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Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
7.3.b.a \(1\) \(0.191\) \(\Q\) \(\Q(\sqrt{-7}) \) \(-3\) \(0\) \(0\) \(-7\) \(q-3q^{2}+5q^{4}-7q^{7}-3q^{8}+9q^{9}+\cdots\)
8.3.d.a \(1\) \(0.218\) \(\Q\) \(\Q(\sqrt{-2}) \) \(-2\) \(-2\) \(0\) \(0\) \(q-2q^{2}-2q^{3}+4q^{4}+4q^{6}-8q^{8}+\cdots\)
9.3.d.a \(2\) \(0.245\) \(\Q(\sqrt{-3}) \) None \(-3\) \(-3\) \(6\) \(-2\) \(q+(-1-\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
10.3.c.a \(2\) \(0.272\) \(\Q(\sqrt{-1}) \) None \(-2\) \(-4\) \(0\) \(4\) \(q+(-1-i)q^{2}+(-2+2i)q^{3}+2iq^{4}+\cdots\)
11.3.b.a \(1\) \(0.300\) \(\Q\) \(\Q(\sqrt{-11}) \) \(0\) \(-5\) \(-1\) \(0\) \(q-5q^{3}+4q^{4}-q^{5}+2^{4}q^{9}-11q^{11}+\cdots\)
11.3.d.a \(4\) \(0.300\) \(\Q(\zeta_{10})\) None \(-5\) \(0\) \(-4\) \(10\) \(q+(-2\zeta_{10}+2\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-2+\cdots)q^{3}+\cdots\)
12.3.c.a \(1\) \(0.327\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(-3\) \(0\) \(2\) \(q-3q^{3}+2q^{7}+9q^{9}-22q^{13}+26q^{19}+\cdots\)
12.3.d.a \(2\) \(0.327\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-4\) \(0\) \(q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
13.3.d.a \(4\) \(0.354\) \(\Q(i, \sqrt{10})\) None \(-4\) \(-4\) \(8\) \(-12\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}+(-1-\beta _{1}+\beta _{3})q^{3}+\cdots\)
13.3.f.a \(4\) \(0.354\) \(\Q(\zeta_{12})\) None \(-2\) \(-2\) \(-14\) \(16\) \(q+(-1+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
14.3.d.a \(4\) \(0.381\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-6\) \(-6\) \(8\) \(q+\beta _{1}q^{2}+(-2-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+\cdots\)
15.3.c.a \(2\) \(0.409\) \(\Q(\sqrt{-5}) \) None \(0\) \(-4\) \(0\) \(-12\) \(q+\beta q^{2}+(-2-\beta )q^{3}-q^{4}-\beta q^{5}+\cdots\)
15.3.d.a \(1\) \(0.409\) \(\Q\) \(\Q(\sqrt{-15}) \) \(-1\) \(3\) \(-5\) \(0\) \(q-q^{2}+3q^{3}-3q^{4}-5q^{5}-3q^{6}+\cdots\)
15.3.d.b \(1\) \(0.409\) \(\Q\) \(\Q(\sqrt{-15}) \) \(1\) \(-3\) \(5\) \(0\) \(q+q^{2}-3q^{3}-3q^{4}+5q^{5}-3q^{6}+\cdots\)
15.3.f.a \(4\) \(0.409\) \(\Q(i, \sqrt{6})\) None \(-4\) \(0\) \(-4\) \(4\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}+\beta _{3}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
16.3.c.a \(1\) \(0.436\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-6\) \(0\) \(q-6q^{5}+9q^{9}+10q^{13}-30q^{17}+\cdots\)
16.3.f.a \(6\) \(0.436\) 6.0.399424.1 None \(-2\) \(-2\) \(-2\) \(-4\) \(q+\beta _{2}q^{2}+(-1-\beta _{2}+\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots\)
17.3.e.a \(8\) \(0.463\) \(\Q(\zeta_{16})\) None \(-8\) \(-8\) \(16\) \(8\) \(q+(-1+\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots\)
17.3.e.b \(8\) \(0.463\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(-24\) \(-16\) \(q+(-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(2\zeta_{16}^{2}+\cdots)q^{3}+\cdots\)
18.3.b.a \(2\) \(0.490\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-8\) \(q+\beta q^{2}-2q^{4}-3\beta q^{5}-4q^{7}-2\beta q^{8}+\cdots\)
18.3.d.a \(4\) \(0.490\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(-18\) \(2\) \(q+\beta _{1}q^{2}+(1-2\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\cdots\)
19.3.b.a \(1\) \(0.518\) \(\Q\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(-9\) \(-5\) \(q+4q^{4}-9q^{5}-5q^{7}+9q^{9}+3q^{11}+\cdots\)
19.3.b.b \(2\) \(0.518\) \(\Q(\sqrt{-13}) \) None \(0\) \(0\) \(8\) \(-10\) \(q+\beta q^{2}-\beta q^{3}-9q^{4}+4q^{5}+13q^{6}+\cdots\)
19.3.d.a \(6\) \(0.518\) 6.0.6967728.1 None \(-3\) \(-9\) \(-2\) \(0\) \(q+(-1-\beta _{5})q^{2}+(\beta _{1}+2\beta _{2}+\beta _{3}+\beta _{5})q^{3}+\cdots\)
19.3.f.a \(12\) \(0.518\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-6\) \(0\) \(-6\) \(6\) \(q+\beta _{10}q^{2}+(\beta _{1}-\beta _{4}-\beta _{5}+\beta _{6}-\beta _{7}+\cdots)q^{3}+\cdots\)
20.3.b.a \(4\) \(0.545\) \(\Q(\zeta_{10})\) None \(-2\) \(0\) \(0\) \(0\) \(q-\zeta_{10}^{2}q^{2}+\zeta_{10}^{3}q^{3}+(-2-\zeta_{10}+\cdots)q^{4}+\cdots\)
20.3.d.a \(1\) \(0.545\) \(\Q\) \(\Q(\sqrt{-5}) \) \(-2\) \(4\) \(-5\) \(-4\) \(q-2q^{2}+4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots\)
20.3.d.b \(1\) \(0.545\) \(\Q\) \(\Q(\sqrt{-5}) \) \(2\) \(-4\) \(-5\) \(4\) \(q+2q^{2}-4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots\)
20.3.d.c \(2\) \(0.545\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(6\) \(0\) \(q+iq^{2}-4q^{4}+(3-2i)q^{5}-4iq^{8}+\cdots\)
20.3.f.a \(2\) \(0.545\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-6\) \(-14\) \(q+(1-i)q^{3}+(-3+4i)q^{5}+(-7-7i)q^{7}+\cdots\)
21.3.b.a \(4\) \(0.572\) 4.0.65856.1 None \(0\) \(-2\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(-3+\cdots)q^{4}+\cdots\)
21.3.d.a \(2\) \(0.572\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(0\) \(2\) \(q+q^{2}+\zeta_{6}q^{3}-3q^{4}-4\zeta_{6}q^{5}+\zeta_{6}q^{6}+\cdots\)
21.3.f.a \(2\) \(0.572\) \(\Q(\sqrt{-3}) \) None \(-3\) \(-3\) \(9\) \(13\) \(q-3\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(-5+5\zeta_{6})q^{4}+\cdots\)
21.3.f.b \(2\) \(0.572\) \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(-9\) \(-7\) \(q-\zeta_{6}q^{2}+(1+\zeta_{6})q^{3}+(3-3\zeta_{6})q^{4}+\cdots\)
21.3.f.c \(2\) \(0.572\) \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(-6\) \(-7\) \(q+2\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+\cdots\)
21.3.h.a \(2\) \(0.572\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(3\) \(0\) \(-13\) \(q+3\zeta_{6}q^{3}-4\zeta_{6}q^{4}+(-5-3\zeta_{6})q^{7}+\cdots\)
21.3.h.b \(4\) \(0.572\) \(\Q(\sqrt{-3}, \sqrt{-5})\) None \(0\) \(-4\) \(0\) \(14\) \(q+\beta _{1}q^{2}+(-\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots\)
22.3.b.a \(2\) \(0.599\) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(-2\) \(0\) \(q+\beta q^{2}+q^{3}-2q^{4}-q^{5}+\beta q^{6}-6\beta q^{7}+\cdots\)
22.3.d.a \(8\) \(0.599\) 8.0.64000000.1 None \(0\) \(-2\) \(2\) \(-30\) \(q+\beta _{1}q^{2}+(1-\beta _{1}-2\beta _{2}+\beta _{3}+2\beta _{4}+\cdots)q^{3}+\cdots\)
23.3.b.a \(3\) \(0.627\) 3.3.621.1 \(\Q(\sqrt{-23}) \) \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{2})q^{2}+(-2\beta _{1}-\beta _{2})q^{3}+(4+\cdots)q^{4}+\cdots\)
23.3.d.a \(30\) \(0.627\) None \(-11\) \(-11\) \(-11\) \(-11\)
24.3.b.a \(4\) \(0.654\) 4.0.4752.1 None \(2\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{2})q^{2}+\beta _{2}q^{3}+(-2-\beta _{2}+\cdots)q^{4}+\cdots\)
24.3.e.a \(2\) \(0.654\) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(-12\) \(q+(1+\beta )q^{3}-2\beta q^{5}-6q^{7}+(-7+2\beta )q^{9}+\cdots\)
24.3.h.a \(1\) \(0.654\) \(\Q\) \(\Q(\sqrt{-6}) \) \(-2\) \(3\) \(2\) \(-10\) \(q-2q^{2}+3q^{3}+4q^{4}+2q^{5}-6q^{6}+\cdots\)
24.3.h.b \(1\) \(0.654\) \(\Q\) \(\Q(\sqrt{-6}) \) \(2\) \(-3\) \(-2\) \(-10\) \(q+2q^{2}-3q^{3}+4q^{4}-2q^{5}-6q^{6}+\cdots\)
24.3.h.c \(4\) \(0.654\) \(\Q(\sqrt{2}, \sqrt{-7})\) None \(0\) \(0\) \(0\) \(16\) \(q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(-3+\beta _{3})q^{4}+\cdots\)
25.3.c.a \(4\) \(0.681\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{3}q^{3}-\beta _{2}q^{4}-3q^{6}-4\beta _{1}q^{7}+\cdots\)
25.3.f.a \(32\) \(0.681\) None \(-10\) \(-10\) \(-10\) \(-10\)
26.3.d.a \(2\) \(0.708\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(-6\) \(4\) \(q+(1+i)q^{2}+2iq^{4}+(-3-3i)q^{5}+\cdots\)
26.3.f.a \(4\) \(0.708\) \(\Q(\zeta_{12})\) None \(2\) \(0\) \(0\) \(-22\) \(q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\)
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