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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1375.1.c.a \(4\) \(0.686\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{10}+\zeta_{10}^{4})q^{2}+(-1+\zeta_{10}^{2}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots\)
1375.1.c.b \(4\) \(0.686\) \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{7}-\beta _{3}q^{8}+\cdots\)
1375.1.d.a \(2\) \(0.686\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-55}) \) None \(-1\) \(0\) \(0\) \(-1\) \(q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{7}-q^{8}+\cdots\)
1375.1.d.b \(2\) \(0.686\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-55}) \) None \(1\) \(0\) \(0\) \(1\) \(q+(1-\beta )q^{2}+(1-\beta )q^{4}+\beta q^{7}+q^{8}+\cdots\)
1375.1.d.c \(4\) \(0.686\) \(\Q(\zeta_{20})^+\) \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{3}q^{7}+(-\beta _{1}+\cdots)q^{8}+\cdots\)
1375.1.q.a \(4\) \(0.686\) \(\Q(\zeta_{10})\) None \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{10}^{4}q^{4}+\zeta_{10}^{2}q^{9}-\zeta_{10}^{4}q^{11}+\cdots\)
1375.1.s.a \(4\) \(0.686\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{10}+\zeta_{10}^{2})q^{3}-\zeta_{10}^{4}q^{4}+(\zeta_{10}^{2}+\cdots)q^{9}+\cdots\)
1375.1.s.b \(8\) \(0.686\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{20}^{7}-\zeta_{20}^{9})q^{3}-\zeta_{20}^{8}q^{4}+(-\zeta_{20}^{4}+\cdots)q^{9}+\cdots\)
1375.1.v.a \(4\) \(0.686\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-11}) \) None \(0\) \(2\) \(0\) \(0\) \(q+(\zeta_{10}-\zeta_{10}^{2})q^{3}+\zeta_{10}^{4}q^{4}+(\zeta_{10}^{2}+\cdots)q^{9}+\cdots\)
1375.1.v.b \(8\) \(0.686\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{20}^{7}+\zeta_{20}^{9})q^{3}+\zeta_{20}^{8}q^{4}+(-\zeta_{20}^{4}+\cdots)q^{9}+\cdots\)
1375.1.x.a \(4\) \(0.686\) \(\Q(\zeta_{10})\) None \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{10}^{3}q^{4}-\zeta_{10}^{4}q^{9}+\zeta_{10}^{3}q^{11}+\cdots\)
1375.1.bz.a \(20\) \(0.686\) \(\Q(\zeta_{50})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(5\) \(0\) \(q+(\zeta_{50}^{7}-\zeta_{50}^{21})q^{3}-\zeta_{50}^{4}q^{4}-\zeta_{50}^{20}q^{5}+\cdots\)
1375.1.ch.a \(20\) \(0.686\) \(\Q(\zeta_{50})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(-5\) \(0\) \(q+(\zeta_{50}^{4}+\zeta_{50}^{18})q^{3}-\zeta_{50}^{21}q^{4}+\cdots\)
1375.2.a.a \(2\) \(10.979\) \(\Q(\sqrt{5}) \) None None \(-1\) \(2\) \(0\) \(-1\) \(+\) \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
1375.2.a.b \(2\) \(10.979\) \(\Q(\sqrt{5}) \) None None \(1\) \(-2\) \(0\) \(1\) \(+\) \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
1375.2.a.c \(8\) \(10.979\) 8.8.6988960000.1 None None \(0\) \(0\) \(0\) \(0\) \(+\) \(q+\beta _{1}q^{2}+\beta _{7}q^{3}+\beta _{2}q^{4}+(-1-\beta _{3}+\cdots)q^{6}+\cdots\)
1375.2.a.d \(10\) \(10.979\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(-7\) \(0\) \(0\) \(-5\) \(+\) \(q+(-1+\beta _{1})q^{2}+\beta _{9}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1375.2.a.e \(10\) \(10.979\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(-5\) \(-8\) \(0\) \(-3\) \(+\) \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{2})q^{3}+(2+\cdots)q^{4}+\cdots\)
1375.2.a.f \(10\) \(10.979\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(5\) \(8\) \(0\) \(3\) \(-\) \(q+(1-\beta _{1})q^{2}+(1-\beta _{2})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
1375.2.a.g \(10\) \(10.979\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(7\) \(0\) \(0\) \(5\) \(-\) \(q+(1-\beta _{1})q^{2}-\beta _{9}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1375.2.a.h \(12\) \(10.979\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(-\) \(q+\beta _{1}q^{2}+(\beta _{3}+\beta _{9})q^{3}+(\beta _{4}-\beta _{5})q^{4}+\cdots\)
1375.2.a.i \(16\) \(10.979\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(-\) \(q+\beta _{1}q^{2}-\beta _{14}q^{3}+(2+\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots\)
1375.2.b.a \(4\) \(10.979\) \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+\beta _{2}q^{6}+\cdots\)
1375.2.b.b \(8\) \(10.979\) 8.0.\(\cdots\).10 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}+(-1+\beta _{3}+\cdots)q^{6}+\cdots\)
1375.2.b.c \(12\) \(10.979\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{4}-\beta _{9})q^{3}+(\beta _{3}-\beta _{5})q^{4}+\cdots\)
1375.2.b.d \(16\) \(10.979\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{14}q^{3}+(-2+\beta _{2})q^{4}+\cdots\)
1375.2.b.e \(20\) \(10.979\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{7}q^{2}+\beta _{18}q^{3}+(-2+\beta _{6})q^{4}+\cdots\)
1375.2.b.f \(20\) \(10.979\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{14}q^{3}+(-2+\beta _{6}+\beta _{8}+\cdots)q^{4}+\cdots\)
1375.4.a.a \(24\) \(81.128\) None None \(0\) \(0\) \(0\) \(0\) \(-\)
1375.4.a.b \(28\) \(81.128\) None None \(0\) \(0\) \(0\) \(0\) \(-\)
1375.4.a.c \(30\) \(81.128\) None None \(-15\) \(-24\) \(0\) \(-26\) \(-\)
1375.4.a.d \(30\) \(81.128\) None None \(-9\) \(0\) \(0\) \(-30\) \(-\)
1375.4.a.e \(30\) \(81.128\) None None \(9\) \(0\) \(0\) \(30\) \(+\)
1375.4.a.f \(30\) \(81.128\) None None \(15\) \(24\) \(0\) \(26\) \(+\)
1375.4.a.g \(32\) \(81.128\) None None \(0\) \(0\) \(0\) \(0\) \(+\)
1375.4.a.h \(36\) \(81.128\) None None \(0\) \(0\) \(0\) \(0\) \(+\)
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