Learn more about

Refine search

Results (displaying matches 1-50 of 28440) Next

Label Dim. \(A\) Field CM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
5.4.a.a \(1\) \(0.295\) \(\Q\) None \(-4\) \(2\) \(-5\) \(6\) \(+\) \(q-4q^{2}+2q^{3}+8q^{4}-5q^{5}-8q^{6}+\cdots\)
6.4.a.a \(1\) \(0.354\) \(\Q\) None \(-2\) \(-3\) \(6\) \(-16\) \(+\) \(q-2q^{2}-3q^{3}+4q^{4}+6q^{5}+6q^{6}+\cdots\)
7.4.a.a \(1\) \(0.413\) \(\Q\) None \(-1\) \(-2\) \(16\) \(-7\) \(+\) \(q-q^{2}-2q^{3}-7q^{4}+2^{4}q^{5}+2q^{6}+\cdots\)
7.4.c.a \(2\) \(0.413\) \(\Q(\sqrt{-3}) \) None \(-2\) \(-7\) \(-7\) \(28\) \(q+(-2+2\zeta_{6})q^{2}-7\zeta_{6}q^{3}+4\zeta_{6}q^{4}+\cdots\)
8.4.a.a \(1\) \(0.472\) \(\Q\) None \(0\) \(-4\) \(-2\) \(24\) \(+\) \(q-4q^{3}-2q^{5}+24q^{7}-11q^{9}-44q^{11}+\cdots\)
8.4.b.a \(2\) \(0.472\) \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(-16\) \(q+(-1-\beta )q^{2}+2\beta q^{3}+(-6+2\beta )q^{4}+\cdots\)
9.4.a.a \(1\) \(0.531\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(20\) \(+\) \(q-8q^{4}+20q^{7}-70q^{13}+2^{6}q^{16}+\cdots\)
9.4.c.a \(4\) \(0.531\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-3\) \(-3\) \(-15\) \(-7\) \(q+(-\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
10.4.a.a \(1\) \(0.590\) \(\Q\) None \(2\) \(-8\) \(5\) \(-4\) \(+\) \(q+2q^{2}-8q^{3}+4q^{4}+5q^{5}-2^{4}q^{6}+\cdots\)
10.4.b.a \(2\) \(0.590\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-10\) \(0\) \(q+iq^{2}-iq^{3}-4q^{4}+(-5-5i)q^{5}+\cdots\)
11.4.a.a \(2\) \(0.649\) \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(2\) \(20\) \(+\) \(q+(1+\beta )q^{2}+(-1-4\beta )q^{3}+(-4+2\beta )q^{4}+\cdots\)
11.4.c.a \(8\) \(0.649\) 8.0.\(\cdots\).1 None \(-7\) \(-3\) \(-7\) \(-35\) \(q+(-1+\beta _{1}+\beta _{2}-\beta _{4})q^{2}+(-2-2\beta _{2}+\cdots)q^{3}+\cdots\)
12.4.a.a \(1\) \(0.708\) \(\Q\) None \(0\) \(3\) \(-18\) \(8\) \(+\) \(q+3q^{3}-18q^{5}+8q^{7}+9q^{9}+6^{2}q^{11}+\cdots\)
12.4.b.a \(4\) \(0.708\) \(\Q(\sqrt{3}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)
13.4.a.a \(1\) \(0.767\) \(\Q\) None \(-5\) \(-7\) \(-7\) \(-13\) \(-\) \(q-5q^{2}-7q^{3}+17q^{4}-7q^{5}+35q^{6}+\cdots\)
13.4.a.b \(2\) \(0.767\) \(\Q(\sqrt{17}) \) None \(1\) \(5\) \(-3\) \(-9\) \(+\) \(q+\beta q^{2}+(4-3\beta )q^{3}+(-4+\beta )q^{4}+\cdots\)
13.4.b.a \(2\) \(0.767\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+iq^{2}-q^{3}-q^{4}-3iq^{5}-iq^{6}+\cdots\)
13.4.c.a \(2\) \(0.767\) \(\Q(\sqrt{-3}) \) None \(-4\) \(-2\) \(34\) \(-20\) \(q+(-4+4\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}+\cdots\)
13.4.c.b \(4\) \(0.767\) \(\Q(\sqrt{-3}, \sqrt{17})\) None \(5\) \(-5\) \(-30\) \(-15\) \(q+(2-\beta _{1}-2\beta _{2}-\beta _{3})q^{2}+(-1+3\beta _{1}+\cdots)q^{3}+\cdots\)
13.4.e.a \(2\) \(0.767\) \(\Q(\sqrt{-3}) \) None \(-6\) \(7\) \(0\) \(39\) \(q+(-2-2\zeta_{6})q^{2}+(7-7\zeta_{6})q^{3}+4\zeta_{6}q^{4}+\cdots\)
13.4.e.b \(2\) \(0.767\) \(\Q(\sqrt{-3}) \) None \(3\) \(-2\) \(0\) \(-24\) \(q+(1+\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}-5\zeta_{6}q^{4}+\cdots\)
14.4.a.a \(1\) \(0.826\) \(\Q\) None \(-2\) \(8\) \(-14\) \(-7\) \(+\) \(q-2q^{2}+8q^{3}+4q^{4}-14q^{5}-2^{4}q^{6}+\cdots\)
14.4.a.b \(1\) \(0.826\) \(\Q\) None \(2\) \(-2\) \(-12\) \(7\) \(+\) \(q+2q^{2}-2q^{3}+4q^{4}-12q^{5}-4q^{6}+\cdots\)
14.4.c.a \(2\) \(0.826\) \(\Q(\sqrt{-3}) \) None \(-2\) \(5\) \(9\) \(-28\) \(q+(-2+2\zeta_{6})q^{2}+5\zeta_{6}q^{3}-4\zeta_{6}q^{4}+\cdots\)
14.4.c.b \(2\) \(0.826\) \(\Q(\sqrt{-3}) \) None \(2\) \(1\) \(-7\) \(-20\) \(q+(2-2\zeta_{6})q^{2}+\zeta_{6}q^{3}-4\zeta_{6}q^{4}+(-7+\cdots)q^{5}+\cdots\)
15.4.a.a \(1\) \(0.885\) \(\Q\) None \(1\) \(3\) \(5\) \(-24\) \(+\) \(q+q^{2}+3q^{3}-7q^{4}+5q^{5}+3q^{6}+\cdots\)
15.4.a.b \(1\) \(0.885\) \(\Q\) None \(3\) \(-3\) \(-5\) \(20\) \(+\) \(q+3q^{2}-3q^{3}+q^{4}-5q^{5}-9q^{6}+\cdots\)
15.4.b.a \(4\) \(0.885\) \(\Q(i, \sqrt{41})\) None \(0\) \(0\) \(6\) \(0\) \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(-5+\beta _{3})q^{4}+(2+\cdots)q^{5}+\cdots\)
15.4.e.a \(8\) \(0.885\) 8.0.\(\cdots\).8 None \(0\) \(-6\) \(0\) \(-16\) \(q-\beta _{3}q^{2}+(-1-\beta _{2}+\beta _{5})q^{3}+(\beta _{2}+\cdots)q^{4}+\cdots\)
16.4.a.a \(1\) \(0.944\) \(\Q\) None \(0\) \(4\) \(-2\) \(-24\) \(+\) \(q+4q^{3}-2q^{5}-24q^{7}-11q^{9}+44q^{11}+\cdots\)
16.4.e.a \(10\) \(0.944\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(-2\) \(-2\) \(0\) \(q-\beta _{4}q^{2}-\beta _{5}q^{3}+(1-\beta _{2}+\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots\)
17.4.a.a \(1\) \(1.003\) \(\Q\) None \(-3\) \(-8\) \(6\) \(-28\) \(-\) \(q-3q^{2}-8q^{3}+q^{4}+6q^{5}+24q^{6}+\cdots\)
17.4.a.b \(3\) \(1.003\) 3.3.2636.1 None \(1\) \(4\) \(-8\) \(22\) \(+\) \(q+(\beta _{1}-\beta _{2})q^{2}+(2-\beta _{1}+2\beta _{2})q^{3}+\cdots\)
17.4.b.a \(4\) \(1.003\) 4.0.4669632.2 None \(-2\) \(0\) \(0\) \(0\) \(q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}+(1-\beta _{2})q^{4}+\cdots\)
17.4.c.a \(8\) \(1.003\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(14\) \(2\) \(q+(\beta _{1}-\beta _{3})q^{2}+\beta _{4}q^{3}+(-5-\beta _{2}+\cdots)q^{4}+\cdots\)
17.4.d.a \(12\) \(1.003\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-4\) \(-4\) \(-20\) \(-4\) \(q+(-\beta _{3}-\beta _{10})q^{2}+\beta _{8}q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots\)
18.4.a.a \(1\) \(1.062\) \(\Q\) None \(2\) \(0\) \(-6\) \(-16\) \(+\) \(q+2q^{2}+4q^{4}-6q^{5}-2^{4}q^{7}+8q^{8}+\cdots\)
18.4.c.a \(2\) \(1.062\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(9\) \(31\) \(q-2\zeta_{6}q^{2}+(3-6\zeta_{6})q^{3}+(-4+4\zeta_{6})q^{4}+\cdots\)
18.4.c.b \(4\) \(1.062\) \(\Q(\sqrt{-3}, \sqrt{-35})\) None \(4\) \(3\) \(9\) \(-19\) \(q-2\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-4-4\beta _{1}+\cdots)q^{4}+\cdots\)
19.4.a.a \(1\) \(1.121\) \(\Q\) None \(-3\) \(-5\) \(-12\) \(11\) \(-\) \(q-3q^{2}-5q^{3}+q^{4}-12q^{5}+15q^{6}+\cdots\)
19.4.a.b \(3\) \(1.121\) 3.3.3144.1 None \(3\) \(1\) \(14\) \(-35\) \(+\) \(q+(1+\beta _{1}-\beta _{2})q^{2}+(-\beta _{1}+2\beta _{2})q^{3}+\cdots\)
19.4.c.a \(4\) \(1.121\) \(\Q(\sqrt{-3}, \sqrt{55})\) None \(-2\) \(0\) \(14\) \(-28\) \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(7+7\beta _{2})q^{4}+\cdots\)
19.4.c.b \(4\) \(1.121\) \(\Q(\sqrt{-3}, \sqrt{73})\) None \(-1\) \(-2\) \(-19\) \(40\) \(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(-11+\beta _{1}+10\beta _{2}+\cdots)q^{4}+\cdots\)
19.4.e.a \(24\) \(1.121\) None \(-6\) \(-3\) \(-6\) \(3\)
20.4.a.a \(1\) \(1.180\) \(\Q\) None \(0\) \(4\) \(5\) \(-16\) \(+\) \(q+4q^{3}+5q^{5}-2^{4}q^{7}-11q^{9}-60q^{11}+\cdots\)
20.4.c.a \(2\) \(1.180\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(14\) \(0\) \(q-\beta q^{3}+(7+\beta )q^{5}+\beta q^{7}-7^{2}q^{9}+\cdots\)
20.4.e.a \(2\) \(1.180\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(4\) \(0\) \(-4\) \(0\) \(q+(2+2i)q^{2}+8iq^{4}+(-2-11i)q^{5}+\cdots\)
20.4.e.b \(12\) \(1.180\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-6\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{5})q^{2}-\beta _{9}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
21.4.a.a \(1\) \(1.239\) \(\Q\) None \(-3\) \(-3\) \(-18\) \(7\) \(-\) \(q-3q^{2}-3q^{3}+q^{4}-18q^{5}+9q^{6}+\cdots\)
21.4.a.b \(1\) \(1.239\) \(\Q\) None \(4\) \(-3\) \(-4\) \(-7\) \(+\) \(q+4q^{2}-3q^{3}+8q^{4}-4q^{5}-12q^{6}+\cdots\)
Next

Download all search results for