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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
23.1.b.a \(1\) \(0.011\) \(\Q\) \(\Q(\sqrt{-23}) \) None \(-1\) \(-1\) \(0\) \(0\) \(q-q^{2}-q^{3}+q^{6}+q^{8}-q^{13}-q^{16}+\cdots\)
31.1.b.a \(1\) \(0.015\) \(\Q\) \(\Q(\sqrt{-31}) \) None \(-1\) \(0\) \(-1\) \(-1\) \(q-q^{2}-q^{5}-q^{7}+q^{8}+q^{9}+q^{10}+\cdots\)
39.1.d.a \(1\) \(0.019\) \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-39}) \) \(\Q(\sqrt{13}) \) \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}-q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\cdots\)
44.1.d.a \(1\) \(0.022\) \(\Q\) \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(-1\) \(0\) \(q-q^{3}-q^{5}+q^{11}+q^{15}-q^{23}+q^{27}+\cdots\)
47.1.b.a \(2\) \(0.023\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-47}) \) None \(-1\) \(-1\) \(0\) \(-1\) \(q+(-1+\beta )q^{2}-\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots\)
52.1.j.a \(2\) \(0.026\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) None \(-1\) \(0\) \(-2\) \(0\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots\)
55.1.d.a \(1\) \(0.027\) \(\Q\) \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-55}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(-1\) \(0\) \(q-q^{4}-q^{5}+q^{9}-q^{11}+q^{16}+q^{20}+\cdots\)
56.1.h.a \(1\) \(0.028\) \(\Q\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \) \(\Q(\sqrt{2}) \) \(-1\) \(0\) \(0\) \(-1\) \(q-q^{2}+q^{4}-q^{7}-q^{8}-q^{9}+q^{14}+\cdots\)
57.1.h.a \(2\) \(0.028\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-2\) \(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-q^{7}-\zeta_{6}q^{9}+q^{12}+\cdots\)
59.1.b.a \(1\) \(0.029\) \(\Q\) \(\Q(\sqrt{-59}) \) None \(0\) \(-1\) \(-1\) \(-1\) \(q-q^{3}+q^{4}-q^{5}-q^{7}-q^{12}+q^{15}+\cdots\)
63.1.d.a \(1\) \(0.031\) \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{21}) \) \(0\) \(0\) \(0\) \(-1\) \(q-q^{4}-q^{7}+q^{16}+q^{25}+q^{28}-2q^{37}+\cdots\)
68.1.d.a \(1\) \(0.034\) \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-17}) \) \(\Q(\sqrt{17}) \) \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}-q^{9}-2q^{13}+q^{16}+\cdots\)
68.1.f.a \(2\) \(0.034\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{2}-q^{4}+(-1-i)q^{5}-iq^{8}+\cdots\)
71.1.b.a \(3\) \(0.035\) \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-71}) \) None \(-1\) \(-1\) \(-1\) \(0\) \(q-\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
72.1.p.a \(2\) \(0.036\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(-1\) \(-1\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots\)
76.1.c.a \(1\) \(0.038\) \(\Q\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-1\) \(-1\) \(q-q^{5}-q^{7}+q^{9}-q^{11}-q^{17}+q^{19}+\cdots\)
77.1.j.a \(4\) \(0.038\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(-1\) \(q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots\)
79.1.b.a \(2\) \(0.039\) \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-79}) \) None \(-1\) \(0\) \(-1\) \(0\) \(q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{5}-q^{8}+\cdots\)
80.1.h.a \(1\) \(0.040\) \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(-1\) \(0\) \(q-q^{5}-q^{9}+q^{25}+2q^{29}-2q^{41}+\cdots\)
83.1.b.a \(1\) \(0.041\) \(\Q\) \(\Q(\sqrt{-83}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q-q^{3}+q^{4}-q^{7}-q^{11}-q^{12}+q^{16}+\cdots\)
84.1.p.a \(2\) \(0.042\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}-q^{13}+\cdots\)
87.1.d.a \(1\) \(0.043\) \(\Q\) \(\Q(\sqrt{-87}) \) None \(-1\) \(1\) \(0\) \(-1\) \(q-q^{2}+q^{3}-q^{6}-q^{7}+q^{8}+q^{9}+\cdots\)
87.1.d.b \(1\) \(0.043\) \(\Q\) \(\Q(\sqrt{-87}) \) None \(1\) \(-1\) \(0\) \(-1\) \(q+q^{2}-q^{3}-q^{6}-q^{7}-q^{8}+q^{9}+\cdots\)
88.1.l.a \(4\) \(0.044\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-2}) \) None \(-1\) \(-2\) \(0\) \(0\) \(q-\zeta_{10}q^{2}+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{3}+\zeta_{10}^{2}q^{4}+\cdots\)
93.1.l.a \(4\) \(0.046\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-2\) \(q-\zeta_{10}q^{3}-\zeta_{10}^{3}q^{4}+(\zeta_{10}^{2}+\zeta_{10}^{4}+\cdots)q^{7}+\cdots\)
95.1.d.a \(1\) \(0.047\) \(\Q\) \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-95}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(1\) \(0\) \(q-q^{4}+q^{5}-q^{9}-2q^{11}+q^{16}+q^{19}+\cdots\)
95.1.d.b \(2\) \(0.047\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-\beta q^{2}+\beta q^{3}+q^{4}-q^{5}-2q^{6}+q^{9}+\cdots\)
99.1.h.a \(2\) \(0.049\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(1\) \(0\) \(q+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{9}+\cdots\)
100.1.j.a \(4\) \(0.050\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-1}) \) None \(-1\) \(0\) \(-1\) \(0\) \(q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+\zeta_{10}^{4}q^{5}+\zeta_{10}^{4}q^{8}+\cdots\)
11.2.a.a \(1\) \(0.088\) \(\Q\) None None \(-2\) \(-1\) \(1\) \(-2\) \(-\) \(q-2q^{2}-q^{3}+2q^{4}+q^{5}+2q^{6}-2q^{7}+\cdots\)
13.2.e.a \(2\) \(0.104\) \(\Q(\sqrt{-3}) \) None None \(-3\) \(-2\) \(0\) \(0\) \(q+(-1-\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
14.2.a.a \(1\) \(0.112\) \(\Q\) None None \(-1\) \(-2\) \(0\) \(1\) \(-\) \(q-q^{2}-2q^{3}+q^{4}+2q^{6}+q^{7}-q^{8}+\cdots\)
15.2.a.a \(1\) \(0.120\) \(\Q\) None None \(-1\) \(-1\) \(1\) \(0\) \(-\) \(q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+3q^{8}+\cdots\)
16.2.e.a \(2\) \(0.128\) \(\Q(\sqrt{-1}) \) None None \(-2\) \(-2\) \(-2\) \(0\) \(q+(-1-i)q^{2}+(-1+i)q^{3}+2iq^{4}+\cdots\)
17.2.a.a \(1\) \(0.136\) \(\Q\) None None \(-1\) \(0\) \(-2\) \(4\) \(-\) \(q-q^{2}-q^{4}-2q^{5}+4q^{7}+3q^{8}-3q^{9}+\cdots\)
17.2.d.a \(4\) \(0.136\) \(\Q(\zeta_{8})\) None None \(-4\) \(-4\) \(0\) \(-4\) \(q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\cdots)q^{3}+\cdots\)
18.2.c.a \(2\) \(0.144\) \(\Q(\sqrt{-3}) \) None None \(-1\) \(-3\) \(0\) \(-2\) \(q-\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
19.2.a.a \(1\) \(0.152\) \(\Q\) None None \(0\) \(-2\) \(3\) \(-1\) \(-\) \(q-2q^{3}-2q^{4}+3q^{5}-q^{7}+q^{9}+3q^{11}+\cdots\)
19.2.e.a \(6\) \(0.152\) \(\Q(\zeta_{18})\) None None \(-6\) \(-3\) \(-6\) \(0\) \(q+(-1+\zeta_{18}-\zeta_{18}^{2})q^{2}+(-1+\zeta_{18}^{2}+\cdots)q^{3}+\cdots\)
20.2.a.a \(1\) \(0.160\) \(\Q\) None None \(0\) \(-2\) \(-1\) \(2\) \(-\) \(q-2q^{3}-q^{5}+2q^{7}+q^{9}+2q^{13}+\cdots\)
20.2.e.a \(2\) \(0.160\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(-4\) \(0\) \(q+(-1-i)q^{2}+2iq^{4}+(-2+i)q^{5}+\cdots\)
21.2.a.a \(1\) \(0.168\) \(\Q\) None None \(-1\) \(1\) \(-2\) \(-1\) \(-\) \(q-q^{2}+q^{3}-q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
21.2.e.a \(2\) \(0.168\) \(\Q(\sqrt{-3}) \) None None \(-2\) \(-1\) \(2\) \(-5\) \(q+(-2+2\zeta_{6})q^{2}-\zeta_{6}q^{3}-2\zeta_{6}q^{4}+\cdots\)
21.2.g.a \(2\) \(0.168\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(0\) \(1\) \(q+(-1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(2+\cdots)q^{7}+\cdots\)
22.2.c.a \(4\) \(0.176\) \(\Q(\zeta_{10})\) None None \(-1\) \(-4\) \(-6\) \(2\) \(q-\zeta_{10}q^{2}+(-1+\zeta_{10}-\zeta_{10}^{3})q^{3}+\cdots\)
23.2.a.a \(2\) \(0.184\) \(\Q(\sqrt{5}) \) None None \(-1\) \(0\) \(-2\) \(2\) \(-\) \(q-\beta q^{2}+(-1+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
23.2.c.a \(10\) \(0.184\) \(\Q(\zeta_{22})\) None None \(-7\) \(-7\) \(-3\) \(-5\) \(q+(-\zeta_{22}+\zeta_{22}^{4}-\zeta_{22}^{5}+\zeta_{22}^{6}+\cdots)q^{2}+\cdots\)
24.2.a.a \(1\) \(0.192\) \(\Q\) None None \(0\) \(-1\) \(-2\) \(0\) \(-\) \(q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
24.2.d.a \(2\) \(0.192\) \(\Q(\sqrt{-1}) \) None None \(-2\) \(0\) \(0\) \(-4\) \(q+(-1+i)q^{2}+iq^{3}-2iq^{4}-2iq^{5}+\cdots\)
24.2.f.a \(2\) \(0.192\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+\beta q^{2}+(-1-\beta )q^{3}-2q^{4}+(2-\beta )q^{6}+\cdots\)
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