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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
605.1.f.a \(2\) \(0.302\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(2\) \(0\) \(0\) \(q+(1+i)q^{3}+iq^{4}-iq^{5}+iq^{9}+(-1+\cdots)q^{12}+\cdots\)
605.1.h.a \(4\) \(0.302\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-55}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(1\) \(0\) \(q+\zeta_{10}^{3}q^{4}+\zeta_{10}q^{5}+\zeta_{10}^{4}q^{9}-\zeta_{10}q^{16}+\cdots\)
605.1.l.a \(8\) \(0.302\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-11}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+(-\zeta_{20}-\zeta_{20}^{6})q^{3}-\zeta_{20}^{9}q^{4}-\zeta_{20}^{3}q^{5}+\cdots\)
605.2.a.a \(1\) \(4.831\) \(\Q\) None None \(-1\) \(-3\) \(1\) \(-3\) \(+\) \(q-q^{2}-3q^{3}-q^{4}+q^{5}+3q^{6}-3q^{7}+\cdots\)
605.2.a.b \(1\) \(4.831\) \(\Q\) None None \(-1\) \(0\) \(1\) \(0\) \(+\) \(q-q^{2}-q^{4}+q^{5}+3q^{8}-3q^{9}-q^{10}+\cdots\)
605.2.a.c \(1\) \(4.831\) \(\Q\) None None \(1\) \(-3\) \(1\) \(3\) \(+\) \(q+q^{2}-3q^{3}-q^{4}+q^{5}-3q^{6}+3q^{7}+\cdots\)
605.2.a.d \(2\) \(4.831\) \(\Q(\sqrt{2}) \) None None \(-2\) \(0\) \(-2\) \(4\) \(-\) \(q+(-1+\beta )q^{2}+2\beta q^{3}+(1-2\beta )q^{4}+\cdots\)
605.2.a.e \(2\) \(4.831\) \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(-2\) \(0\) \(+\) \(q+\beta q^{2}-q^{3}+q^{4}-q^{5}-\beta q^{6}-\beta q^{7}+\cdots\)
605.2.a.f \(2\) \(4.831\) \(\Q(\sqrt{3}) \) None None \(0\) \(4\) \(2\) \(0\) \(-\) \(q+\beta q^{2}+2q^{3}+q^{4}+q^{5}+2\beta q^{6}+\cdots\)
605.2.a.g \(3\) \(4.831\) 3.3.404.1 None None \(-1\) \(1\) \(-3\) \(1\) \(-\) \(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(3+\beta _{1}-\beta _{2})q^{4}+\cdots\)
605.2.a.h \(3\) \(4.831\) 3.3.404.1 None None \(1\) \(1\) \(-3\) \(-1\) \(-\) \(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(3+\beta _{1}-\beta _{2})q^{4}+\cdots\)
605.2.a.i \(4\) \(4.831\) 4.4.2525.1 None None \(-3\) \(-2\) \(4\) \(-11\) \(+\) \(q+(-1-\beta _{3})q^{2}-\beta _{1}q^{3}+(1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
605.2.a.j \(4\) \(4.831\) 4.4.725.1 None None \(-1\) \(0\) \(-4\) \(-3\) \(+\) \(q-\beta _{1}q^{2}+(-1+\beta _{2}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
605.2.a.k \(4\) \(4.831\) 4.4.725.1 None None \(1\) \(0\) \(-4\) \(3\) \(-\) \(q+\beta _{1}q^{2}+(-1+\beta _{2}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
605.2.a.l \(4\) \(4.831\) 4.4.2525.1 None None \(3\) \(-2\) \(4\) \(11\) \(-\) \(q+(1+\beta _{2}-\beta _{3})q^{2}+(-1+\beta _{1})q^{3}+\cdots\)
605.2.a.m \(6\) \(4.831\) 6.6.27433728.1 None None \(0\) \(6\) \(6\) \(0\) \(-\) \(q+\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
605.2.b.a \(2\) \(4.831\) \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(3\) \(0\) \(q+(-1+2\beta )q^{3}+2q^{4}+(1+\beta )q^{5}+\cdots\)
605.2.b.b \(4\) \(4.831\) 4.0.4400.1 \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(-2-\beta _{3})q^{4}+\beta _{3}q^{5}-\beta _{1}q^{7}+\cdots\)
605.2.b.c \(4\) \(4.831\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(0\) \(-3\) \(0\) \(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+\cdots\)
605.2.b.d \(4\) \(4.831\) \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
605.2.b.e \(4\) \(4.831\) \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
605.2.b.f \(8\) \(4.831\) 8.0.1480160000.1 None None \(0\) \(0\) \(4\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{6}+\beta _{7})q^{3}+\beta _{2}q^{4}+\cdots\)
605.2.b.g \(8\) \(4.831\) 8.0.1480160000.1 None None \(0\) \(0\) \(4\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{6}-\beta _{7})q^{3}+\beta _{2}q^{4}+\cdots\)
605.2.b.h \(12\) \(4.831\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(-6\) \(0\) \(q+\beta _{9}q^{2}-\beta _{8}q^{3}+(-2-\beta _{6})q^{4}+\beta _{4}q^{5}+\cdots\)
605.2.e.a \(20\) \(4.831\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(4\) \(4\) \(0\) \(q+\beta _{1}q^{2}-\beta _{12}q^{3}+(-\beta _{4}+\beta _{10}-\beta _{13}+\cdots)q^{4}+\cdots\)
605.2.e.b \(32\) \(4.831\) None None \(0\) \(-4\) \(8\) \(0\)
605.2.e.c \(40\) \(4.831\) None None \(0\) \(8\) \(-4\) \(0\)
605.2.g.a \(4\) \(4.831\) \(\Q(\zeta_{10})\) None None \(-1\) \(0\) \(-1\) \(0\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
605.2.g.b \(4\) \(4.831\) \(\Q(\zeta_{10})\) None None \(-1\) \(3\) \(-1\) \(-3\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
605.2.g.c \(4\) \(4.831\) \(\Q(\zeta_{10})\) None None \(1\) \(0\) \(-1\) \(0\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{4}+\cdots\)
605.2.g.d \(4\) \(4.831\) \(\Q(\zeta_{10})\) None None \(1\) \(3\) \(-1\) \(3\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-3\zeta_{10}^{2}q^{3}+\cdots\)
605.2.g.e \(8\) \(4.831\) 8.0.13140625.1 None None \(-3\) \(5\) \(2\) \(-4\) \(q-\beta _{2}q^{2}+(1-\beta _{2}+\beta _{5}+\beta _{7})q^{3}+(1+\cdots)q^{4}+\cdots\)
605.2.g.f \(8\) \(4.831\) 8.0.64000000.2 None None \(-2\) \(0\) \(2\) \(4\) \(q+(-1-\beta _{2}+\beta _{3}-\beta _{4}-\beta _{6})q^{2}+(2\beta _{1}+\cdots)q^{3}+\cdots\)
605.2.g.g \(8\) \(4.831\) 8.0.159390625.1 None None \(-1\) \(1\) \(-2\) \(8\) \(q+(1-\beta _{2}-\beta _{3}-\beta _{5}-\beta _{6})q^{2}+(-\beta _{1}+\cdots)q^{3}+\cdots\)
605.2.g.h \(8\) \(4.831\) 8.0.324000000.3 None None \(0\) \(-4\) \(-2\) \(0\) \(q+\beta _{7}q^{2}+2\beta _{6}q^{3}+\beta _{4}q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
605.2.g.i \(8\) \(4.831\) 8.0.324000000.3 None None \(0\) \(2\) \(2\) \(0\) \(q+\beta _{7}q^{2}-\beta _{6}q^{3}+\beta _{4}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
605.2.g.j \(8\) \(4.831\) 8.0.159390625.1 None None \(1\) \(1\) \(-2\) \(-8\) \(q+(-1+\beta _{2}+\beta _{3}+\beta _{5}+\beta _{6})q^{2}+(-\beta _{1}+\cdots)q^{3}+\cdots\)
605.2.g.k \(8\) \(4.831\) 8.0.13140625.1 None None \(2\) \(-5\) \(2\) \(1\) \(q+\beta _{6}q^{2}+(-1+\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)
605.2.g.l \(8\) \(4.831\) 8.0.64000000.2 None None \(2\) \(0\) \(2\) \(-4\) \(q+(-\beta _{2}+\beta _{7})q^{2}+2\beta _{1}q^{3}+(2\beta _{1}+2\beta _{3}+\cdots)q^{4}+\cdots\)
605.2.g.m \(8\) \(4.831\) 8.0.13140625.1 None None \(3\) \(5\) \(2\) \(4\) \(q+\beta _{2}q^{2}+(1-\beta _{2}+\beta _{5}+\beta _{7})q^{3}+(1+\cdots)q^{4}+\cdots\)
605.2.g.n \(8\) \(4.831\) 8.0.159390625.1 None None \(4\) \(1\) \(-2\) \(3\) \(q+(\beta _{1}+\beta _{2}-\beta _{4})q^{2}+\beta _{1}q^{3}+(-2+\cdots)q^{4}+\cdots\)
605.2.g.o \(12\) \(4.831\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-1\) \(-1\) \(3\) \(1\) \(q-\beta _{11}q^{2}+\beta _{8}q^{3}+(-\beta _{1}-3\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
605.2.g.p \(12\) \(4.831\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(1\) \(-1\) \(3\) \(-1\) \(q+\beta _{9}q^{2}-\beta _{1}q^{3}+(-3+\beta _{3}+3\beta _{4}+\cdots)q^{4}+\cdots\)
605.2.g.q \(24\) \(4.831\) None None \(0\) \(-6\) \(-6\) \(0\)
605.2.j.a \(8\) \(4.831\) 8.0.484000000.6 \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(-10\) \(0\) \(q+(\beta _{1}-\beta _{4})q^{2}+(1+\beta _{2}-3\beta _{3}+3\beta _{5}+\cdots)q^{4}+\cdots\)
605.2.j.b \(8\) \(4.831\) 8.0.228765625.1 \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(-3\) \(0\) \(q+(-\beta _{4}-2\beta _{5})q^{3}+(-2+2\beta _{3}+2\beta _{4}+\cdots)q^{4}+\cdots\)
605.2.j.c \(8\) \(4.831\) 8.0.484000000.6 \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(10\) \(0\) \(q+(\beta _{1}-\beta _{6})q^{2}+(-2\beta _{2}+2\beta _{3}-3\beta _{5}+\cdots)q^{4}+\cdots\)
605.2.j.d \(16\) \(4.831\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(-2\) \(0\) \(q+(\beta _{1}-\beta _{12}-\beta _{13})q^{2}+(-\beta _{5}-\beta _{13}+\cdots)q^{3}+\cdots\)
605.2.j.e \(16\) \(4.831\) 16.0.\(\cdots\).7 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{12}q^{2}+\beta _{3}q^{3}-\beta _{10}q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
605.2.j.f \(16\) \(4.831\) 16.0.\(\cdots\).7 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{12}q^{2}-\beta _{3}q^{3}-\beta _{10}q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
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