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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
729.1.f.a \(6\) \(0.364\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{18}q^{4}-\zeta_{18}^{8}q^{7}-\zeta_{18}^{4}q^{13}+\cdots\)
729.2.a.a \(6\) \(5.821\) 6.6.1397493.1 None None \(-3\) \(0\) \(-6\) \(0\) \(+\) \(q+(-\beta _{1}-\beta _{5})q^{2}+(\beta _{1}-\beta _{2}-\beta _{3})q^{4}+\cdots\)
729.2.a.b \(6\) \(5.821\) 6.6.7459857.1 None None \(-3\) \(0\) \(3\) \(6\) \(-\) \(q+(-\beta _{1}-\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
729.2.a.c \(6\) \(5.821\) \(\Q(\zeta_{36})^+\) None None \(0\) \(0\) \(0\) \(-12\) \(+\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
729.2.a.d \(6\) \(5.821\) 6.6.1397493.1 None None \(3\) \(0\) \(6\) \(0\) \(-\) \(q+(\beta _{1}+\beta _{5})q^{2}+(\beta _{1}-\beta _{2}-\beta _{3})q^{4}+\cdots\)
729.2.a.e \(6\) \(5.821\) 6.6.7459857.1 None None \(3\) \(0\) \(-3\) \(6\) \(-\) \(q+(\beta _{1}+\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
729.2.c.a \(12\) \(5.821\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(-3\) \(0\) \(3\) \(-6\) \(q+(-\beta _{1}+\beta _{2}-\beta _{3}-\beta _{6})q^{2}+(-1+\cdots)q^{4}+\cdots\)
729.2.c.b \(12\) \(5.821\) 12.0.\(\cdots\).1 None None \(-3\) \(0\) \(-6\) \(0\) \(q+(\beta _{6}+\beta _{8}-\beta _{10})q^{2}+(-1+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
729.2.c.c \(12\) \(5.821\) \(\Q(\zeta_{36})\) None None \(0\) \(0\) \(0\) \(12\) \(q+(-\zeta_{36}^{7}-\zeta_{36}^{8}+\zeta_{36}^{10})q^{2}-\zeta_{36}^{11}q^{4}+\cdots\)
729.2.c.d \(12\) \(5.821\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(3\) \(0\) \(-3\) \(-6\) \(q+(\beta _{2}-\beta _{3}+\beta _{5}-\beta _{6}+\beta _{9})q^{2}+(-1+\cdots)q^{4}+\cdots\)
729.2.c.e \(12\) \(5.821\) 12.0.\(\cdots\).1 None None \(3\) \(0\) \(6\) \(0\) \(q+(-\beta _{6}-\beta _{8}+\beta _{10})q^{2}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
729.2.e.a \(6\) \(5.821\) \(\Q(\zeta_{18})\) None None \(-6\) \(0\) \(-3\) \(-9\) \(q+(-1-\zeta_{18}+\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots\)
729.2.e.b \(6\) \(5.821\) \(\Q(\zeta_{18})\) None None \(-3\) \(0\) \(-6\) \(9\) \(q+(-1+\zeta_{18}-\zeta_{18}^{2}+\zeta_{18}^{3}-\zeta_{18}^{4}+\cdots)q^{2}+\cdots\)
729.2.e.c \(6\) \(5.821\) \(\Q(\zeta_{18})\) None None \(-3\) \(0\) \(3\) \(0\) \(q+(\zeta_{18}+\zeta_{18}^{2}-\zeta_{18}^{3}-\zeta_{18}^{4})q^{2}+\cdots\)
729.2.e.d \(6\) \(5.821\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2\zeta_{18}^{5}q^{4}+5\zeta_{18}^{4}q^{7}+2\zeta_{18}^{2}q^{13}+\cdots\)
729.2.e.e \(6\) \(5.821\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2\zeta_{18}^{5}q^{4}-4\zeta_{18}^{4}q^{7}-7\zeta_{18}^{2}q^{13}+\cdots\)
729.2.e.f \(6\) \(5.821\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2\zeta_{18}^{5}q^{4}-\zeta_{18}^{4}q^{7}+5\zeta_{18}^{2}q^{13}+\cdots\)
729.2.e.g \(6\) \(5.821\) \(\Q(\zeta_{18})\) None None \(3\) \(0\) \(6\) \(9\) \(q+(1-\zeta_{18}+\zeta_{18}^{2}-\zeta_{18}^{3}+\zeta_{18}^{4}+\cdots)q^{2}+\cdots\)
729.2.e.h \(6\) \(5.821\) \(\Q(\zeta_{18})\) None None \(3\) \(0\) \(-3\) \(0\) \(q+(-\zeta_{18}-\zeta_{18}^{2}+\zeta_{18}^{3}+\zeta_{18}^{4}+\cdots)q^{2}+\cdots\)
729.2.e.i \(6\) \(5.821\) \(\Q(\zeta_{18})\) None None \(6\) \(0\) \(3\) \(-9\) \(q+(1+\zeta_{18}-\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+(1+\cdots)q^{4}+\cdots\)
729.2.e.j \(12\) \(5.821\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(-6\) \(0\) \(6\) \(-3\) \(q+(-1-\beta _{6}-\beta _{7}+\beta _{11})q^{2}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
729.2.e.k \(12\) \(5.821\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(-3\) \(0\) \(-6\) \(6\) \(q+(-\beta _{5}-\beta _{7}+\beta _{10})q^{2}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)
729.2.e.l \(12\) \(5.821\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(-3\) \(0\) \(12\) \(-3\) \(q+\beta _{2}q^{2}+(-2\beta _{1}-\beta _{2}+\beta _{3}-\beta _{5}+\cdots)q^{4}+\cdots\)
729.2.e.m \(12\) \(5.821\) \(\Q(\zeta_{36})\) None None \(0\) \(0\) \(0\) \(6\) \(q+(-\zeta_{36}^{2}+\zeta_{36}^{7}-\zeta_{36}^{9}+\zeta_{36}^{11})q^{2}+\cdots\)
729.2.e.n \(12\) \(5.821\) \(\Q(\zeta_{36})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{36}^{8}q^{2}+(-\zeta_{36}^{2}+\zeta_{36}^{7})q^{4}+\cdots\)
729.2.e.o \(12\) \(5.821\) \(\Q(\zeta_{36})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{36}^{8}q^{2}+(-\zeta_{36}^{2}+\zeta_{36}^{7})q^{4}+\cdots\)
729.2.e.p \(12\) \(5.821\) 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{2}+4\beta _{5}q^{4}+\beta _{11}q^{5}-2\beta _{7}q^{7}+\cdots\)
729.2.e.q \(12\) \(5.821\) \(\Q(\zeta_{36})\) None None \(0\) \(0\) \(0\) \(-12\) \(q+\zeta_{36}^{9}q^{2}+(1+\zeta_{36}-\zeta_{36}^{4})q^{4}+\cdots\)
729.2.e.r \(12\) \(5.821\) \(\Q(\zeta_{36})\) None None \(0\) \(0\) \(0\) \(6\) \(q+(-\zeta_{36}^{9}+\zeta_{36}^{10})q^{2}+(1+\zeta_{36}^{3}+\cdots)q^{4}+\cdots\)
729.2.e.s \(12\) \(5.821\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(3\) \(0\) \(-12\) \(-3\) \(q+(1-\beta _{5}+\beta _{6}+\beta _{10}-\beta _{11})q^{2}+(\beta _{1}+\cdots)q^{4}+\cdots\)
729.2.e.t \(12\) \(5.821\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(3\) \(0\) \(6\) \(6\) \(q+(\beta _{1}+\beta _{2}+\beta _{5}-\beta _{6}-\beta _{8})q^{2}+(1+\cdots)q^{4}+\cdots\)
729.2.e.u \(12\) \(5.821\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(6\) \(0\) \(-6\) \(-3\) \(q+(\beta _{1}+\beta _{5}-\beta _{6}-\beta _{8})q^{2}+(-1+2\beta _{1}+\cdots)q^{4}+\cdots\)
729.2.g.a \(144\) \(5.821\) None None \(-9\) \(0\) \(-9\) \(9\)
729.2.g.b \(144\) \(5.821\) None None \(-9\) \(0\) \(-9\) \(9\)
729.2.g.c \(144\) \(5.821\) None None \(9\) \(0\) \(9\) \(9\)
729.2.g.d \(144\) \(5.821\) None None \(9\) \(0\) \(9\) \(9\)
729.2.i.a \(1404\) \(5.821\) None None \(54\) \(0\) \(54\) \(-54\)
729.2.k.a \(12960\) \(5.821\) None None \(-162\) \(-162\) \(-162\) \(-162\)
729.3.b.a \(30\) \(19.864\) None None \(0\) \(0\) \(0\) \(0\)
729.3.b.b \(36\) \(19.864\) None None \(0\) \(0\) \(0\) \(0\)
729.4.a.a \(12\) \(43.012\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-6\) \(0\) \(-12\) \(-42\) \(-\) \(q+(-1+\beta _{1})q^{2}+(3+\beta _{2}+\beta _{3})q^{4}+\cdots\)
729.4.a.b \(12\) \(43.012\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(6\) \(0\) \(12\) \(-42\) \(-\) \(q+(1-\beta _{1})q^{2}+(3+\beta _{2}+\beta _{3})q^{4}+(1+\cdots)q^{5}+\cdots\)
729.4.a.c \(24\) \(43.012\) None None \(-6\) \(0\) \(-30\) \(0\) \(-\)
729.4.a.d \(24\) \(43.012\) None None \(6\) \(0\) \(30\) \(0\) \(+\)
729.4.a.e \(30\) \(43.012\) None None \(0\) \(0\) \(0\) \(84\) \(+\)
729.6.a.a \(24\) \(116.920\) None None \(-12\) \(0\) \(-33\) \(294\) \(-\)
729.6.a.b \(24\) \(116.920\) None None \(12\) \(0\) \(33\) \(294\) \(-\)
729.6.a.c \(42\) \(116.920\) None None \(-12\) \(0\) \(-150\) \(0\) \(+\)
729.6.a.d \(42\) \(116.920\) None None \(0\) \(0\) \(0\) \(-588\) \(+\)
729.6.a.e \(42\) \(116.920\) None None \(12\) \(0\) \(150\) \(0\) \(-\)
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