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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
576.1.b.a \(2\) \(0.287\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{7}+q^{25}+iq^{31}-3q^{49}-q^{73}+\cdots\)
576.1.e.a \(2\) \(0.287\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{5}-\beta q^{17}-q^{25}+\beta q^{29}+2q^{37}+\cdots\)
576.1.g.a \(1\) \(0.287\) \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{3}) \) \(0\) \(0\) \(0\) \(0\) \(q+2q^{13}-q^{25}-2q^{37}+q^{49}-2q^{61}+\cdots\)
576.1.n.a \(4\) \(0.287\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}+\zeta_{12}^{2}q^{9}+(-\zeta_{12}^{3}-\zeta_{12}^{5}+\cdots)q^{11}+\cdots\)
576.1.o.a \(4\) \(0.287\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-2\) \(0\) \(q-\zeta_{12}^{3}q^{3}-\zeta_{12}^{2}q^{5}-\zeta_{12}q^{7}-q^{9}+\cdots\)
576.2.a.a \(1\) \(4.599\) \(\Q\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(-\) \(q-4q^{5}+6q^{13}+8q^{17}+11q^{25}+\cdots\)
576.2.a.b \(1\) \(4.599\) \(\Q\) None None \(0\) \(0\) \(-2\) \(0\) \(+\) \(q-2q^{5}-4q^{11}+2q^{13}-2q^{17}-4q^{19}+\cdots\)
576.2.a.c \(1\) \(4.599\) \(\Q\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(+\) \(q-2q^{5}-6q^{13}-2q^{17}-q^{25}-10q^{29}+\cdots\)
576.2.a.d \(1\) \(4.599\) \(\Q\) None None \(0\) \(0\) \(-2\) \(0\) \(-\) \(q-2q^{5}+4q^{11}+2q^{13}-2q^{17}+4q^{19}+\cdots\)
576.2.a.e \(1\) \(4.599\) \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-4\) \(+\) \(q-4q^{7}-2q^{13}-8q^{19}-5q^{25}-4q^{31}+\cdots\)
576.2.a.f \(1\) \(4.599\) \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(4\) \(-\) \(q+4q^{7}-2q^{13}+8q^{19}-5q^{25}+4q^{31}+\cdots\)
576.2.a.g \(1\) \(4.599\) \(\Q\) None None \(0\) \(0\) \(2\) \(-4\) \(-\) \(q+2q^{5}-4q^{7}+4q^{11}+2q^{13}+6q^{17}+\cdots\)
576.2.a.h \(1\) \(4.599\) \(\Q\) None None \(0\) \(0\) \(2\) \(4\) \(-\) \(q+2q^{5}+4q^{7}-4q^{11}+2q^{13}+6q^{17}+\cdots\)
576.2.a.i \(1\) \(4.599\) \(\Q\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(-\) \(q+4q^{5}+6q^{13}-8q^{17}+11q^{25}+\cdots\)
576.2.c.a \(2\) \(4.599\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{5}-4q^{13}+\beta q^{17}-13q^{25}+\cdots\)
576.2.c.b \(2\) \(4.599\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{5}+4q^{13}+5\beta q^{17}+3q^{25}+\cdots\)
576.2.c.c \(4\) \(4.599\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{5}+\zeta_{8}q^{7}+\zeta_{8}^{3}q^{11}-4q^{13}+\cdots\)
576.2.d.a \(2\) \(4.599\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{11}+6q^{17}+iq^{19}+5q^{25}+\cdots\)
576.2.d.b \(4\) \(4.599\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{5}-\zeta_{12}q^{7}-6q^{17}-\zeta_{12}^{3}q^{19}+\cdots\)
576.2.d.c \(4\) \(4.599\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{7}-\zeta_{12}^{2}q^{13}-\zeta_{12}^{3}q^{19}+\cdots\)
576.2.f.a \(8\) \(4.599\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{2}q^{5}-\zeta_{24}q^{7}-\zeta_{24}^{6}q^{11}+\cdots\)
576.2.i.a \(2\) \(4.599\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(0\) \(2\) \(q+(-1-\zeta_{6})q^{3}+(2-2\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)
576.2.i.b \(2\) \(4.599\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(4\) \(2\) \(q+(-1-\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+\cdots\)
576.2.i.c \(2\) \(4.599\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(-3\) \(q+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+\cdots\)
576.2.i.d \(2\) \(4.599\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(3\) \(q+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+\cdots\)
576.2.i.e \(2\) \(4.599\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(3\) \(-1\) \(q+(-1+2\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots\)
576.2.i.f \(2\) \(4.599\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(3\) \(1\) \(q+(1-2\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots\)
576.2.i.g \(2\) \(4.599\) \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(0\) \(-2\) \(q+(1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)
576.2.i.h \(2\) \(4.599\) \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(4\) \(-2\) \(q+(1+\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+\cdots\)
576.2.i.i \(4\) \(4.599\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(-4\) \(-2\) \(-2\) \(q+(-1+\beta _{3})q^{3}-\beta _{2}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
576.2.i.j \(4\) \(4.599\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(-1\) \(-1\) \(-3\) \(q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
576.2.i.k \(4\) \(4.599\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-2\) \(0\) \(q-\zeta_{12}^{3}q^{3}+(-1+\zeta_{12})q^{5}-\zeta_{12}^{2}q^{7}+\cdots\)
576.2.i.l \(4\) \(4.599\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(1\) \(-1\) \(3\) \(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
576.2.i.m \(4\) \(4.599\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(4\) \(-2\) \(2\) \(q+(1-\beta _{3})q^{3}+(-1+\beta _{2})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
576.2.i.n \(8\) \(4.599\) 8.0.170772624.1 None None \(0\) \(0\) \(-2\) \(0\) \(q+(-\beta _{1}+\beta _{5})q^{3}+(-1+\beta _{4}-\beta _{7})q^{5}+\cdots\)
576.2.k.a \(2\) \(4.599\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(0\) \(q+(1+i)q^{5}+2iq^{7}+(1+i)q^{11}+(-1+\cdots)q^{13}+\cdots\)
576.2.k.b \(8\) \(4.599\) 8.0.18939904.2 None None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{4}+\beta _{6})q^{5}+(\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{7}+\cdots\)
576.2.k.c \(8\) \(4.599\) 8.0.629407744.1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{5}+(\beta _{3}-\beta _{7})q^{7}+(-\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)
576.2.l.a \(16\) \(4.599\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{5}-\beta _{9}q^{7}+(\beta _{2}+\beta _{14})q^{11}+\cdots\)
576.2.p.a \(16\) \(4.599\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(-6\) \(0\) \(q-\beta _{12}q^{3}+(\beta _{3}-\beta _{4}-\beta _{7})q^{5}+(\beta _{6}+\cdots)q^{7}+\cdots\)
576.2.p.b \(16\) \(4.599\) 16.0.\(\cdots\).3 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{3}+(\beta _{3}+\beta _{6})q^{5}+(-\beta _{14}-\beta _{15})q^{7}+\cdots\)
576.2.p.c \(16\) \(4.599\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(6\) \(0\) \(q-\beta _{12}q^{3}+(-\beta _{3}+\beta _{4}+\beta _{7})q^{5}+(-\beta _{6}+\cdots)q^{7}+\cdots\)
576.2.r.a \(4\) \(4.599\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-12\) \(0\) \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(-2-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
576.2.r.b \(4\) \(4.599\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(12\) \(0\) \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(2+2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
576.2.r.c \(8\) \(4.599\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}^{4}+\zeta_{24}^{6})q^{3}+(-1+\zeta_{24}+\cdots)q^{9}+\cdots\)
576.2.r.d \(8\) \(4.599\) 8.0.12960000.1 None None \(0\) \(0\) \(0\) \(0\) \(q+(-2\beta _{1}-\beta _{3})q^{3}-\beta _{4}q^{5}+(-\beta _{5}+\cdots)q^{7}+\cdots\)
576.2.r.e \(12\) \(4.599\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(-18\) \(0\) \(q+(-\beta _{4}+\beta _{5})q^{3}+(-2-\beta _{6})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
576.2.r.f \(12\) \(4.599\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(18\) \(0\) \(q+(-\beta _{4}+\beta _{5})q^{3}+(2+\beta _{6})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
576.2.s.a \(2\) \(4.599\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(6\) \(6\) \(q+(-1-\zeta_{6})q^{3}+(4-2\zeta_{6})q^{5}+(2+2\zeta_{6})q^{7}+\cdots\)
576.2.s.b \(2\) \(4.599\) \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-3\) \(-3\) \(q+(-1+2\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
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