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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 \(-4\) \(2\) \(-5\) \(6\) $+$ \(q-4q^{2}+2q^{3}+8q^{4}-5q^{5}-8q^{6}+\cdots\)
5.5.c.a $2$ $0.517$ \(\Q(\sqrt{-1}) \) None \(-2\) \(-12\) \(40\) \(-52\) $-$ \(q+(-1-i)q^{2}+(-6+6i)q^{3}-14iq^{4}+\cdots\)
5.6.a.a $1$ $0.802$ \(\Q\) None \(2\) \(-4\) \(25\) \(192\) $-$ \(q+2q^{2}-4q^{3}-28q^{4}+5^{2}q^{5}-8q^{6}+\cdots\)
5.6.b.a $2$ $0.802$ \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(-90\) \(0\) $-$ \(q-\beta q^{2}+3\beta q^{3}-12q^{4}+(-45-5\beta )q^{5}+\cdots\)
5.7.c.a $4$ $1.150$ \(\Q(i, \sqrt{201})\) None \(-10\) \(30\) \(-70\) \(550\) $-$ \(q+(-2+2\beta _{1}+\beta _{3})q^{2}+(7+8\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
5.8.a.a $1$ $1.562$ \(\Q\) None \(-14\) \(-48\) \(125\) \(-1644\) $-$ \(q-14q^{2}-48q^{3}+68q^{4}+5^{3}q^{5}+\cdots\)
5.8.a.b $2$ $1.562$ \(\Q(\sqrt{19}) \) None \(20\) \(20\) \(-250\) \(-100\) $+$ \(q+(10+\beta )q^{2}+(10-8\beta )q^{3}+(48+20\beta )q^{4}+\cdots\)
5.8.b.a $2$ $1.562$ \(\Q(\sqrt{-29}) \) None \(0\) \(0\) \(150\) \(0\) $-$ \(q+\beta q^{2}+3\beta q^{3}+12q^{4}+(75-5^{2}\beta )q^{5}+\cdots\)
5.9.c.a $6$ $2.037$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-2\) \(-72\) \(220\) \(-2352\) $-$ \(q-\beta _{3}q^{2}+(-12-12\beta _{1}-\beta _{2}-\beta _{5})q^{3}+\cdots\)
5.10.a.a $1$ $2.575$ \(\Q\) None \(-8\) \(-114\) \(-625\) \(4242\) $+$ \(q-8q^{2}-114q^{3}-448q^{4}-5^{4}q^{5}+\cdots\)
5.10.a.b $2$ $2.575$ \(\Q(\sqrt{1009}) \) None \(-10\) \(260\) \(1250\) \(1700\) $-$ \(q+(-5-\beta )q^{2}+(130+2\beta )q^{3}+(522+\cdots)q^{4}+\cdots\)
5.10.b.a $4$ $2.575$ 4.0.49740556.1 None \(0\) \(0\) \(1140\) \(0\) $-$ \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-342+\cdots)q^{4}+\cdots\)
5.11.c.a $8$ $3.177$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(30\) \(60\) \(-5340\) \(-14500\) $-$ \(q+(4+4\beta _{1}-\beta _{3})q^{2}+(8-8\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
5.12.a.a $1$ $3.842$ \(\Q\) None \(34\) \(-792\) \(3125\) \(-17556\) $-$ \(q+34q^{2}-792q^{3}-892q^{4}+5^{5}q^{5}+\cdots\)
5.12.a.b $2$ $3.842$ \(\Q(\sqrt{151}) \) None \(-20\) \(-220\) \(-6250\) \(57900\) $+$ \(q+(-10+3\beta )q^{2}+(-110+2^{4}\beta )q^{3}+\cdots\)
5.12.b.a $4$ $3.842$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(0\) \(-300\) \(0\) $-$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-18-\beta _{2})q^{4}+\cdots\)
5.13.c.a $10$ $4.570$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(-2\) \(318\) \(-4250\) \(279598\) $-$ \(q+\beta _{5}q^{2}+(31-31\beta _{1}-\beta _{3}+3\beta _{6}+\cdots)q^{3}+\cdots\)
5.14.a.a $2$ $5.362$ \(\Q(\sqrt{499}) \) None \(-80\) \(780\) \(-31250\) \(-616300\) $+$ \(q+(-40+\beta )q^{2}+(390-12\beta )q^{3}+(1392+\cdots)q^{4}+\cdots\)
5.14.a.b $3$ $5.362$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(142\) \(416\) \(46875\) \(448292\) $-$ \(q+(47-\beta _{1})q^{2}+(138-3\beta _{1}-\beta _{2})q^{3}+\cdots\)
5.14.b.a $6$ $5.362$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(24570\) \(0\) $-$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-5492-\beta _{3}+\cdots)q^{4}+\cdots\)
5.15.c.a $12$ $6.216$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-130\) \(-2160\) \(17240\) \(-1646400\) $-$ \(q+(-11+11\beta _{2}-\beta _{3})q^{2}+(-180+\cdots)q^{3}+\cdots\)
5.16.a.a $2$ $7.135$ \(\Q(\sqrt{3169}) \) None \(-310\) \(1740\) \(156250\) \(-3420900\) $-$ \(q+(-155-\beta )q^{2}+(870-2\beta )q^{3}+(19778+\cdots)q^{4}+\cdots\)
5.16.a.b $3$ $7.135$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(4\) \(3518\) \(-234375\) \(-905206\) $+$ \(q+(1-\beta _{1})q^{2}+(1170-2^{4}\beta _{1}+8\beta _{2})q^{3}+\cdots\)
5.16.b.a $6$ $7.135$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(-238350\) \(0\) $-$ \(q+\beta _{1}q^{2}+(2\beta _{1}-\beta _{2})q^{3}+(-6428+\cdots)q^{4}+\cdots\)
5.17.c.a $14$ $8.116$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(-2\) \(7908\) \(192880\) \(-386452\) $-$ \(q-\beta _{2}q^{2}+(565-3\beta _{1}-565\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)
5.18.a.a $2$ $9.161$ \(\Q(\sqrt{39}) \) None \(680\) \(-10980\) \(-781250\) \(-22820700\) $+$ \(q+(340+\beta )q^{2}+(-5490-52\beta )q^{3}+\cdots\)
5.18.a.b $3$ $9.161$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(118\) \(15944\) \(1171875\) \(2139308\) $-$ \(q+(39-\beta _{1})q^{2}+(5317+8\beta _{1}+\beta _{2})q^{3}+\cdots\)
5.18.b.a $8$ $9.161$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(379200\) \(0\) $-$ \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-72387+\beta _{3}+\cdots)q^{4}+\cdots\)
5.19.c.a $16$ $10.269$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(510\) \(-20130\) \(3145170\) \(78767350\) $-$ \(q+(2^{5}+\beta _{2}+2^{5}\beta _{4})q^{2}+(-1259-5\beta _{1}+\cdots)q^{3}+\cdots\)
5.20.a.a $3$ $11.441$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-1006\) \(-73452\) \(5859375\) \(-54910456\) $-$ \(q+(-335+\beta _{1})q^{2}+(-24478+18\beta _{1}+\cdots)q^{3}+\cdots\)
5.20.a.b $4$ $11.441$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-420\) \(3080\) \(-7812500\) \(214021400\) $+$ \(q+(-105-\beta _{1})q^{2}+(770+14\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
5.20.b.a $8$ $11.441$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(147000\) \(0\) $-$ \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-202593+\cdots)q^{4}+\cdots\)
5.21.c.a $18$ $12.676$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(-2\) \(29448\) \(-7302140\) \(-585532752\) $-$ \(q-\beta _{1}q^{2}+(1636-\beta _{2}-1636\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)
5.22.a.a $3$ $13.974$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-1312\) \(52194\) \(-29296875\) \(684416558\) $+$ \(q+(-437+\beta _{1})q^{2}+(17400+8\beta _{1}+\cdots)q^{3}+\cdots\)
5.22.a.b $4$ $13.974$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(2910\) \(83240\) \(39062500\) \(512613800\) $-$ \(q+(728-\beta _{1})q^{2}+(20803+14\beta _{1}+\beta _{3})q^{3}+\cdots\)
5.22.b.a $10$ $13.974$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(-25175970\) \(0\) $-$ \(q+\beta _{1}q^{2}+(-6\beta _{1}-\beta _{4})q^{3}+(-927372+\cdots)q^{4}+\cdots\)
5.23.c.a $20$ $15.335$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(-2050\) \(33900\) \(9244700\) \(1362465500\) $-$ \(q+(-102-\beta _{1}-103\beta _{4})q^{2}+(1697+\cdots)q^{3}+\cdots\)
5.24.a.a $3$ $16.760$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(666\) \(-139428\) \(146484375\) \(-2432683344\) $-$ \(q+(222+\beta _{1})q^{2}+(-46476+2^{6}\beta _{1}+\cdots)q^{3}+\cdots\)
5.24.a.b $4$ $16.760$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-780\) \(-206680\) \(-195312500\) \(-1010710600\) $+$ \(q+(-195-\beta _{1})q^{2}+(-51670-39\beta _{1}+\cdots)q^{3}+\cdots\)
5.24.b.a $10$ $16.760$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(124761750\) \(0\) $-$ \(q+\beta _{1}q^{2}+(18\beta _{1}-\beta _{3})q^{3}+(-4127268+\cdots)q^{4}+\cdots\)
5.25.c.a $22$ $18.248$ None \(-2\) \(-434562\) \(-413381810\) \(9255727198\) $-$
5.26.a.a $4$ $19.800$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(600\) \(-798600\) \(-976562500\) \(-48938107000\) $+$ \(q+(150-\beta _{1})q^{2}+(-199650+17\beta _{1}+\cdots)q^{3}+\cdots\)
5.26.a.b $5$ $19.800$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-4602\) \(626204\) \(1220703125\) \(55481235808\) $-$ \(q+(-920-\beta _{1})q^{2}+(125251-5^{2}\beta _{1}+\cdots)q^{3}+\cdots\)
5.26.b.a $12$ $19.800$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(549543060\) \(0\) $-$ \(q+\beta _{1}q^{2}+(-19\beta _{1}-\beta _{3})q^{3}+(-13890962+\cdots)q^{4}+\cdots\)
5.27.c.a $24$ $21.415$ None \(8190\) \(1867680\) \(-140947920\) \(-99234643200\) $-$
5.28.a.a $4$ $23.093$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-11550\) \(-2473800\) \(4882812500\) \(-215015185000\) $-$ \(q+(-2887+\beta _{1})q^{2}+(-618547-195\beta _{1}+\cdots)q^{3}+\cdots\)
5.28.a.b $5$ $23.093$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(19916\) \(4870682\) \(-6103515625\) \(155646348206\) $+$ \(q+(3983-\beta _{1})q^{2}+(974132-24\beta _{1}+\cdots)q^{3}+\cdots\)
5.28.b.a $12$ $23.093$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(-1634543100\) \(0\) $-$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(-65836838+\beta _{2}+\cdots)q^{4}+\cdots\)
5.29.c.a $26$ $24.834$ None \(-2\) \(-5427372\) \(2639800120\) \(523124011148\) $-$
5.30.a.a $4$ $26.639$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-15600\) \(2712600\) \(-24414062500\) \(11\!\cdots\!00\) $+$ \(q+(-3900+\beta _{1})q^{2}+(678150+50\beta _{1}+\cdots)q^{3}+\cdots\)
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