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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1078.2.a.a \(1\) \(8.608\) \(\Q\) None \(-1\) \(-3\) \(-4\) \(0\) \(+\) \(q-q^{2}-3q^{3}+q^{4}-4q^{5}+3q^{6}-q^{8}+\cdots\)
1078.2.a.b \(1\) \(8.608\) \(\Q\) None \(-1\) \(-2\) \(-2\) \(0\) \(+\) \(q-q^{2}-2q^{3}+q^{4}-2q^{5}+2q^{6}-q^{8}+\cdots\)
1078.2.a.c \(1\) \(8.608\) \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}-2q^{9}+\cdots\)
1078.2.a.d \(1\) \(8.608\) \(\Q\) None \(-1\) \(0\) \(4\) \(0\) \(-\) \(q-q^{2}+q^{4}+4q^{5}-q^{8}-3q^{9}-4q^{10}+\cdots\)
1078.2.a.e \(1\) \(8.608\) \(\Q\) None \(-1\) \(1\) \(0\) \(0\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}-2q^{9}+\cdots\)
1078.2.a.f \(1\) \(8.608\) \(\Q\) None \(-1\) \(3\) \(4\) \(0\) \(-\) \(q-q^{2}+3q^{3}+q^{4}+4q^{5}-3q^{6}-q^{8}+\cdots\)
1078.2.a.g \(1\) \(8.608\) \(\Q\) None \(1\) \(-3\) \(-2\) \(0\) \(+\) \(q+q^{2}-3q^{3}+q^{4}-2q^{5}-3q^{6}+q^{8}+\cdots\)
1078.2.a.h \(1\) \(8.608\) \(\Q\) None \(1\) \(-2\) \(-2\) \(0\) \(-\) \(q+q^{2}-2q^{3}+q^{4}-2q^{5}-2q^{6}+q^{8}+\cdots\)
1078.2.a.i \(1\) \(8.608\) \(\Q\) None \(1\) \(-1\) \(0\) \(0\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-2q^{9}+\cdots\)
1078.2.a.j \(1\) \(8.608\) \(\Q\) None \(1\) \(0\) \(-2\) \(0\) \(+\) \(q+q^{2}+q^{4}-2q^{5}+q^{8}-3q^{9}-2q^{10}+\cdots\)
1078.2.a.k \(1\) \(8.608\) \(\Q\) None \(1\) \(1\) \(0\) \(0\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}-2q^{9}+\cdots\)
1078.2.a.l \(1\) \(8.608\) \(\Q\) None \(1\) \(2\) \(2\) \(0\) \(-\) \(q+q^{2}+2q^{3}+q^{4}+2q^{5}+2q^{6}+q^{8}+\cdots\)
1078.2.a.m \(1\) \(8.608\) \(\Q\) None \(1\) \(3\) \(2\) \(0\) \(-\) \(q+q^{2}+3q^{3}+q^{4}+2q^{5}+3q^{6}+q^{8}+\cdots\)
1078.2.a.n \(2\) \(8.608\) \(\Q(\sqrt{7}) \) None \(-2\) \(0\) \(-2\) \(0\) \(+\) \(q-q^{2}+\beta q^{3}+q^{4}+(-1-\beta )q^{5}-\beta q^{6}+\cdots\)
1078.2.a.o \(2\) \(8.608\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) \(+\) \(q-q^{2}+q^{4}+\beta q^{5}-q^{8}-3q^{9}-\beta q^{10}+\cdots\)
1078.2.a.p \(2\) \(8.608\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) \(-\) \(q-q^{2}+q^{4}-2\beta q^{5}-q^{8}-3q^{9}+2\beta q^{10}+\cdots\)
1078.2.a.q \(2\) \(8.608\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) \(+\) \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{5}-\beta q^{6}-q^{8}+\cdots\)
1078.2.a.r \(2\) \(8.608\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) \(-\) \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{8}+5q^{9}+\cdots\)
1078.2.a.s \(2\) \(8.608\) \(\Q(\sqrt{7}) \) None \(-2\) \(0\) \(2\) \(0\) \(-\) \(q-q^{2}+\beta q^{3}+q^{4}+(1-\beta )q^{5}-\beta q^{6}+\cdots\)
1078.2.a.t \(2\) \(8.608\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(-4\) \(0\) \(+\) \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-2-\beta )q^{5}+\cdots\)
1078.2.a.u \(2\) \(8.608\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(q+q^{2}+\beta q^{3}+q^{4}+3\beta q^{5}+\beta q^{6}+\cdots\)
1078.2.a.v \(2\) \(8.608\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) \(-\) \(q+q^{2}+2\beta q^{3}+q^{4}+2\beta q^{6}+q^{8}+\cdots\)
1078.2.a.w \(2\) \(8.608\) \(\Q(\sqrt{5}) \) None \(2\) \(2\) \(-2\) \(0\) \(-\) \(q+q^{2}+(1+\beta )q^{3}+q^{4}+(-1-\beta )q^{5}+\cdots\)
1078.2.a.x \(2\) \(8.608\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(4\) \(0\) \(-\) \(q+q^{2}+(1+\beta )q^{3}+q^{4}+(2-\beta )q^{5}+\cdots\)
1078.2.c.a \(8\) \(8.608\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}q^{2}+(-\zeta_{16}^{2}-\zeta_{16}^{4})q^{3}-q^{4}+\cdots\)
1078.2.c.b \(16\) \(8.608\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{9}q^{2}+\beta _{14}q^{3}-q^{4}+(-\beta _{8}+\beta _{11}+\cdots)q^{5}+\cdots\)
1078.2.c.c \(16\) \(8.608\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}-\beta _{5}q^{3}-q^{4}+(-\beta _{9}+\beta _{11}+\cdots)q^{5}+\cdots\)
1078.2.e.a \(2\) \(8.608\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-2\) \(-2\) \(0\) \(q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.b \(2\) \(8.608\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-2\) \(0\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-2\zeta_{6}q^{5}+\cdots\)
1078.2.e.c \(2\) \(8.608\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(2\) \(0\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+2\zeta_{6}q^{5}+\cdots\)
1078.2.e.d \(2\) \(8.608\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(0\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.e \(2\) \(8.608\) \(\Q(\sqrt{-3}) \) None \(-1\) \(2\) \(2\) \(0\) \(q-\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.f \(2\) \(8.608\) \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(2\) \(0\) \(q-\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.g \(2\) \(8.608\) \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(-4\) \(0\) \(q+\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.h \(2\) \(8.608\) \(\Q(\sqrt{-3}) \) None \(1\) \(-2\) \(-2\) \(0\) \(q+\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.i \(2\) \(8.608\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-4\) \(0\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-4\zeta_{6}q^{5}+\cdots\)
1078.2.e.j \(2\) \(8.608\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(4\) \(0\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+4\zeta_{6}q^{5}+\cdots\)
1078.2.e.k \(2\) \(8.608\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(0\) \(0\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.l \(2\) \(8.608\) \(\Q(\sqrt{-3}) \) None \(1\) \(2\) \(2\) \(0\) \(q+\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1078.2.e.m \(4\) \(8.608\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(-2\) \(-4\) \(0\) \(q+\beta _{2}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1078.2.e.n \(4\) \(8.608\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-2\) \(-2\) \(2\) \(0\) \(q+\beta _{1}q^{2}+(-1-\beta _{1}-\beta _{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1078.2.e.o \(4\) \(8.608\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+2\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+\cdots\)
1078.2.e.p \(4\) \(8.608\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(-3\beta _{1}+\cdots)q^{5}+\cdots\)
1078.2.e.q \(4\) \(8.608\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-2\) \(2\) \(-2\) \(0\) \(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
1078.2.e.r \(4\) \(8.608\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}-\beta _{3}q^{6}+\cdots\)
1078.2.e.s \(4\) \(8.608\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
1078.2.e.t \(4\) \(8.608\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(0\) \(0\) \(q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}-2\beta _{1}q^{5}-q^{8}+\cdots\)
1078.2.e.u \(4\) \(8.608\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(0\) \(0\) \(q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}-\beta _{1}q^{5}-q^{8}+\cdots\)
1078.2.e.v \(4\) \(8.608\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(2\) \(0\) \(2\) \(0\) \(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
1078.2.i.a \(16\) \(8.608\) \(\Q(\zeta_{48})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{48}q^{2}+(-\zeta_{48}^{2}+\zeta_{48}^{7}-\zeta_{48}^{10}+\cdots)q^{3}+\cdots\)
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