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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1248.1.b.a \(4\) \(0.623\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{3}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}-q^{9}+\cdots\)
1248.1.l.a \(4\) \(0.623\) \(\Q(\zeta_{8})\) None \(\Q(\sqrt{39}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{3}+(\zeta_{8}-\zeta_{8}^{3})q^{5}+(\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{7}+\cdots\)
1248.1.bs.a \(8\) \(0.623\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{5}q^{3}-\zeta_{24}^{6}q^{5}+(\zeta_{24}+\zeta_{24}^{7}+\cdots)q^{7}+\cdots\)
1248.1.cm.a \(16\) \(0.623\) \(\Q(\zeta_{32})\) \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{32}^{3}q^{2}+\zeta_{32}^{10}q^{3}+\zeta_{32}^{6}q^{4}+\cdots\)
1248.2.a.a \(1\) \(9.965\) \(\Q\) None None \(0\) \(-1\) \(-2\) \(-2\) \(+\) \(q-q^{3}-2q^{5}-2q^{7}+q^{9}+6q^{11}+\cdots\)
1248.2.a.b \(1\) \(9.965\) \(\Q\) None None \(0\) \(-1\) \(-2\) \(0\) \(+\) \(q-q^{3}-2q^{5}+q^{9}+4q^{11}+q^{13}+\cdots\)
1248.2.a.c \(1\) \(9.965\) \(\Q\) None None \(0\) \(-1\) \(0\) \(-2\) \(+\) \(q-q^{3}-2q^{7}+q^{9}+q^{13}+2q^{17}+\cdots\)
1248.2.a.d \(1\) \(9.965\) \(\Q\) None None \(0\) \(-1\) \(0\) \(2\) \(-\) \(q-q^{3}+2q^{7}+q^{9}+4q^{11}+q^{13}+\cdots\)
1248.2.a.e \(1\) \(9.965\) \(\Q\) None None \(0\) \(-1\) \(2\) \(-2\) \(-\) \(q-q^{3}+2q^{5}-2q^{7}+q^{9}+2q^{11}+\cdots\)
1248.2.a.f \(1\) \(9.965\) \(\Q\) None None \(0\) \(1\) \(-2\) \(0\) \(+\) \(q+q^{3}-2q^{5}+q^{9}-4q^{11}+q^{13}+\cdots\)
1248.2.a.g \(1\) \(9.965\) \(\Q\) None None \(0\) \(1\) \(-2\) \(2\) \(+\) \(q+q^{3}-2q^{5}+2q^{7}+q^{9}-6q^{11}+\cdots\)
1248.2.a.h \(1\) \(9.965\) \(\Q\) None None \(0\) \(1\) \(0\) \(-2\) \(+\) \(q+q^{3}-2q^{7}+q^{9}-4q^{11}+q^{13}+\cdots\)
1248.2.a.i \(1\) \(9.965\) \(\Q\) None None \(0\) \(1\) \(0\) \(2\) \(-\) \(q+q^{3}+2q^{7}+q^{9}+q^{13}+2q^{17}+\cdots\)
1248.2.a.j \(1\) \(9.965\) \(\Q\) None None \(0\) \(1\) \(2\) \(2\) \(-\) \(q+q^{3}+2q^{5}+2q^{7}+q^{9}-2q^{11}+\cdots\)
1248.2.a.k \(2\) \(9.965\) \(\Q(\sqrt{5}) \) None None \(0\) \(-2\) \(-2\) \(6\) \(-\) \(q-q^{3}+(-1-\beta )q^{5}+(3-\beta )q^{7}+q^{9}+\cdots\)
1248.2.a.l \(2\) \(9.965\) \(\Q(\sqrt{5}) \) None None \(0\) \(-2\) \(2\) \(-2\) \(+\) \(q-q^{3}+(1+\beta )q^{5}+(-1-\beta )q^{7}+q^{9}+\cdots\)
1248.2.a.m \(2\) \(9.965\) \(\Q(\sqrt{5}) \) None None \(0\) \(2\) \(-2\) \(-6\) \(+\) \(q+q^{3}+(-1-\beta )q^{5}+(-3+\beta )q^{7}+\cdots\)
1248.2.a.n \(2\) \(9.965\) \(\Q(\sqrt{5}) \) None None \(0\) \(2\) \(2\) \(2\) \(-\) \(q+q^{3}+(1+\beta )q^{5}+(1+\beta )q^{7}+q^{9}+\cdots\)
1248.2.a.o \(3\) \(9.965\) 3.3.148.1 None None \(0\) \(-3\) \(2\) \(0\) \(-\) \(q-q^{3}+(1+\beta _{1})q^{5}+\beta _{2}q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
1248.2.a.p \(3\) \(9.965\) 3.3.148.1 None None \(0\) \(3\) \(2\) \(0\) \(-\) \(q+q^{3}+(1+\beta _{1})q^{5}-\beta _{2}q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
1248.2.c.a \(6\) \(9.965\) 6.0.153664.1 None None \(0\) \(-6\) \(0\) \(0\) \(q-q^{3}+\beta _{1}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+q^{9}+\cdots\)
1248.2.c.b \(6\) \(9.965\) 6.0.153664.1 None None \(0\) \(6\) \(0\) \(0\) \(q+q^{3}+\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)
1248.2.c.c \(8\) \(9.965\) 8.0.134560000.4 None None \(0\) \(-8\) \(0\) \(0\) \(q-q^{3}+\beta _{1}q^{5}-\beta _{6}q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
1248.2.c.d \(8\) \(9.965\) 8.0.134560000.4 None None \(0\) \(8\) \(0\) \(0\) \(q+q^{3}+\beta _{1}q^{5}+\beta _{6}q^{7}+q^{9}+(\beta _{1}+\beta _{3}+\cdots)q^{11}+\cdots\)
1248.2.d.a \(4\) \(9.965\) \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{3}+(\zeta_{8}-\zeta_{8}^{2})q^{7}+(1+\zeta_{8}^{3})q^{9}+\cdots\)
1248.2.d.b \(8\) \(9.965\) \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{6}q^{3}+\zeta_{24}^{2}q^{5}+\zeta_{24}^{5}q^{7}+\cdots\)
1248.2.d.c \(16\) \(9.965\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{3}-\beta _{4}q^{5}-\beta _{2}q^{7}+(-1-\beta _{4}+\cdots)q^{9}+\cdots\)
1248.2.d.d \(20\) \(9.965\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{3}+\beta _{15}q^{5}+\beta _{7}q^{7}-\beta _{16}q^{9}+\cdots\)
1248.2.g.a \(8\) \(9.965\) \(\Q(\zeta_{20})\) None None \(0\) \(0\) \(0\) \(-4\) \(q+\zeta_{20}q^{3}+(-\zeta_{20}+\zeta_{20}^{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1248.2.g.b \(16\) \(9.965\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(-4\) \(q+\beta _{6}q^{3}+\beta _{12}q^{5}-\beta _{5}q^{7}-q^{9}+\beta _{10}q^{11}+\cdots\)
1248.2.h.a \(8\) \(9.965\) 8.0.\(\cdots\).21 \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}-\beta _{4}q^{5}+3q^{9}+(-\beta _{3}+\beta _{6}+\cdots)q^{11}+\cdots\)
1248.2.h.b \(12\) \(9.965\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) \(\Q(\sqrt{-26}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{3}+\beta _{9}q^{5}+(-\beta _{1}+\beta _{11})q^{7}+\cdots\)
1248.2.h.c \(32\) \(9.965\) None None \(0\) \(4\) \(0\) \(0\)
1248.2.j.a \(48\) \(9.965\) None None \(0\) \(0\) \(0\) \(0\)
1248.2.m.a \(2\) \(9.965\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-4\) \(0\) \(q-iq^{3}-2q^{5}-q^{9}+4q^{11}+(3-2i)q^{13}+\cdots\)
1248.2.m.b \(2\) \(9.965\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(4\) \(0\) \(q+iq^{3}+2q^{5}-q^{9}-4q^{11}+(-3+\cdots)q^{13}+\cdots\)
1248.2.m.c \(24\) \(9.965\) None None \(0\) \(0\) \(0\) \(0\)
1248.2.n.a \(4\) \(9.965\) \(\Q(\zeta_{8})\) None None \(0\) \(-4\) \(-8\) \(8\) \(q+(-1-\zeta_{8}^{2})q^{3}+(-2+\zeta_{8}^{3})q^{5}+\cdots\)
1248.2.n.b \(4\) \(9.965\) \(\Q(\zeta_{8})\) None None \(0\) \(-4\) \(8\) \(-8\) \(q+(-1+\zeta_{8}^{2})q^{3}+(2+\zeta_{8}^{3})q^{5}+(-2+\cdots)q^{7}+\cdots\)
1248.2.n.c \(4\) \(9.965\) \(\Q(\zeta_{8})\) None None \(0\) \(4\) \(-8\) \(-8\) \(q+(1+\zeta_{8}^{2})q^{3}+(-2+\zeta_{8}^{3})q^{5}+(-2+\cdots)q^{7}+\cdots\)
1248.2.n.d \(4\) \(9.965\) \(\Q(\zeta_{8})\) None None \(0\) \(4\) \(8\) \(8\) \(q+(1-\zeta_{8}^{2})q^{3}+(2-\zeta_{8}^{3})q^{5}+(2-\zeta_{8}^{3})q^{7}+\cdots\)
1248.2.n.e \(40\) \(9.965\) None None \(0\) \(0\) \(0\) \(0\)
1248.2.q.a \(2\) \(9.965\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(0\) \(1\) \(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+(6+\cdots)q^{11}+\cdots\)
1248.2.q.b \(2\) \(9.965\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(6\) \(2\) \(q+(-1+\zeta_{6})q^{3}+3q^{5}+2\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
1248.2.q.c \(2\) \(9.965\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(8\) \(-3\) \(q+(-1+\zeta_{6})q^{3}+4q^{5}-3\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
1248.2.q.d \(2\) \(9.965\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(0\) \(-1\) \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+(-6+\cdots)q^{11}+\cdots\)
1248.2.q.e \(2\) \(9.965\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(6\) \(-2\) \(q+(1-\zeta_{6})q^{3}+3q^{5}-2\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
1248.2.q.f \(2\) \(9.965\) \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(8\) \(3\) \(q+(1-\zeta_{6})q^{3}+4q^{5}+3\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
1248.2.q.g \(4\) \(9.965\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(-2\) \(-4\) \(0\) \(q+(-1-\beta _{2})q^{3}+(-1+\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1248.2.q.h \(4\) \(9.965\) \(\Q(\sqrt{-3}, \sqrt{17})\) None None \(0\) \(-2\) \(-2\) \(-5\) \(q+(-1+\beta _{2})q^{3}+\beta _{3}q^{5}+(\beta _{1}-3\beta _{2}+\cdots)q^{7}+\cdots\)
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