}+\cdots\)
1340.2.a.h \(4\) \(10.700\) 4.4.60513.1 None None \(0\) \(-1\) \(4\) \(5\) \(-\) \(q-\beta _{1}q^{3}+q^{5}+(1+\beta _{3})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
1340.2.a.i \(5\) \(10.700\) 5.5.1465016.1 None None \(0\) \(-2\) \(-5\) \(-10\) \(+\) \(q-\beta _{1}q^{3}-q^{5}+(-2+\beta _{2})q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots\)
1340.2.d.a \(2\) \(10.700\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-4\) \(0\) \(q+iq^{3}+(-2+i)q^{5}+3iq^{7}+2q^{9}+\cdots\)
1340.2.d.b \(8\) \(10.700\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(0\) \(16\) \(0\) \(q+\beta _{6}q^{3}+(2-\beta _{5})q^{5}+(-\beta _{1}-\beta _{5}+\cdots)q^{7}+\cdots\)
1340.2.d.c \(24\) \(10.700\) None None \(0\) \(0\) \(-10\) \(0\)
1340.2.i.a \(2\) \(10.700\) \(\Q(\sqrt{-3}) \) None None \(0\) \(2\) \(2\) \(1\) \(q+q^{3}+q^{5}+\zeta_{6}q^{7}-2q^{9}+6\zeta_{6}q^{11}+\cdots\)
1340.2.i.b \(8\) \(10.700\) 8.0.5808268944.1 None None \(0\) \(2\) \(-8\) \(2\) \(q-\beta _{3}q^{3}-q^{5}+(\beta _{1}-\beta _{6})q^{7}+\beta _{2}q^{9}+\cdots\)
1340.2.i.c \(16\) \(10.700\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(-2\) \(-16\) \(0\) \(q-\beta _{6}q^{3}-q^{5}+\beta _{11}q^{7}+(2+\beta _{2})q^{9}+\cdots\)
1340.2.i.d \(18\) \(10.700\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(0\) \(-2\) \(18\) \(3\) \(q+(-\beta _{1}+\beta _{5})q^{3}+q^{5}-\beta _{10}q^{7}+(1+\cdots)q^{9}+\cdots\)
1340.2.j.a \(68\) \(10.700\) None None \(0\) \(0\) \(0\) \(0\)
1340.2.o.a \(68\) \(10.700\) None None \(0\) \(0\) \(-2\) \(0\)
1340.3.b.a \(2\) \(36.512\) \(\Q(\sqrt{-5}) \) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{3}-\beta q^{5}-\beta q^{7}+4q^{9}+6\beta q^{11}+\cdots\)
1340.3.b.b \(42\) \(36.512\) None None \(0\) \(0\) \(0\) \(0\)
1340.3.g.a \(68\) \(36.512\) None None \(0\) \(0\) \(0\) \(0\)
1340.3.q.a \(92\) \(36.512\) None None \(0\) \(0\) \(0\) \(18\)
1340.4.a.a \(1\) \(79.063\) \(\Q\) None None \(0\) \(-4\) \(-5\) \(-16\) \(-\) \(q-4q^{3}-5q^{5}-2^{4}q^{7}-11q^{9}-2^{6}q^{11}+\cdots\)
1340.4.a.b \(16\) \(79.063\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(-8\) \(80\) \(-43\) \(-\) \(q-\beta _{1}q^{3}+5q^{5}+(-3-\beta _{8})q^{7}+(8+\cdots)q^{9}+\cdots\)
1340.4.a.c \(16\) \(79.063\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(-80\) \(-39\) \(-\) \(q+\beta _{1}q^{3}-5q^{5}+(-2-\beta _{4})q^{7}+(11+\cdots)q^{9}+\cdots\)
1340.4.a.d \(16\) \(79.063\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(8\) \(-80\) \(43\) \(+\) \(q+(1-\beta _{1})q^{3}-5q^{5}+(3-\beta _{4})q^{7}+(8+\cdots)q^{9}+\cdots\)
1340.4.a.e \(17\) \(79.063\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None None \(0\) \(4\) \(85\) \(55\) \(+\) \(q+\beta _{1}q^{3}+5q^{5}+(3-\beta _{6})q^{7}+(11+\beta _{1}+\cdots)q^{9}+\cdots\)
1340.4.d.a \(98\) \(79.063\) None None \(0\) \(0\) \(-20\) \(0\)
1340.5.b.a \(92\) \(138.516\) None None \(0\) \(0\) \(0\) \(0\)
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