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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
432.1.e.a \(1\) \(0.216\) \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q+q^{7}-q^{13}+q^{19}+q^{25}-2q^{31}+\cdots\)
432.1.g.a \(2\) \(0.216\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{6}+\zeta_{6}^{2})q^{7}+q^{13}+(-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)
432.1.j.a \(4\) \(0.216\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+\zeta_{8}^{2}q^{7}+\cdots\)
432.2.a.a \(1\) \(3.450\) \(\Q\) None None \(0\) \(0\) \(-4\) \(3\) \(-\) \(q-4q^{5}+3q^{7}+4q^{11}+q^{13}+4q^{17}+\cdots\)
432.2.a.b \(1\) \(3.450\) \(\Q\) None None \(0\) \(0\) \(-3\) \(1\) \(+\) \(q-3q^{5}+q^{7}-3q^{11}-4q^{13}-2q^{19}+\cdots\)
432.2.a.c \(1\) \(3.450\) \(\Q\) None None \(0\) \(0\) \(-1\) \(-3\) \(+\) \(q-q^{5}-3q^{7}-5q^{11}+4q^{13}-8q^{17}+\cdots\)
432.2.a.d \(1\) \(3.450\) \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-5\) \(+\) \(q-5q^{7}-7q^{13}+q^{19}-5q^{25}+4q^{31}+\cdots\)
432.2.a.e \(1\) \(3.450\) \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(-\) \(q+q^{7}+5q^{13}+7q^{19}-5q^{25}+4q^{31}+\cdots\)
432.2.a.f \(1\) \(3.450\) \(\Q\) None None \(0\) \(0\) \(1\) \(-3\) \(-\) \(q+q^{5}-3q^{7}+5q^{11}+4q^{13}+8q^{17}+\cdots\)
432.2.a.g \(1\) \(3.450\) \(\Q\) None None \(0\) \(0\) \(3\) \(1\) \(-\) \(q+3q^{5}+q^{7}+3q^{11}-4q^{13}-2q^{19}+\cdots\)
432.2.a.h \(1\) \(3.450\) \(\Q\) None None \(0\) \(0\) \(4\) \(3\) \(-\) \(q+4q^{5}+3q^{7}-4q^{11}+q^{13}-4q^{17}+\cdots\)
432.2.c.a \(2\) \(3.450\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{7}-5q^{13}-\zeta_{6}q^{19}+5q^{25}+\cdots\)
432.2.c.b \(2\) \(3.450\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{7}+7q^{13}-5\zeta_{6}q^{19}+5q^{25}+\cdots\)
432.2.c.c \(4\) \(3.450\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{5}+\zeta_{12}^{2}q^{7}-\zeta_{12}^{3}q^{11}+\cdots\)
432.2.i.a \(2\) \(3.450\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(-3\) \(q-\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(-5+5\zeta_{6})q^{11}+\cdots\)
432.2.i.b \(2\) \(3.450\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(0\) \(2\) \(q+(2-2\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}-2\zeta_{6}q^{13}+\cdots\)
432.2.i.c \(2\) \(3.450\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(3\) \(-1\) \(q+3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
432.2.i.d \(4\) \(3.450\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(0\) \(-1\) \(3\) \(q+(-\beta _{1}+\beta _{3})q^{5}+(2-\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\cdots\)
432.2.k.a \(4\) \(3.450\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-2q^{4}-\zeta_{8}q^{5}+3\zeta_{8}^{2}q^{7}+\cdots\)
432.2.k.b \(4\) \(3.450\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-2q^{4}-\zeta_{8}q^{5}-3\zeta_{8}^{2}q^{7}+\cdots\)
432.2.k.c \(24\) \(3.450\) None None \(0\) \(0\) \(0\) \(0\)
432.2.k.d \(32\) \(3.450\) None None \(0\) \(0\) \(0\) \(0\)
432.2.l.a \(32\) \(3.450\) None None \(0\) \(0\) \(0\) \(0\)
432.2.l.b \(32\) \(3.450\) None None \(0\) \(0\) \(0\) \(0\)
432.2.s.a \(2\) \(3.450\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-3\) \(-3\) \(q+(-2+\zeta_{6})q^{5}+(-1-\zeta_{6})q^{7}+(-3+\cdots)q^{11}+\cdots\)
432.2.s.b \(2\) \(3.450\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-3\) \(3\) \(q+(-2+\zeta_{6})q^{5}+(1+\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots\)
432.2.s.c \(2\) \(3.450\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(6\) \(-6\) \(q+(4-2\zeta_{6})q^{5}+(-2-2\zeta_{6})q^{7}+(3+\cdots)q^{11}+\cdots\)
432.2.s.d \(2\) \(3.450\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(6\) \(6\) \(q+(4-2\zeta_{6})q^{5}+(2+2\zeta_{6})q^{7}+(-3+\cdots)q^{11}+\cdots\)
432.2.s.e \(4\) \(3.450\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-6\) \(0\) \(q+(-2+\zeta_{12}^{2})q^{5}+\zeta_{12}q^{7}+(-\zeta_{12}+\cdots)q^{11}+\cdots\)
432.2.u.a \(6\) \(3.450\) \(\Q(\zeta_{18})\) None None \(0\) \(0\) \(-3\) \(-3\) \(q+(-2\zeta_{18}^{2}+\zeta_{18}^{5})q^{3}+(-\zeta_{18}^{2}+\cdots)q^{5}+\cdots\)
432.2.u.b \(12\) \(3.450\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(-3\) \(3\) \(q+(\beta _{3}-\beta _{4}-\beta _{11})q^{3}+(-\beta _{1}+\beta _{5}+\cdots)q^{5}+\cdots\)
432.2.u.c \(12\) \(3.450\) 12.0.\(\cdots\).1 None None \(0\) \(6\) \(-3\) \(6\) \(q+(-\beta _{2}+\beta _{6}+\beta _{7}-\beta _{9})q^{3}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
432.2.u.d \(18\) \(3.450\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(0\) \(0\) \(3\) \(0\) \(q-\beta _{12}q^{3}+(-1+\beta _{1}-\beta _{4}-\beta _{6}-\beta _{7}+\cdots)q^{5}+\cdots\)
432.2.u.e \(24\) \(3.450\) None None \(0\) \(0\) \(0\) \(3\)
432.2.u.f \(30\) \(3.450\) None None \(0\) \(0\) \(0\) \(-3\)
432.2.v.a \(88\) \(3.450\) None None \(6\) \(0\) \(6\) \(-4\)
432.2.y.a \(4\) \(3.450\) \(\Q(\zeta_{12})\) None None \(-2\) \(0\) \(-2\) \(-12\) \(q+(-1-\zeta_{12}+\zeta_{12}^{2})q^{2}+(2\zeta_{12}-2\zeta_{12}^{3})q^{4}+\cdots\)
432.2.y.b \(4\) \(3.450\) \(\Q(\zeta_{12})\) None None \(2\) \(0\) \(-4\) \(6\) \(q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}-2\zeta_{12}q^{4}+\cdots\)
432.2.y.c \(4\) \(3.450\) \(\Q(\zeta_{12})\) None None \(2\) \(0\) \(8\) \(-6\) \(q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}-2\zeta_{12}q^{4}+\cdots\)
432.2.y.d \(4\) \(3.450\) \(\Q(\zeta_{12})\) None None \(4\) \(0\) \(4\) \(12\) \(q+(1+\zeta_{12}^{3})q^{2}+2\zeta_{12}^{3}q^{4}+(1+\zeta_{12}+\cdots)q^{5}+\cdots\)
432.2.y.e \(72\) \(3.450\) None None \(-4\) \(0\) \(-4\) \(0\)
432.2.be.a \(36\) \(3.450\) None None \(0\) \(0\) \(-6\) \(0\)
432.2.be.b \(36\) \(3.450\) None None \(0\) \(0\) \(3\) \(0\)
432.2.be.c \(36\) \(3.450\) None None \(0\) \(0\) \(3\) \(0\)
432.2.bg.a \(840\) \(3.450\) None None \(-12\) \(-12\) \(-12\) \(0\)
432.2.bj.a \(840\) \(3.450\) None None \(-12\) \(-12\) \(-12\) \(-24\)
432.3.e.a \(1\) \(11.771\) \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-11\) \(q-11q^{7}+23q^{13}+37q^{19}+5^{2}q^{25}+\cdots\)
432.3.e.b \(1\) \(11.771\) \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(13\) \(q+13q^{7}-q^{13}-11q^{19}+5^{2}q^{25}+\cdots\)
432.3.e.c \(2\) \(11.771\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-10\) \(q+iq^{5}-5q^{7}-5iq^{11}-10q^{13}+\cdots\)
432.3.e.d \(2\) \(11.771\) \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(-10\) \(q+\beta q^{5}-5q^{7}+\beta q^{11}-q^{13}-3\beta q^{17}+\cdots\)
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