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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
441.1.b.a \(2\) \(0.220\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{2}-q^{4}-\beta q^{11}-q^{16}-2q^{22}+\cdots\)
441.1.m.a \(2\) \(0.220\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{21}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{4}-\zeta_{6}q^{16}+\zeta_{6}^{2}q^{25}+\zeta_{6}q^{37}+\cdots\)
441.1.q.a \(4\) \(0.220\) \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{3})q^{11}+\cdots\)
441.1.v.a \(6\) \(0.220\) \(\Q(\zeta_{14})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q-\zeta_{14}^{4}q^{4}-\zeta_{14}^{2}q^{7}+(\zeta_{14}-\zeta_{14}^{3}+\cdots)q^{13}+\cdots\)
441.2.a.a \(1\) \(3.521\) \(\Q\) None None \(-2\) \(0\) \(-2\) \(0\) \(+\) \(q-2q^{2}+2q^{4}-2q^{5}+4q^{10}+2q^{11}+\cdots\)
441.2.a.b \(1\) \(3.521\) \(\Q\) None None \(-2\) \(0\) \(2\) \(0\) \(-\) \(q-2q^{2}+2q^{4}+2q^{5}-4q^{10}+2q^{11}+\cdots\)
441.2.a.c \(1\) \(3.521\) \(\Q\) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(0\) \(+\) \(q-q^{2}-q^{4}+3q^{8}-4q^{11}-q^{16}+\cdots\)
441.2.a.d \(1\) \(3.521\) \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(+\) \(q-2q^{4}-7q^{13}+4q^{16}-7q^{19}-5q^{25}+\cdots\)
441.2.a.e \(1\) \(3.521\) \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(q-2q^{4}+7q^{13}+4q^{16}+7q^{19}-5q^{25}+\cdots\)
441.2.a.f \(1\) \(3.521\) \(\Q\) None None \(1\) \(0\) \(-2\) \(0\) \(+\) \(q+q^{2}-q^{4}-2q^{5}-3q^{8}-2q^{10}+\cdots\)
441.2.a.g \(2\) \(3.521\) \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(0\) \(0\) \(-\) \(q+\beta q^{2}+q^{4}+2\beta q^{5}-\beta q^{8}+6q^{10}+\cdots\)
441.2.a.h \(2\) \(3.521\) \(\Q(\sqrt{7}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(q+\beta q^{2}+5q^{4}+3\beta q^{8}-2\beta q^{11}+11q^{16}+\cdots\)
441.2.a.i \(2\) \(3.521\) \(\Q(\sqrt{2}) \) None None \(2\) \(0\) \(-4\) \(0\) \(-\) \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(-2+\beta )q^{5}+\cdots\)
441.2.a.j \(2\) \(3.521\) \(\Q(\sqrt{2}) \) None None \(2\) \(0\) \(4\) \(0\) \(-\) \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(2-\beta )q^{5}+\cdots\)
441.2.c.a \(4\) \(3.521\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{3}q^{5}-2\beta _{1}q^{8}-2\beta _{2}q^{10}+\cdots\)
441.2.c.b \(8\) \(3.521\) \(\Q(\zeta_{16})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{16}-\zeta_{16}^{2})q^{2}+(-1+2\zeta_{16}^{3}+\cdots)q^{4}+\cdots\)
441.2.e.a \(2\) \(3.521\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(0\) \(-2\) \(0\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-2\zeta_{6}q^{5}-3q^{8}+\cdots\)
441.2.e.b \(2\) \(3.521\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(0\) \(2\) \(0\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+2\zeta_{6}q^{5}-3q^{8}+\cdots\)
441.2.e.c \(2\) \(3.521\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(2-2\zeta_{6})q^{4}+7q^{13}-4\zeta_{6}q^{16}+\cdots\)
441.2.e.d \(2\) \(3.521\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(0\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+3q^{8}+(4-4\zeta_{6})q^{11}+\cdots\)
441.2.e.e \(2\) \(3.521\) \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(2\) \(0\) \(q+2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{4}+2\zeta_{6}q^{5}+\cdots\)
441.2.e.f \(4\) \(3.521\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(-2\) \(0\) \(-4\) \(0\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}+(-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
441.2.e.g \(4\) \(3.521\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(-2\) \(0\) \(4\) \(0\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}+(-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
441.2.e.h \(4\) \(3.521\) \(\Q(\sqrt{-3}, \sqrt{7})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+5\beta _{2}q^{4}+3\beta _{3}q^{8}+(2\beta _{1}+\cdots)q^{11}+\cdots\)
441.2.e.i \(4\) \(3.521\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{2}+(-1+\zeta_{12})q^{4}-2\zeta_{12}^{2}q^{5}+\cdots\)
441.2.e.j \(4\) \(3.521\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{2}+(-1+\zeta_{12})q^{4}+2\zeta_{12}^{2}q^{5}+\cdots\)
441.2.f.a \(2\) \(3.521\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(-3\) \(-1\) \(0\) \(q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
441.2.f.b \(2\) \(3.521\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(3\) \(1\) \(0\) \(q+(-1+\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
441.2.f.c \(6\) \(3.521\) \(\Q(\zeta_{18})\) None None \(-3\) \(0\) \(3\) \(0\) \(q+(-1+\zeta_{18}+\zeta_{18}^{5})q^{2}+(\zeta_{18}^{3}-\zeta_{18}^{5})q^{3}+\cdots\)
441.2.f.d \(6\) \(3.521\) 6.0.309123.1 None None \(1\) \(4\) \(-5\) \(0\) \(q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}+(-\beta _{2}+\cdots)q^{3}+\cdots\)
441.2.f.e \(10\) \(3.521\) 10.0.\(\cdots\).1 None None \(2\) \(-1\) \(4\) \(0\) \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-1-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
441.2.f.f \(10\) \(3.521\) 10.0.\(\cdots\).1 None None \(2\) \(1\) \(-4\) \(0\) \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-1-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
441.2.f.g \(12\) \(3.521\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-2\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{6})q^{2}+\beta _{10}q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
441.2.f.h \(24\) \(3.521\) None None \(4\) \(0\) \(0\) \(0\)
441.2.g.a \(2\) \(3.521\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(3\) \(2\) \(0\) \(q+(-1+\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
441.2.g.b \(6\) \(3.521\) \(\Q(\zeta_{18})\) None None \(-3\) \(0\) \(-6\) \(0\) \(q+(-1+\zeta_{18}+\zeta_{18}^{5})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{4}+\cdots)q^{3}+\cdots\)
441.2.g.c \(6\) \(3.521\) \(\Q(\zeta_{18})\) None None \(-3\) \(0\) \(6\) \(0\) \(q+(-1+\zeta_{18}+\zeta_{18}^{5})q^{2}+(-\zeta_{18}^{2}+\cdots)q^{3}+\cdots\)
441.2.g.d \(6\) \(3.521\) 6.0.309123.1 None None \(1\) \(-2\) \(10\) \(0\) \(q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}+(-1+\cdots)q^{3}+\cdots\)
441.2.g.e \(6\) \(3.521\) 6.0.309123.1 None None \(1\) \(2\) \(-10\) \(0\) \(q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}+(1-\beta _{1}+\cdots)q^{3}+\cdots\)
441.2.g.f \(10\) \(3.521\) 10.0.\(\cdots\).1 None None \(2\) \(-2\) \(8\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{2}+\beta _{7})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
441.2.g.g \(12\) \(3.521\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-2\) \(0\) \(0\) \(0\) \(q+(-\beta _{2}+\beta _{5})q^{2}+(-\beta _{8}-\beta _{10})q^{3}+\cdots\)
441.2.g.h \(24\) \(3.521\) None None \(4\) \(0\) \(0\) \(0\)
441.2.h.a \(2\) \(3.521\) \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(-1\) \(0\) \(q+q^{2}+(1-2\zeta_{6})q^{3}-q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
441.2.h.b \(6\) \(3.521\) 6.0.309123.1 None None \(-2\) \(-2\) \(-5\) \(0\) \(q+(\beta _{2}+\beta _{3})q^{2}+(-\beta _{1}-\beta _{2}+\beta _{5})q^{3}+\cdots\)
441.2.h.c \(6\) \(3.521\) 6.0.309123.1 None None \(-2\) \(2\) \(5\) \(0\) \(q+(\beta _{2}+\beta _{3})q^{2}+(\beta _{1}+\beta _{2}-\beta _{5})q^{3}+\cdots\)
441.2.h.d \(6\) \(3.521\) \(\Q(\zeta_{18})\) None None \(6\) \(0\) \(-3\) \(0\) \(q+(1-\zeta_{18}^{3}-\zeta_{18}^{4})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{5})q^{3}+\cdots\)
441.2.h.e \(6\) \(3.521\) \(\Q(\zeta_{18})\) None None \(6\) \(0\) \(3\) \(0\) \(q+(1-\zeta_{18}^{3}-\zeta_{18}^{4})q^{2}+(-\zeta_{18}^{2}+\cdots)q^{3}+\cdots\)
441.2.h.f \(10\) \(3.521\) 10.0.\(\cdots\).1 None None \(-4\) \(1\) \(-4\) \(0\) \(q+(-\beta _{1}+\beta _{5})q^{2}+\beta _{8}q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots\)
441.2.h.g \(12\) \(3.521\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(4\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+\beta _{10}q^{3}+(1+\beta _{2}+\beta _{4})q^{4}+\cdots\)
441.2.h.h \(24\) \(3.521\) None None \(-8\) \(0\) \(0\) \(0\)
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