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Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
115.2.a.a \(1\) \(0.918\) \(\Q\) None \(2\) \(0\) \(-1\) \(1\) \(-\) \(q+2q^{2}+2q^{4}-q^{5}+q^{7}-3q^{9}-2q^{10}+\cdots\)
115.2.a.b \(2\) \(0.918\) \(\Q(\sqrt{5}) \) None \(-3\) \(-2\) \(-2\) \(-2\) \(+\) \(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}-q^{5}+\cdots\)
115.2.a.c \(4\) \(0.918\) 4.4.15317.1 None \(2\) \(-2\) \(4\) \(-3\) \(-\) \(q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
115.2.b.a \(2\) \(0.918\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+2iq^{2}-2iq^{3}-2q^{4}+(2+i)q^{5}+\cdots\)
115.2.b.b \(8\) \(0.918\) 8.0.527896576.2 None \(0\) \(0\) \(-6\) \(0\) \(q+\beta _{7}q^{2}+(-\beta _{1}-\beta _{3}+\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots\)
115.2.e.a \(20\) \(0.918\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-4\) \(-8\) \(0\) \(0\) \(q-\beta _{3}q^{2}+\beta _{2}q^{3}+\beta _{4}q^{4}+\beta _{18}q^{5}+\cdots\)
115.2.g.a \(10\) \(0.918\) \(\Q(\zeta_{22})\) None \(5\) \(1\) \(1\) \(5\) \(q+(\zeta_{22}+\zeta_{22}^{3}-\zeta_{22}^{4}+\zeta_{22}^{5}+\zeta_{22}^{7}+\cdots)q^{2}+\cdots\)
115.2.g.b \(20\) \(0.918\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-4\) \(1\) \(2\) \(-4\) \(q+(-1+\beta _{2}+\beta _{3}+\beta _{4}+\beta _{6}+\beta _{8}+\cdots)q^{2}+\cdots\)
115.2.g.c \(50\) \(0.918\) None \(-5\) \(-2\) \(-5\) \(-5\)
115.2.j.a \(100\) \(0.918\) None \(0\) \(0\) \(-9\) \(0\)
115.2.l.a \(200\) \(0.918\) None \(-18\) \(-14\) \(-22\) \(-22\)
115.3.c.a \(1\) \(3.134\) \(\Q\) \(\Q(\sqrt{-115}) \) \(0\) \(0\) \(-5\) \(9\) \(q+4q^{4}-5q^{5}+9q^{7}+9q^{9}+2^{4}q^{16}+\cdots\)
115.3.c.b \(1\) \(3.134\) \(\Q\) \(\Q(\sqrt{-115}) \) \(0\) \(0\) \(5\) \(-9\) \(q+4q^{4}+5q^{5}-9q^{7}+9q^{9}+2^{4}q^{16}+\cdots\)
115.3.c.c \(20\) \(3.134\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}-\beta _{4}q^{3}+(-3+\beta _{7}-\beta _{8}+\cdots)q^{4}+\cdots\)
115.3.d.a \(6\) \(3.134\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-6\) \(2\) \(0\) \(0\) \(q-q^{2}+\beta _{4}q^{3}-3q^{4}-\beta _{3}q^{5}-\beta _{4}q^{6}+\cdots\)
115.3.d.b \(10\) \(3.134\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(2\) \(-2\) \(0\) \(0\) \(q+\beta _{4}q^{2}-\beta _{7}q^{3}+(3+\beta _{6})q^{4}+\beta _{5}q^{5}+\cdots\)
115.3.f.a \(44\) \(3.134\) None \(-4\) \(0\) \(-8\) \(-16\)
115.3.h.a \(160\) \(3.134\) None \(4\) \(0\) \(0\) \(0\)
115.3.i.a \(220\) \(3.134\) None \(0\) \(0\) \(-11\) \(0\)
115.3.k.a \(440\) \(3.134\) None \(-18\) \(-22\) \(-14\) \(-6\)
115.4.a.a \(1\) \(6.785\) \(\Q\) None \(1\) \(4\) \(-5\) \(-32\) \(-\) \(q+q^{2}+4q^{3}-7q^{4}-5q^{5}+4q^{6}+\cdots\)
115.4.a.b \(1\) \(6.785\) \(\Q\) None \(2\) \(-3\) \(5\) \(-2\) \(-\) \(q+2q^{2}-3q^{3}-4q^{4}+5q^{5}-6q^{6}+\cdots\)
115.4.a.c \(2\) \(6.785\) \(\Q(\sqrt{109}) \) None \(-6\) \(-3\) \(10\) \(1\) \(-\) \(q-3q^{2}+(-1-\beta )q^{3}+q^{4}+5q^{5}+\cdots\)
115.4.a.d \(5\) \(6.785\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-5\) \(-6\) \(-25\) \(-15\) \(-\) \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{2}-\beta _{3}-\beta _{4})q^{3}+\cdots\)
115.4.a.e \(5\) \(6.785\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(6\) \(4\) \(-25\) \(-3\) \(+\) \(q+(1+\beta _{1})q^{2}+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{3}+\cdots\)
115.4.a.f \(8\) \(6.785\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(6\) \(0\) \(40\) \(11\) \(+\) \(q+(1-\beta _{1})q^{2}+\beta _{6}q^{3}+(5+\beta _{2})q^{4}+\cdots\)
115.4.b.a \(34\) \(6.785\) None \(0\) \(0\) \(14\) \(0\)
115.4.e.a \(68\) \(6.785\) None \(-4\) \(4\) \(0\) \(0\)
115.4.g.a \(110\) \(6.785\) None \(-2\) \(6\) \(-55\) \(-10\)
115.4.g.b \(130\) \(6.785\) None \(6\) \(-6\) \(65\) \(38\)
115.4.j.a \(340\) \(6.785\) None \(0\) \(0\) \(-25\) \(0\)
115.4.l.a \(680\) \(6.785\) None \(-18\) \(-26\) \(-22\) \(-22\)
115.5.c.a \(1\) \(11.888\) \(\Q\) \(\Q(\sqrt{-115}) \) \(0\) \(0\) \(-25\) \(17\) \(q+2^{4}q^{4}-5^{2}q^{5}+17q^{7}+3^{4}q^{9}+\cdots\)
115.5.c.b \(1\) \(11.888\) \(\Q\) \(\Q(\sqrt{-115}) \) \(0\) \(0\) \(25\) \(-17\) \(q+2^{4}q^{4}+5^{2}q^{5}-17q^{7}+3^{4}q^{9}+\cdots\)
115.5.c.c \(44\) \(11.888\) None \(0\) \(0\) \(0\) \(0\)
115.5.d.a \(32\) \(11.888\) None \(12\) \(0\) \(0\) \(0\)
115.5.f.a \(88\) \(11.888\) None \(0\) \(0\) \(-48\) \(160\)
115.5.h.a \(320\) \(11.888\) None \(-12\) \(0\) \(0\) \(0\)
115.5.i.a \(460\) \(11.888\) None \(0\) \(0\) \(-11\) \(0\)
115.5.k.a \(920\) \(11.888\) None \(-18\) \(2\) \(-54\) \(-78\)
115.6.a.a \(2\) \(18.444\) \(\Q(\sqrt{1821}) \) None \(4\) \(3\) \(-50\) \(53\) \(-\) \(q+2q^{2}+(2-\beta )q^{3}-28q^{4}-5^{2}q^{5}+\cdots\)
115.6.a.b \(7\) \(18.444\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-12\) \(4\) \(175\) \(-275\) \(+\) \(q+(-2+\beta _{1})q^{2}+(1-\beta _{1}-\beta _{6})q^{3}+\cdots\)
115.6.a.c \(7\) \(18.444\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(4\) \(-3\) \(-175\) \(33\) \(-\) \(q+(1-\beta _{1})q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+\cdots\)
115.6.a.d \(10\) \(18.444\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-12\) \(-18\) \(-250\) \(-15\) \(+\) \(q+(-1-\beta _{1})q^{2}+(-2+\beta _{3})q^{3}+(14+\cdots)q^{4}+\cdots\)
115.6.a.e \(12\) \(18.444\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(8\) \(22\) \(300\) \(16\) \(-\) \(q+(1-\beta _{1})q^{2}+(2-\beta _{1}-\beta _{4})q^{3}+(5^{2}+\cdots)q^{4}+\cdots\)
115.6.b.a \(54\) \(18.444\) None \(0\) \(0\) \(98\) \(0\)
115.7.c.a \(1\) \(26.456\) \(\Q\) \(\Q(\sqrt{-115}) \) \(0\) \(0\) \(-125\) \(-594\) \(q+2^{6}q^{4}-5^{3}q^{5}-594q^{7}+3^{6}q^{9}+\cdots\)
115.7.c.b \(1\) \(26.456\) \(\Q\) \(\Q(\sqrt{-115}) \) \(0\) \(0\) \(125\) \(594\) \(q+2^{6}q^{4}+5^{3}q^{5}+594q^{7}+3^{6}q^{9}+\cdots\)
115.7.c.c \(68\) \(26.456\) None \(0\) \(0\) \(0\) \(0\)
115.7.d.a \(48\) \(26.456\) None \(-20\) \(0\) \(0\) \(0\)
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