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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
750.2.a.a \(2\) \(5.989\) \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(0\) \(-6\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+(-2-2\beta )q^{7}+\cdots\)
750.2.a.b \(2\) \(5.989\) \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(0\) \(-1\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+(-1+\beta )q^{7}+\cdots\)
750.2.a.c \(2\) \(5.989\) \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(0\) \(2\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+2\beta q^{7}-q^{8}+\cdots\)
750.2.a.d \(2\) \(5.989\) \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(0\) \(7\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+(4-\beta )q^{7}+\cdots\)
750.2.a.e \(2\) \(5.989\) \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(0\) \(-7\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+(-3-\beta )q^{7}+\cdots\)
750.2.a.f \(2\) \(5.989\) \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(0\) \(-2\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-2\beta q^{7}+q^{8}+\cdots\)
750.2.a.g \(2\) \(5.989\) \(\Q(\sqrt{5}) \) None \(2\) \(2\) \(0\) \(1\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+(1-\beta )q^{7}+\cdots\)
750.2.a.h \(2\) \(5.989\) \(\Q(\sqrt{5}) \) None \(2\) \(2\) \(0\) \(6\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+(4-2\beta )q^{7}+\cdots\)
750.2.c.a \(4\) \(5.989\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}-\beta _{3}q^{3}-q^{4}-q^{6}+(\beta _{1}+4\beta _{3})q^{7}+\cdots\)
750.2.c.b \(4\) \(5.989\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}+\beta _{3}q^{3}-q^{4}-q^{6}+2\beta _{1}q^{7}+\cdots\)
750.2.c.c \(4\) \(5.989\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}+\beta _{3}q^{3}-q^{4}+q^{6}+(2\beta _{1}+\cdots)q^{7}+\cdots\)
750.2.c.d \(4\) \(5.989\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}+\beta _{3}q^{3}-q^{4}+q^{6}+\beta _{1}q^{7}+\cdots\)
750.2.e.a \(32\) \(5.989\) None \(0\) \(0\) \(0\) \(0\)
750.2.e.b \(32\) \(5.989\) None \(0\) \(0\) \(0\) \(0\)
750.2.g.a \(4\) \(5.989\) \(\Q(\zeta_{10})\) None \(-1\) \(-1\) \(0\) \(-8\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
750.2.g.b \(4\) \(5.989\) \(\Q(\zeta_{10})\) None \(1\) \(-1\) \(0\) \(-6\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{3}+\cdots\)
750.2.g.c \(8\) \(5.989\) \(\Q(\zeta_{20})\) None \(-2\) \(2\) \(0\) \(-8\) \(q-\zeta_{20}^{4}q^{2}+\zeta_{20}q^{3}-\zeta_{20}q^{4}+(1+\cdots)q^{6}+\cdots\)
750.2.g.d \(8\) \(5.989\) 8.0.1064390625.3 None \(-2\) \(2\) \(0\) \(2\) \(q-\beta _{3}q^{2}+(1-\beta _{2}-\beta _{3}-\beta _{4})q^{3}+(-1+\cdots)q^{4}+\cdots\)
750.2.g.e \(8\) \(5.989\) \(\Q(\zeta_{20})\) None \(2\) \(-2\) \(0\) \(8\) \(q-\zeta_{20}^{3}q^{2}+(-1+\zeta_{20}-\zeta_{20}^{3}+\zeta_{20}^{4}+\cdots)q^{3}+\cdots\)
750.2.g.f \(16\) \(5.989\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-4\) \(-4\) \(0\) \(8\) \(q-\beta _{5}q^{2}+\beta _{6}q^{3}+\beta _{6}q^{4}-\beta _{3}q^{6}+\cdots\)
750.2.g.g \(16\) \(5.989\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(4\) \(4\) \(0\) \(-8\) \(q+\beta _{3}q^{2}+\beta _{4}q^{3}-\beta _{4}q^{4}-\beta _{1}q^{6}+\cdots\)
750.2.h.a \(8\) \(5.989\) \(\Q(\zeta_{20})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}q^{2}+\zeta_{20}^{7}q^{3}+\zeta_{20}^{2}q^{4}+(-1+\cdots)q^{6}+\cdots\)
750.2.h.b \(8\) \(5.989\) \(\Q(\zeta_{20})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}q^{2}-\zeta_{20}^{7}q^{3}+\zeta_{20}^{2}q^{4}+(1+\cdots)q^{6}+\cdots\)
750.2.h.c \(8\) \(5.989\) \(\Q(\zeta_{20})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}q^{2}-\zeta_{20}^{7}q^{3}+\zeta_{20}^{2}q^{4}+(1+\cdots)q^{6}+\cdots\)
750.2.h.d \(16\) \(5.989\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{2}+\beta _{3}q^{3}+\beta _{8}q^{4}+\beta _{2}q^{6}+\cdots\)
750.2.h.e \(16\) \(5.989\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{11}q^{2}+\beta _{7}q^{3}+\beta _{9}q^{4}+(1+\beta _{1}+\cdots)q^{6}+\cdots\)
750.2.l.a \(80\) \(5.989\) None \(0\) \(-4\) \(0\) \(-4\)
750.2.l.b \(80\) \(5.989\) None \(0\) \(-4\) \(0\) \(-4\)
750.2.l.c \(80\) \(5.989\) None \(0\) \(4\) \(0\) \(4\)
750.2.m.a \(100\) \(5.989\) None \(0\) \(0\) \(-20\) \(5\)
750.2.m.b \(120\) \(5.989\) None \(0\) \(0\) \(20\) \(-5\)
750.2.m.c \(120\) \(5.989\) None \(0\) \(0\) \(20\) \(-5\)
750.2.m.d \(140\) \(5.989\) None \(0\) \(0\) \(-20\) \(5\)
750.2.o.a \(240\) \(5.989\) None \(0\) \(0\) \(0\) \(0\)
750.2.o.b \(280\) \(5.989\) None \(0\) \(0\) \(0\) \(0\)
750.2.r.a \(2000\) \(5.989\) None \(0\) \(0\) \(0\) \(0\)
750.3.b.a \(16\) \(20.436\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-10\) \(0\) \(0\) \(q+\beta _{5}q^{2}+(-1+\beta _{1})q^{3}+2q^{4}+(\beta _{4}+\cdots)q^{6}+\cdots\)
750.3.b.b \(16\) \(20.436\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(10\) \(0\) \(0\) \(q+\beta _{5}q^{2}+(1+\beta _{2})q^{3}+2q^{4}+(\beta _{5}+\beta _{14}+\cdots)q^{6}+\cdots\)
750.3.b.c \(32\) \(20.436\) None \(0\) \(0\) \(0\) \(0\)
750.3.d.a \(32\) \(20.436\) None \(0\) \(0\) \(0\) \(0\)
750.3.d.b \(32\) \(20.436\) None \(0\) \(0\) \(0\) \(0\)
750.3.f.a \(16\) \(20.436\) 16.0.\(\cdots\).9 None \(-16\) \(0\) \(0\) \(-16\) \(q+(-1+\beta _{2})q^{2}-\beta _{1}q^{3}-2\beta _{2}q^{4}+\cdots\)
750.3.f.b \(16\) \(20.436\) 16.0.\(\cdots\).2 None \(-16\) \(0\) \(0\) \(24\) \(q+(-1-\beta _{1})q^{2}-\beta _{2}q^{3}+2\beta _{1}q^{4}+\cdots\)
750.3.f.c \(16\) \(20.436\) 16.0.\(\cdots\).2 None \(16\) \(0\) \(0\) \(-24\) \(q+(1-\beta _{1})q^{2}-\beta _{7}q^{3}-2\beta _{1}q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots\)
750.3.f.d \(16\) \(20.436\) 16.0.\(\cdots\).9 None \(16\) \(0\) \(0\) \(16\) \(q+(1+\beta _{2})q^{2}-\beta _{3}q^{3}+2\beta _{2}q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
750.4.a.a \(2\) \(44.251\) \(\Q(\sqrt{5}) \) None \(-4\) \(-6\) \(0\) \(28\) \(+\) \(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}+(10+8\beta )q^{7}+\cdots\)
750.4.a.b \(2\) \(44.251\) \(\Q(\sqrt{5}) \) None \(-4\) \(-6\) \(0\) \(43\) \(-\) \(q-2q^{2}-3q^{3}+4q^{4}+6q^{6}+(26-9\beta )q^{7}+\cdots\)
750.4.a.c \(2\) \(44.251\) \(\Q(\sqrt{5}) \) None \(-4\) \(6\) \(0\) \(-16\) \(-\) \(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+(-4+\cdots)q^{7}+\cdots\)
750.4.a.d \(2\) \(44.251\) \(\Q(\sqrt{5}) \) None \(-4\) \(6\) \(0\) \(-1\) \(-\) \(q-2q^{2}+3q^{3}+4q^{4}-6q^{6}+(4-9\beta )q^{7}+\cdots\)
750.4.a.e \(2\) \(44.251\) \(\Q(\sqrt{5}) \) None \(4\) \(-6\) \(0\) \(1\) \(-\) \(q+2q^{2}-3q^{3}+4q^{4}-6q^{6}+(-4+\cdots)q^{7}+\cdots\)
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