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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
322.2.a.a \(1\) \(2.571\) \(\Q\) None \(-1\) \(0\) \(-2\) \(1\) \(+\) \(q-q^{2}+q^{4}-2q^{5}+q^{7}-q^{8}-3q^{9}+\cdots\)
322.2.a.b \(1\) \(2.571\) \(\Q\) None \(-1\) \(2\) \(0\) \(1\) \(-\) \(q-q^{2}+2q^{3}+q^{4}-2q^{6}+q^{7}-q^{8}+\cdots\)
322.2.a.c \(1\) \(2.571\) \(\Q\) None \(1\) \(-2\) \(-2\) \(-1\) \(+\) \(q+q^{2}-2q^{3}+q^{4}-2q^{5}-2q^{6}-q^{7}+\cdots\)
322.2.a.d \(1\) \(2.571\) \(\Q\) None \(1\) \(2\) \(-2\) \(1\) \(-\) \(q+q^{2}+2q^{3}+q^{4}-2q^{5}+2q^{6}+q^{7}+\cdots\)
322.2.a.e \(2\) \(2.571\) \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(-2\) \(-2\) \(+\) \(q-q^{2}+(-1-\beta )q^{3}+q^{4}+(-1+\beta )q^{5}+\cdots\)
322.2.a.f \(2\) \(2.571\) \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(2\) \(2\) \(-\) \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(1+\beta )q^{5}+\cdots\)
322.2.a.g \(3\) \(2.571\) 3.3.316.1 None \(3\) \(2\) \(4\) \(-3\) \(-\) \(q+q^{2}+(1+\beta _{2})q^{3}+q^{4}+(1-\beta _{2})q^{5}+\cdots\)
322.2.c.a \(4\) \(2.571\) \(\Q(\sqrt{-2}, \sqrt{7})\) None \(-4\) \(0\) \(0\) \(0\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}-\beta _{3}q^{7}+\cdots\)
322.2.c.b \(4\) \(2.571\) \(\Q(\sqrt{-2}, \sqrt{-7})\) None \(-4\) \(0\) \(0\) \(0\) \(q-q^{2}+\beta _{2}q^{3}+q^{4}+\beta _{1}q^{5}-\beta _{2}q^{6}+\cdots\)
322.2.c.c \(4\) \(2.571\) 4.0.2312.1 None \(4\) \(0\) \(-8\) \(-2\) \(q+q^{2}-\beta _{2}q^{3}+q^{4}-2q^{5}-\beta _{2}q^{6}+\cdots\)
322.2.c.d \(4\) \(2.571\) 4.0.2312.1 None \(4\) \(0\) \(8\) \(2\) \(q+q^{2}-\beta _{2}q^{3}+q^{4}+2q^{5}-\beta _{2}q^{6}+\cdots\)
322.2.e.a \(8\) \(2.571\) 8.0.310217769.2 None \(-4\) \(-3\) \(-7\) \(-1\) \(q+(-1+\beta _{5})q^{2}+(\beta _{1}+\beta _{2}-\beta _{5})q^{3}+\cdots\)
322.2.e.b \(8\) \(2.571\) 8.0.1767277521.3 None \(-4\) \(5\) \(5\) \(1\) \(q-\beta _{5}q^{2}+(1+\beta _{2}-\beta _{5}+\beta _{6})q^{3}+(-1+\cdots)q^{4}+\cdots\)
322.2.e.c \(8\) \(2.571\) 8.0.1767277521.3 None \(4\) \(-1\) \(-3\) \(-1\) \(q+(1-\beta _{6})q^{2}+(\beta _{4}+\beta _{5}-\beta _{6}-\beta _{7})q^{3}+\cdots\)
322.2.e.d \(8\) \(2.571\) 8.0.6498455769.2 None \(4\) \(-1\) \(5\) \(-3\) \(q+(1-\beta _{5})q^{2}-\beta _{1}q^{3}-\beta _{5}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
322.2.g.a \(16\) \(2.571\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(-8\) \(6\) \(0\) \(0\) \(q-\beta _{5}q^{2}-\beta _{1}q^{3}+(-1+\beta _{5})q^{4}+\beta _{6}q^{5}+\cdots\)
322.2.g.b \(16\) \(2.571\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(8\) \(-6\) \(0\) \(0\) \(q-\beta _{6}q^{2}+\beta _{11}q^{3}+(-1-\beta _{6})q^{4}+\cdots\)
322.2.i.a \(10\) \(2.571\) \(\Q(\zeta_{22})\) None \(1\) \(-3\) \(5\) \(1\) \(q-\zeta_{22}^{4}q^{2}+(-1-\zeta_{22}^{2}+\zeta_{22}^{3}+\cdots)q^{3}+\cdots\)
322.2.i.b \(10\) \(2.571\) \(\Q(\zeta_{22})\) None \(1\) \(5\) \(8\) \(1\) \(q-\zeta_{22}^{4}q^{2}+(1+\zeta_{22}^{2}-\zeta_{22}^{3}+\zeta_{22}^{6}+\cdots)q^{3}+\cdots\)
322.2.i.c \(20\) \(2.571\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-2\) \(4\) \(-5\) \(-2\) \(q+\beta _{19}q^{2}+(\beta _{1}+\beta _{2}+\beta _{4}+\beta _{5}-\beta _{6}+\cdots)q^{3}+\cdots\)
322.2.i.d \(40\) \(2.571\) None \(-4\) \(0\) \(9\) \(4\)
322.2.i.e \(40\) \(2.571\) None \(4\) \(2\) \(-9\) \(-4\)
322.2.k.a \(80\) \(2.571\) None \(-8\) \(0\) \(0\) \(-11\)
322.2.k.b \(80\) \(2.571\) None \(8\) \(0\) \(0\) \(11\)
322.2.m.a \(160\) \(2.571\) None \(-8\) \(2\) \(-2\) \(15\)
322.2.m.b \(160\) \(2.571\) None \(8\) \(-2\) \(2\) \(-11\)
322.2.o.a \(160\) \(2.571\) None \(-8\) \(6\) \(0\) \(-11\)
322.2.o.b \(160\) \(2.571\) None \(8\) \(-6\) \(0\) \(11\)
322.3.b.a \(32\) \(8.774\) None \(0\) \(0\) \(0\) \(-12\)
322.3.d.a \(24\) \(8.774\) None \(0\) \(8\) \(0\) \(0\)
322.3.f.a \(64\) \(8.774\) None \(0\) \(0\) \(0\) \(0\)
322.3.h.a \(56\) \(8.774\) None \(0\) \(12\) \(0\) \(-4\)
322.3.j.a \(240\) \(8.774\) None \(0\) \(-8\) \(0\) \(0\)
322.3.l.a \(320\) \(8.774\) None \(0\) \(0\) \(0\) \(12\)
322.3.n.a \(640\) \(8.774\) None \(0\) \(0\) \(12\) \(-12\)
322.3.p.a \(640\) \(8.774\) None \(0\) \(0\) \(0\) \(0\)
322.4.a.a \(2\) \(18.999\) \(\Q(\sqrt{2}) \) None \(-4\) \(-4\) \(16\) \(14\) \(+\) \(q-2q^{2}+(-2+3\beta )q^{3}+4q^{4}+(8-3\beta )q^{5}+\cdots\)
322.4.a.b \(2\) \(18.999\) \(\Q(\sqrt{73}) \) None \(-4\) \(9\) \(-8\) \(14\) \(+\) \(q-2q^{2}+(5-\beta )q^{3}+4q^{4}+(-2-4\beta )q^{5}+\cdots\)
322.4.a.c \(2\) \(18.999\) \(\Q(\sqrt{57}) \) None \(4\) \(1\) \(-18\) \(14\) \(-\) \(q+2q^{2}+\beta q^{3}+4q^{4}+(-8-2\beta )q^{5}+\cdots\)
322.4.a.d \(3\) \(18.999\) 3.3.15384.1 None \(-6\) \(-3\) \(8\) \(-21\) \(+\) \(q-2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+(3+2\beta _{1}+\cdots)q^{5}+\cdots\)
322.4.a.e \(3\) \(18.999\) 3.3.3368.1 None \(6\) \(-7\) \(-8\) \(-21\) \(-\) \(q+2q^{2}+(-2-\beta _{2})q^{3}+4q^{4}+(-3+\cdots)q^{5}+\cdots\)
322.4.a.f \(4\) \(18.999\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-8\) \(-1\) \(-2\) \(28\) \(-\) \(q-2q^{2}-\beta _{1}q^{3}+4q^{4}-\beta _{2}q^{5}+2\beta _{1}q^{6}+\cdots\)
322.4.a.g \(5\) \(18.999\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-10\) \(-9\) \(-2\) \(-35\) \(-\) \(q-2q^{2}+(-2+\beta _{4})q^{3}+4q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
322.4.a.h \(5\) \(18.999\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(10\) \(5\) \(22\) \(-35\) \(+\) \(q+2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(4-\beta _{1}+\cdots)q^{5}+\cdots\)
322.4.a.i \(6\) \(18.999\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(12\) \(13\) \(12\) \(42\) \(+\) \(q+2q^{2}+(2+\beta _{1})q^{3}+4q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\)
322.4.c.a \(24\) \(18.999\) None \(-48\) \(0\) \(0\) \(0\)
322.4.c.b \(24\) \(18.999\) None \(48\) \(0\) \(0\) \(0\)
322.4.e.a \(22\) \(18.999\) None \(-22\) \(-18\) \(-33\) \(33\)
322.4.e.b \(22\) \(18.999\) None \(-22\) \(6\) \(27\) \(1\)
322.4.e.c \(22\) \(18.999\) None \(22\) \(0\) \(-17\) \(11\)
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