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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4100.2.a.a \(2\) \(32.739\) \(\Q(\sqrt{13}) \) None \(0\) \(-2\) \(0\) \(3\) \(+\) \(q-q^{3}+(1+\beta )q^{7}-2q^{9}+(-3+2\beta )q^{11}+\cdots\)
4100.2.a.b \(2\) \(32.739\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(0\) \(1\) \(-\) \(q+q^{3}+(1-\beta )q^{7}-2q^{9}+(3-4\beta )q^{11}+\cdots\)
4100.2.a.c \(4\) \(32.739\) 4.4.25808.1 None \(0\) \(-2\) \(0\) \(0\) \(-\) \(q+(\beta _{1}-\beta _{2})q^{3}+(1-\beta _{1}-\beta _{2}+\beta _{3})q^{7}+\cdots\)
4100.2.a.d \(4\) \(32.739\) 4.4.13068.1 None \(0\) \(0\) \(0\) \(-1\) \(+\) \(q-\beta _{2}q^{3}+\beta _{1}q^{7}+(1-\beta _{1}+\beta _{3})q^{9}+\cdots\)
4100.2.a.e \(4\) \(32.739\) \(\Q(\sqrt{5}, \sqrt{13})\) None \(0\) \(0\) \(0\) \(1\) \(-\) \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{7}+(1+\beta _{2}+\beta _{3})q^{9}+\cdots\)
4100.2.a.f \(6\) \(32.739\) 6.6.3356224.1 None \(0\) \(0\) \(0\) \(0\) \(+\) \(q-\beta _{4}q^{3}-\beta _{3}q^{7}+(-\beta _{1}+\beta _{2})q^{9}+\cdots\)
4100.2.a.g \(7\) \(32.739\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-3\) \(0\) \(0\) \(+\) \(q-\beta _{1}q^{3}+\beta _{4}q^{7}+(\beta _{1}+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
4100.2.a.h \(7\) \(32.739\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-1\) \(0\) \(0\) \(+\) \(q-\beta _{1}q^{3}-\beta _{5}q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots\)
4100.2.a.i \(7\) \(32.739\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(1\) \(0\) \(0\) \(-\) \(q+\beta _{1}q^{3}+\beta _{5}q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots\)
4100.2.a.j \(7\) \(32.739\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(3\) \(0\) \(0\) \(-\) \(q+\beta _{1}q^{3}-\beta _{4}q^{7}+(\beta _{1}+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
4100.2.a.k \(14\) \(32.739\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(q+\beta _{1}q^{3}-\beta _{10}q^{7}+(2+\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots\)
4100.2.b.a \(2\) \(32.739\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{3}-\beta q^{7}+q^{9}-3\beta q^{11}-2\beta q^{17}+\cdots\)
4100.2.b.b \(2\) \(32.739\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{3}-\beta q^{7}+q^{9}+3\beta q^{11}-2\beta q^{17}+\cdots\)
4100.2.b.c \(4\) \(32.739\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+(\beta _{1}-2\beta _{2})q^{7}+(-1+\beta _{3})q^{9}+\cdots\)
4100.2.b.d \(4\) \(32.739\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+(\beta _{1}-2\beta _{2})q^{7}+(-1+\beta _{3})q^{9}+\cdots\)
4100.2.b.e \(4\) \(32.739\) 4.0.25088.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{3}q^{7}+\beta _{2}q^{9}+(-2\beta _{1}+\cdots)q^{11}+\cdots\)
4100.2.b.f \(6\) \(32.739\) 6.0.36433296.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{3}-\beta _{4}q^{7}+(-2-\beta _{3})q^{9}-\beta _{5}q^{11}+\cdots\)
4100.2.b.g \(8\) \(32.739\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{3}-\beta _{4}q^{7}+(-1-\beta _{3})q^{9}+\beta _{5}q^{11}+\cdots\)
4100.2.b.h \(10\) \(32.739\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{9}q^{7}+(-1+\beta _{2})q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
4100.2.b.i \(10\) \(32.739\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{9}q^{7}+(-1+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
4100.2.b.j \(16\) \(32.739\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{9}q^{3}+\beta _{11}q^{7}+(-1+\beta _{1})q^{9}+\cdots\)
4100.2.d.a \(4\) \(32.739\) \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+2q^{9}+(-1+\cdots)q^{11}+\cdots\)
4100.2.d.b \(4\) \(32.739\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{3}+(\beta _{1}+\beta _{3})q^{7}+2q^{9}+(3+4\beta _{2}+\cdots)q^{11}+\cdots\)
4100.2.d.c \(8\) \(32.739\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{2}-\beta _{4}+\beta _{6})q^{3}+(\beta _{2}-\beta _{4}-\beta _{7})q^{7}+\cdots\)
4100.2.d.d \(8\) \(32.739\) 8.0.4569760000.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{5})q^{7}+(-1+\beta _{4}+\cdots)q^{9}+\cdots\)
4100.2.d.e \(8\) \(32.739\) 8.0.2732361984.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{3}+\beta _{5}q^{7}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
4100.2.d.f \(14\) \(32.739\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{11}q^{7}+(-1+\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
4100.2.d.g \(14\) \(32.739\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+\beta _{7}q^{7}+(\beta _{2}+\beta _{3})q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
4100.2.g.a \(4\) \(32.739\) \(\Q(i, \sqrt{5})\) None \(0\) \(-6\) \(0\) \(6\) \(q+(-2-\beta _{2})q^{3}-3\beta _{2}q^{7}+(2+3\beta _{2}+\cdots)q^{9}+\cdots\)
4100.2.g.b \(4\) \(32.739\) \(\Q(i, \sqrt{5})\) None \(0\) \(6\) \(0\) \(-6\) \(q+(2+\beta _{2})q^{3}+3\beta _{2}q^{7}+(2+3\beta _{2})q^{9}+\cdots\)
4100.2.g.c \(8\) \(32.739\) 8.0.629407744.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}-\beta _{5}q^{7}-\beta _{7}q^{9}+(-\beta _{2}-2\beta _{3}+\cdots)q^{11}+\cdots\)
4100.2.g.d \(12\) \(32.739\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{3}-\beta _{8}q^{7}+(2-\beta _{3})q^{9}-\beta _{9}q^{11}+\cdots\)
4100.2.g.e \(16\) \(32.739\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{3}-\beta _{7}q^{7}+(1-\beta _{6})q^{9}-\beta _{10}q^{11}+\cdots\)
4100.2.g.f \(20\) \(32.739\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{3}q^{7}+(1-\beta _{2})q^{9}+(\beta _{13}+\cdots)q^{11}+\cdots\)
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