Learn more about

Refine search

Results (displaying matches 1-50 of 103) Next

Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
308.1.g.a \(1\) \(0.154\) \(\Q\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-77}) \) \(\Q(\sqrt{11}) \) \(-1\) \(0\) \(0\) \(1\) \(q-q^{2}+q^{4}+q^{7}-q^{8}-q^{9}+q^{11}+\cdots\)
308.1.g.b \(1\) \(0.154\) \(\Q\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-77}) \) \(\Q(\sqrt{11}) \) \(1\) \(0\) \(0\) \(-1\) \(q+q^{2}+q^{4}-q^{7}+q^{8}-q^{9}-q^{11}+\cdots\)
308.1.s.a \(4\) \(0.154\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(1\) \(q+\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}-\zeta_{10}^{2}q^{7}+\cdots\)
308.1.s.b \(4\) \(0.154\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(-1\) \(q+\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+\zeta_{10}^{2}q^{7}-\zeta_{10}^{4}q^{8}+\cdots\)
308.2.a.a \(1\) \(2.459\) \(\Q\) None None \(0\) \(-1\) \(-1\) \(-1\) \(+\) \(q-q^{3}-q^{5}-q^{7}-2q^{9}+q^{11}-4q^{13}+\cdots\)
308.2.a.b \(2\) \(2.459\) \(\Q(\sqrt{6}) \) None None \(0\) \(0\) \(4\) \(-2\) \(-\) \(q+\beta q^{3}+2q^{5}-q^{7}+3q^{9}-q^{11}+\cdots\)
308.2.a.c \(3\) \(2.459\) 3.3.1016.1 None None \(0\) \(-1\) \(-1\) \(3\) \(-\) \(q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+q^{7}+(1+\cdots)q^{9}+\cdots\)
308.2.c.a \(4\) \(2.459\) \(\Q(\sqrt{2}, \sqrt{-5})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{3}-\beta _{3}q^{5}+(\beta _{1}-\beta _{2})q^{7}-2q^{9}+\cdots\)
308.2.c.b \(4\) \(2.459\) \(\Q(\sqrt{-2}, \sqrt{-7})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}-2\beta _{2}q^{5}-\beta _{3}q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)
308.2.d.a \(18\) \(2.459\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(-1\) \(0\) \(0\) \(18\) \(q+\beta _{12}q^{2}-\beta _{4}q^{3}-\beta _{8}q^{4}-\beta _{10}q^{5}+\cdots\)
308.2.d.b \(18\) \(2.459\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(1\) \(0\) \(0\) \(-18\) \(q-\beta _{12}q^{2}-\beta _{4}q^{3}-\beta _{8}q^{4}-\beta _{10}q^{5}+\cdots\)
308.2.f.a \(40\) \(2.459\) None None \(0\) \(0\) \(0\) \(0\)
308.2.i.a \(6\) \(2.459\) 6.0.309123.1 None None \(0\) \(-1\) \(2\) \(4\) \(q-\beta _{2}q^{3}+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{5}+\cdots\)
308.2.i.b \(6\) \(2.459\) 6.0.1783323.2 None None \(0\) \(3\) \(2\) \(2\) \(q+(1-\beta _{4}+\beta _{5})q^{3}+(\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots\)
308.2.j.a \(4\) \(2.459\) \(\Q(\zeta_{10})\) None None \(0\) \(4\) \(-2\) \(1\) \(q+(2\zeta_{10}+2\zeta_{10}^{3})q^{3}-2\zeta_{10}q^{5}+\zeta_{10}^{3}q^{7}+\cdots\)
308.2.j.b \(8\) \(2.459\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(-8\) \(-1\) \(2\) \(q+(-2-2\beta _{2}-\beta _{3}-\beta _{6})q^{3}+\beta _{7}q^{5}+\cdots\)
308.2.j.c \(12\) \(2.459\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(6\) \(1\) \(-3\) \(q+(\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{8}-\beta _{9}+\beta _{11})q^{3}+\cdots\)
308.2.l.a \(80\) \(2.459\) None None \(0\) \(0\) \(0\) \(0\)
308.2.n.a \(4\) \(2.459\) \(\Q(\sqrt{-3}, \sqrt{-7})\) None None \(-1\) \(0\) \(0\) \(-2\) \(q-\beta _{3}q^{2}+(1-2\beta _{1}-\beta _{2})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots\)
308.2.n.b \(4\) \(2.459\) \(\Q(\sqrt{-3}, \sqrt{-7})\) None None \(1\) \(0\) \(0\) \(2\) \(q+\beta _{3}q^{2}+(1-2\beta _{1}-\beta _{2})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots\)
308.2.n.c \(80\) \(2.459\) None None \(0\) \(0\) \(-4\) \(0\)
308.2.q.a \(16\) \(2.459\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(6\) \(0\) \(q-\beta _{3}q^{3}+\beta _{5}q^{5}+\beta _{9}q^{7}+\beta _{7}q^{9}+\cdots\)
308.2.t.a \(8\) \(2.459\) 8.0.37515625.1 \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
308.2.t.b \(8\) \(2.459\) 8.0.37515625.1 \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
308.2.t.c \(160\) \(2.459\) None None \(-10\) \(0\) \(0\) \(0\)
308.2.v.a \(72\) \(2.459\) None None \(-1\) \(0\) \(0\) \(18\)
308.2.v.b \(72\) \(2.459\) None None \(1\) \(0\) \(0\) \(-18\)
308.2.w.a \(32\) \(2.459\) None None \(0\) \(0\) \(0\) \(-5\)
308.2.y.a \(16\) \(2.459\) 16.0.\(\cdots\).1 None None \(0\) \(1\) \(-5\) \(14\) \(q+(-\beta _{3}+\beta _{6}+\beta _{7}+\beta _{12}-\beta _{15})q^{3}+\cdots\)
308.2.y.b \(48\) \(2.459\) None None \(0\) \(-1\) \(7\) \(-7\)
308.2.z.a \(64\) \(2.459\) None None \(0\) \(0\) \(-6\) \(5\)
308.2.bc.a \(352\) \(2.459\) None None \(-5\) \(0\) \(-6\) \(0\)
308.2.be.a \(352\) \(2.459\) None None \(-1\) \(0\) \(-18\) \(0\)
308.3.b.a \(12\) \(8.392\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(-6\) \(q+\beta _{1}q^{3}-\beta _{5}q^{5}+(\beta _{1}-\beta _{7})q^{7}+(1+\cdots)q^{9}+\cdots\)
308.3.e.a \(60\) \(8.392\) None None \(0\) \(0\) \(8\) \(0\)
308.3.g.a \(2\) \(8.392\) \(\Q(\sqrt{14}) \) \(\Q(\sqrt{-77}) \) None \(-4\) \(0\) \(0\) \(-14\) \(q-2q^{2}+\beta q^{3}+4q^{4}-2\beta q^{6}-7q^{7}+\cdots\)
308.3.g.b \(2\) \(8.392\) \(\Q(\sqrt{22}) \) \(\Q(\sqrt{-77}) \) None \(-4\) \(0\) \(0\) \(14\) \(q-2q^{2}+\beta q^{3}+4q^{4}-2\beta q^{6}+7q^{7}+\cdots\)
308.3.g.c \(2\) \(8.392\) \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) None \(-3\) \(0\) \(0\) \(14\) \(q+(-1-\beta )q^{2}+(-1+3\beta )q^{4}+7q^{7}+\cdots\)
308.3.g.d \(2\) \(8.392\) \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) None \(3\) \(0\) \(0\) \(-14\) \(q+(1+\beta )q^{2}+(-1+3\beta )q^{4}-7q^{7}+\cdots\)
308.3.g.e \(2\) \(8.392\) \(\Q(\sqrt{22}) \) \(\Q(\sqrt{-77}) \) None \(4\) \(0\) \(0\) \(-14\) \(q+2q^{2}+\beta q^{3}+4q^{4}+2\beta q^{6}-7q^{7}+\cdots\)
308.3.g.f \(2\) \(8.392\) \(\Q(\sqrt{14}) \) \(\Q(\sqrt{-77}) \) None \(4\) \(0\) \(0\) \(14\) \(q+2q^{2}+\beta q^{3}+4q^{4}+2\beta q^{6}+7q^{7}+\cdots\)
308.3.g.g \(80\) \(8.392\) None None \(0\) \(0\) \(0\) \(0\)
308.3.h.a \(12\) \(8.392\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(-10\) \(-6\) \(0\) \(q+(-1+\beta _{3})q^{3}+(-1+\beta _{4})q^{5}+\beta _{5}q^{7}+\cdots\)
308.3.k.a \(32\) \(8.392\) None None \(0\) \(0\) \(-2\) \(0\)
308.3.m.a \(184\) \(8.392\) None None \(0\) \(0\) \(-12\) \(0\)
308.3.o.a \(160\) \(8.392\) None None \(0\) \(0\) \(0\) \(0\)
308.3.p.a \(28\) \(8.392\) None None \(0\) \(-6\) \(0\) \(14\)
308.3.r.a \(48\) \(8.392\) None None \(0\) \(10\) \(6\) \(0\)
308.3.s.a \(8\) \(8.392\) 8.0.37515625.1 \(\Q(\sqrt{-7}) \) None \(-3\) \(0\) \(0\) \(14\) \(q+(-\beta _{4}+\beta _{5})q^{2}+(3\beta _{2}+\beta _{7})q^{4}-7\beta _{3}q^{7}+\cdots\)
308.3.s.b \(8\) \(8.392\) 8.0.37515625.1 \(\Q(\sqrt{-7}) \) None \(3\) \(0\) \(0\) \(-14\) \(q+(1-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{4}+\beta _{5}-\beta _{6}+\cdots)q^{2}+\cdots\)
Next

Download all search results for