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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
230.2.a.a \(2\) \(1.837\) \(\Q(\sqrt{21}) \) None \(-2\) \(-1\) \(-2\) \(1\) \(-\) \(q-q^{2}-\beta q^{3}+q^{4}-q^{5}+\beta q^{6}+(1+\cdots)q^{7}+\cdots\)
230.2.a.b \(2\) \(1.837\) \(\Q(\sqrt{13}) \) None \(-2\) \(3\) \(2\) \(3\) \(-\) \(q-q^{2}+(1+\beta )q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
230.2.a.c \(2\) \(1.837\) \(\Q(\sqrt{5}) \) None \(2\) \(1\) \(2\) \(1\) \(-\) \(q+q^{2}+\beta q^{3}+q^{4}+q^{5}+\beta q^{6}+(1+\cdots)q^{7}+\cdots\)
230.2.a.d \(3\) \(1.837\) 3.3.1101.1 None \(3\) \(1\) \(-3\) \(3\) \(-\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
230.2.b.a \(4\) \(1.837\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}+\beta _{1}q^{3}-q^{4}+(1+2\beta _{2})q^{5}+\cdots\)
230.2.b.b \(8\) \(1.837\) 8.0.\(\cdots\).3 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(\beta _{2}-\beta _{5})q^{3}-q^{4}+(\beta _{1}-\beta _{6}+\cdots)q^{5}+\cdots\)
230.2.e.a \(8\) \(1.837\) 8.0.110166016.2 None \(0\) \(-4\) \(-4\) \(0\) \(q-\beta _{3}q^{2}+(-1-\beta _{2}-\beta _{6}-\beta _{7})q^{3}+\cdots\)
230.2.e.b \(8\) \(1.837\) 8.0.110166016.2 None \(0\) \(-4\) \(4\) \(0\) \(q-\beta _{3}q^{2}+(-1-\beta _{2}-\beta _{6}-\beta _{7})q^{3}+\cdots\)
230.2.e.c \(8\) \(1.837\) \(\Q(\zeta_{16})\) None \(0\) \(16\) \(0\) \(0\) \(q+\zeta_{16}^{6}q^{2}+(2+2\zeta_{16}^{4})q^{3}-\zeta_{16}^{4}q^{4}+\cdots\)
230.2.g.a \(10\) \(1.837\) \(\Q(\zeta_{22})\) None \(-1\) \(3\) \(-1\) \(-15\) \(q+\zeta_{22}^{4}q^{2}+(1-\zeta_{22}+\zeta_{22}^{2}+\zeta_{22}^{4}+\cdots)q^{3}+\cdots\)
230.2.g.b \(20\) \(1.837\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(2\) \(-3\) \(-2\) \(19\) \(q+\beta _{6}q^{2}+(\beta _{1}-\beta _{2}+\beta _{5}-\beta _{13}+\beta _{18}+\cdots)q^{3}+\cdots\)
230.2.g.c \(20\) \(1.837\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(2\) \(1\) \(2\) \(-12\) \(q+\beta _{3}q^{2}+(\beta _{5}+\beta _{18})q^{3}+\beta _{12}q^{4}+\cdots\)
230.2.g.d \(30\) \(1.837\) None \(-3\) \(-1\) \(3\) \(8\)
230.2.j.a \(120\) \(1.837\) None \(0\) \(0\) \(0\) \(0\)
230.2.l.a \(240\) \(1.837\) None \(0\) \(-8\) \(0\) \(0\)
230.3.c.a \(24\) \(6.267\) None \(0\) \(0\) \(0\) \(0\)
230.3.d.a \(16\) \(6.267\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{2}-\beta _{5}q^{3}+2q^{4}+\beta _{2}q^{5}-\beta _{10}q^{6}+\cdots\)
230.3.f.a \(20\) \(6.267\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-20\) \(0\) \(4\) \(8\) \(q+(-1-\beta _{8})q^{2}+\beta _{1}q^{3}+2\beta _{8}q^{4}+\cdots\)
230.3.f.b \(24\) \(6.267\) None \(24\) \(0\) \(4\) \(8\)
230.3.h.a \(160\) \(6.267\) None \(0\) \(0\) \(0\) \(0\)
230.3.i.a \(240\) \(6.267\) None \(0\) \(0\) \(0\) \(0\)
230.3.k.a \(240\) \(6.267\) None \(-24\) \(0\) \(-4\) \(-74\)
230.3.k.b \(240\) \(6.267\) None \(24\) \(8\) \(-4\) \(50\)
230.4.a.a \(1\) \(13.570\) \(\Q\) None \(-2\) \(-5\) \(-5\) \(12\) \(-\) \(q-2q^{2}-5q^{3}+4q^{4}-5q^{5}+10q^{6}+\cdots\)
230.4.a.b \(1\) \(13.570\) \(\Q\) None \(-2\) \(4\) \(-5\) \(3\) \(-\) \(q-2q^{2}+4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots\)
230.4.a.c \(1\) \(13.570\) \(\Q\) None \(-2\) \(7\) \(5\) \(20\) \(+\) \(q-2q^{2}+7q^{3}+4q^{4}+5q^{5}-14q^{6}+\cdots\)
230.4.a.d \(1\) \(13.570\) \(\Q\) None \(2\) \(-1\) \(5\) \(-32\) \(-\) \(q+2q^{2}-q^{3}+4q^{4}+5q^{5}-2q^{6}+\cdots\)
230.4.a.e \(1\) \(13.570\) \(\Q\) None \(2\) \(1\) \(-5\) \(-18\) \(-\) \(q+2q^{2}+q^{3}+4q^{4}-5q^{5}+2q^{6}+\cdots\)
230.4.a.f \(2\) \(13.570\) \(\Q(\sqrt{73}) \) None \(-4\) \(-3\) \(10\) \(-17\) \(-\) \(q-2q^{2}+(-1-\beta )q^{3}+4q^{4}+5q^{5}+\cdots\)
230.4.a.g \(3\) \(13.570\) 3.3.318165.1 None \(-6\) \(-1\) \(15\) \(7\) \(+\) \(q-2q^{2}-\beta _{1}q^{3}+4q^{4}+5q^{5}+2\beta _{1}q^{6}+\cdots\)
230.4.a.h \(4\) \(13.570\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-8\) \(-4\) \(-20\) \(-1\) \(+\) \(q-2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}-5q^{5}+\cdots\)
230.4.a.i \(4\) \(13.570\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(8\) \(4\) \(-20\) \(26\) \(+\) \(q+2q^{2}+(1-\beta _{1})q^{3}+4q^{4}-5q^{5}+\cdots\)
230.4.a.j \(4\) \(13.570\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(8\) \(14\) \(20\) \(8\) \(+\) \(q+2q^{2}+(4-\beta _{1})q^{3}+4q^{4}+5q^{5}+\cdots\)
230.4.b.a \(14\) \(13.570\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(-6\) \(0\) \(q-2\beta _{8}q^{2}+(\beta _{1}-\beta _{8})q^{3}-4q^{4}+(-\beta _{7}+\cdots)q^{5}+\cdots\)
230.4.b.b \(18\) \(13.570\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(0\) \(-6\) \(0\) \(q-2\beta _{5}q^{2}+\beta _{1}q^{3}-4q^{4}+(-\beta _{5}-\beta _{12}+\cdots)q^{5}+\cdots\)
230.4.e.a \(72\) \(13.570\) None \(0\) \(-16\) \(0\) \(0\)
230.4.g.a \(50\) \(13.570\) None \(-10\) \(-5\) \(25\) \(-19\)
230.4.g.b \(60\) \(13.570\) None \(12\) \(-3\) \(-30\) \(100\)
230.4.g.c \(60\) \(13.570\) None \(12\) \(5\) \(30\) \(-3\)
230.4.g.d \(70\) \(13.570\) None \(-14\) \(3\) \(-35\) \(-78\)
230.4.j.a \(360\) \(13.570\) None \(0\) \(0\) \(32\) \(0\)
230.4.l.a \(720\) \(13.570\) None \(0\) \(16\) \(0\) \(0\)
230.5.c.a \(48\) \(23.775\) None \(0\) \(0\) \(0\) \(0\)
230.5.d.a \(32\) \(23.775\) None \(0\) \(0\) \(0\) \(0\)
230.5.f.a \(44\) \(23.775\) None \(-88\) \(0\) \(24\) \(-80\)
230.5.f.b \(44\) \(23.775\) None \(88\) \(0\) \(24\) \(-80\)
230.6.a.a \(1\) \(36.888\) \(\Q\) None \(-4\) \(8\) \(-25\) \(199\) \(+\) \(q-4q^{2}+8q^{3}+2^{4}q^{4}-5^{2}q^{5}-2^{5}q^{6}+\cdots\)
230.6.a.b \(2\) \(36.888\) \(\Q(\sqrt{2}) \) None \(-8\) \(6\) \(-50\) \(-164\) \(+\) \(q-4q^{2}+(3+6\beta )q^{3}+2^{4}q^{4}-5^{2}q^{5}+\cdots\)
230.6.a.c \(3\) \(36.888\) 3.3.27980.1 None \(-12\) \(-26\) \(75\) \(1\) \(+\) \(q-4q^{2}+(-9+\beta _{2})q^{3}+2^{4}q^{4}+5^{2}q^{5}+\cdots\)
230.6.a.d \(3\) \(36.888\) 3.3.27980.1 None \(12\) \(-34\) \(75\) \(-121\) \(+\) \(q+4q^{2}+(-11-\beta _{2})q^{3}+2^{4}q^{4}+5^{2}q^{5}+\cdots\)
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