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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1.12.a.a 1.a 1.a $1$ $0.768$ \(\Q\) None \(-24\) \(252\) \(4830\) \(-16744\) $+$ $\mathrm{SU}(2)$ \(q-24q^{2}+252q^{3}-1472q^{4}+4830q^{5}+\cdots\)
3.12.a.a 3.a 1.a $1$ $2.305$ \(\Q\) None \(78\) \(-243\) \(-5370\) \(-27760\) $+$ $\mathrm{SU}(2)$ \(q+78q^{2}-3^{5}q^{3}+4036q^{4}-5370q^{5}+\cdots\)
4.12.a.a 4.a 1.a $1$ $3.073$ \(\Q\) None \(0\) \(-516\) \(-10530\) \(49304\) $-$ $\mathrm{SU}(2)$ \(q-516q^{3}-10530q^{5}+49304q^{7}+\cdots\)
5.12.a.a 5.a 1.a $1$ $3.842$ \(\Q\) None \(34\) \(-792\) \(3125\) \(-17556\) $-$ $\mathrm{SU}(2)$ \(q+34q^{2}-792q^{3}-892q^{4}+5^{5}q^{5}+\cdots\)
5.12.a.b 5.a 1.a $2$ $3.842$ \(\Q(\sqrt{151}) \) None \(-20\) \(-220\) \(-6250\) \(57900\) $+$ $\mathrm{SU}(2)$ \(q+(-10+3\beta )q^{2}+(-110+2^{4}\beta )q^{3}+\cdots\)
5.12.b.a 5.b 5.b $4$ $3.842$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(0\) \(-300\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-18-\beta _{2})q^{4}+\cdots\)
6.12.a.a 6.a 1.a $1$ $4.610$ \(\Q\) None \(-32\) \(-243\) \(5766\) \(72464\) $+$ $\mathrm{SU}(2)$ \(q-2^{5}q^{2}-3^{5}q^{3}+2^{10}q^{4}+5766q^{5}+\cdots\)
6.12.a.b 6.a 1.a $1$ $4.610$ \(\Q\) None \(-32\) \(243\) \(-11730\) \(-50008\) $-$ $\mathrm{SU}(2)$ \(q-2^{5}q^{2}+3^{5}q^{3}+2^{10}q^{4}-11730q^{5}+\cdots\)
6.12.a.c 6.a 1.a $1$ $4.610$ \(\Q\) None \(32\) \(243\) \(3630\) \(32936\) $+$ $\mathrm{SU}(2)$ \(q+2^{5}q^{2}+3^{5}q^{3}+2^{10}q^{4}+3630q^{5}+\cdots\)
7.12.a.a 7.a 1.a $2$ $5.378$ \(\Q(\sqrt{3369}) \) None \(-54\) \(120\) \(-13500\) \(33614\) $-$ $\mathrm{SU}(2)$ \(q+(-3^{3}-\beta )q^{2}+(60+6\beta )q^{3}+(2050+\cdots)q^{4}+\cdots\)
7.12.a.b 7.a 1.a $3$ $5.378$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(77\) \(-140\) \(5026\) \(-50421\) $+$ $\mathrm{SU}(2)$ \(q+(26+\beta _{2})q^{2}+(-47-11\beta _{1}+10\beta _{2})q^{3}+\cdots\)
7.12.c.a 7.c 7.c $12$ $5.378$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(22\) \(-244\) \(-8782\) \(-504\) $\mathrm{SU}(2)[C_{3}]$ \(q+(4-\beta _{1}-4\beta _{2})q^{2}+(\beta _{1}-40\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots\)
8.12.a.a 8.a 1.a $1$ $6.147$ \(\Q\) None \(0\) \(-36\) \(-3490\) \(-55464\) $-$ $\mathrm{SU}(2)$ \(q-6^{2}q^{3}-3490q^{5}-55464q^{7}-175851q^{9}+\cdots\)
8.12.a.b 8.a 1.a $2$ $6.147$ \(\Q(\sqrt{109}) \) None \(0\) \(56\) \(7868\) \(91056\) $+$ $\mathrm{SU}(2)$ \(q+(28+\beta )q^{3}+(3934-12\beta )q^{5}+(45528+\cdots)q^{7}+\cdots\)
8.12.b.a 8.b 8.b $10$ $6.147$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(22\) \(0\) \(0\) \(-33616\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2+\beta _{1})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(43+2\beta _{1}+\cdots)q^{4}+\cdots\)
9.12.a.a 9.a 1.a $1$ $6.915$ \(\Q\) None \(-78\) \(0\) \(5370\) \(-27760\) $-$ $\mathrm{SU}(2)$ \(q-78q^{2}+4036q^{4}+5370q^{5}-27760q^{7}+\cdots\)
9.12.a.b 9.a 1.a $1$ $6.915$ \(\Q\) None \(24\) \(0\) \(-4830\) \(-16744\) $-$ $\mathrm{SU}(2)$ \(q+24q^{2}-1472q^{4}-4830q^{5}-16744q^{7}+\cdots\)
9.12.a.c 9.a 1.a $2$ $6.915$ \(\Q(\sqrt{70}) \) None \(0\) \(0\) \(0\) \(116200\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+472q^{4}+224\beta q^{5}+58100q^{7}+\cdots\)
9.12.c.a 9.c 9.c $20$ $6.915$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(-33\) \(-12\) \(-7230\) \(8512\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-3\beta _{3})q^{2}+(24-51\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots\)
10.12.a.a 10.a 1.a $1$ $7.683$ \(\Q\) None \(-32\) \(-12\) \(3125\) \(-14176\) $-$ $\mathrm{SU}(2)$ \(q-2^{5}q^{2}-12q^{3}+2^{10}q^{4}+5^{5}q^{5}+\cdots\)
10.12.a.b 10.a 1.a $1$ $7.683$ \(\Q\) None \(-32\) \(738\) \(-3125\) \(25574\) $+$ $\mathrm{SU}(2)$ \(q-2^{5}q^{2}+738q^{3}+2^{10}q^{4}-5^{5}q^{5}+\cdots\)
10.12.a.c 10.a 1.a $1$ $7.683$ \(\Q\) None \(32\) \(-318\) \(-3125\) \(-70714\) $-$ $\mathrm{SU}(2)$ \(q+2^{5}q^{2}-318q^{3}+2^{10}q^{4}-5^{5}q^{5}+\cdots\)
10.12.a.d 10.a 1.a $2$ $7.683$ \(\Q(\sqrt{1969}) \) None \(64\) \(604\) \(6250\) \(14092\) $+$ $\mathrm{SU}(2)$ \(q+2^{5}q^{2}+(302-\beta )q^{3}+2^{10}q^{4}+5^{5}q^{5}+\cdots\)
10.12.b.a 10.b 5.b $6$ $7.683$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(0\) \(530\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(\beta _{1}+3\beta _{2})q^{3}-2^{10}q^{4}+\cdots\)
11.12.a.a 11.a 1.a $3$ $8.452$ 3.3.202533.1 None \(0\) \(-393\) \(-7305\) \(-5082\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-131-2\beta _{1}-4\beta _{2})q^{3}+\cdots\)
11.12.a.b 11.a 1.a $5$ $8.452$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(32\) \(160\) \(-8398\) \(79040\) $+$ $\mathrm{SU}(2)$ \(q+(6+\beta _{1})q^{2}+(2^{5}-\beta _{3})q^{3}+(1239+\cdots)q^{4}+\cdots\)
11.12.c.a 11.c 11.c $40$ $8.452$ None \(11\) \(-276\) \(6038\) \(55440\) $\mathrm{SU}(2)[C_{5}]$
12.12.a.a 12.a 1.a $1$ $9.220$ \(\Q\) None \(0\) \(-243\) \(9990\) \(-86128\) $-$ $\mathrm{SU}(2)$ \(q-3^{5}q^{3}+9990q^{5}-86128q^{7}+3^{10}q^{9}+\cdots\)
12.12.a.b 12.a 1.a $1$ $9.220$ \(\Q\) None \(0\) \(243\) \(2862\) \(9128\) $+$ $\mathrm{SU}(2)$ \(q+3^{5}q^{3}+2862q^{5}+9128q^{7}+3^{10}q^{9}+\cdots\)
12.12.b.a 12.b 12.b $20$ $9.220$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(99+\beta _{2})q^{4}+(-5\beta _{1}+\cdots)q^{5}+\cdots\)
13.12.a.a 13.a 1.a $5$ $9.988$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-41\) \(-496\) \(-2542\) \(-36296\) $-$ $\mathrm{SU}(2)$ \(q+(-8-\beta _{1})q^{2}+(-99-2\beta _{1}-\beta _{4})q^{3}+\cdots\)
13.12.a.b 13.a 1.a $6$ $9.988$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(55\) \(476\) \(3312\) \(-4176\) $+$ $\mathrm{SU}(2)$ \(q+(9+\beta _{1})q^{2}+(80-2\beta _{1}+\beta _{4})q^{3}+\cdots\)
13.12.b.a 13.b 13.b $12$ $9.988$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(-488\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-41-\beta _{2})q^{3}+(-2^{10}+\cdots)q^{4}+\cdots\)
13.12.c.a 13.c 13.c $24$ $9.988$ None \(31\) \(-244\) \(-10436\) \(-2928\) $\mathrm{SU}(2)[C_{3}]$
13.12.e.a 13.e 13.e $22$ $9.988$ None \(-3\) \(242\) \(0\) \(128496\) $\mathrm{SU}(2)[C_{6}]$
14.12.a.a 14.a 1.a $1$ $10.757$ \(\Q\) None \(-32\) \(-396\) \(7350\) \(16807\) $-$ $\mathrm{SU}(2)$ \(q-2^{5}q^{2}-396q^{3}+2^{10}q^{4}+7350q^{5}+\cdots\)
14.12.a.b 14.a 1.a $1$ $10.757$ \(\Q\) None \(32\) \(-90\) \(-7480\) \(-16807\) $-$ $\mathrm{SU}(2)$ \(q+2^{5}q^{2}-90q^{3}+2^{10}q^{4}-7480q^{5}+\cdots\)
14.12.a.c 14.a 1.a $2$ $10.757$ \(\Q(\sqrt{153169}) \) None \(-64\) \(350\) \(266\) \(-33614\) $+$ $\mathrm{SU}(2)$ \(q-2^{5}q^{2}+(175-\beta )q^{3}+2^{10}q^{4}+(133+\cdots)q^{5}+\cdots\)
14.12.a.d 14.a 1.a $2$ $10.757$ \(\Q(\sqrt{352969}) \) None \(64\) \(-350\) \(3738\) \(33614\) $+$ $\mathrm{SU}(2)$ \(q+2^{5}q^{2}+(-175-\beta )q^{3}+2^{10}q^{4}+\cdots\)
14.12.c.a 14.c 7.c $8$ $10.757$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-128\) \(266\) \(7504\) \(-42224\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2^{5}+2^{5}\beta _{2})q^{2}+(67\beta _{2}-\beta _{3})q^{3}+\cdots\)
14.12.c.b 14.c 7.c $8$ $10.757$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(128\) \(-266\) \(3808\) \(110328\) $\mathrm{SU}(2)[C_{3}]$ \(q+2^{5}\beta _{2}q^{2}+(-67+\beta _{1}+67\beta _{2})q^{3}+\cdots\)
15.12.a.a 15.a 1.a $1$ $11.525$ \(\Q\) None \(-56\) \(-243\) \(3125\) \(27984\) $-$ $\mathrm{SU}(2)$ \(q-56q^{2}-3^{5}q^{3}+1088q^{4}+5^{5}q^{5}+\cdots\)
15.12.a.b 15.a 1.a $2$ $11.525$ \(\Q(\sqrt{1609}) \) None \(-22\) \(486\) \(-6250\) \(-10864\) $-$ $\mathrm{SU}(2)$ \(q+(-11-\beta )q^{2}+3^{5}q^{3}+(-318+22\beta )q^{4}+\cdots\)
15.12.a.c 15.a 1.a $2$ $11.525$ \(\Q(\sqrt{1801}) \) None \(-13\) \(-486\) \(-6250\) \(7784\) $+$ $\mathrm{SU}(2)$ \(q+(-6-\beta )q^{2}-3^{5}q^{3}+(-1562+13\beta )q^{4}+\cdots\)
15.12.a.d 15.a 1.a $3$ $11.525$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-1\) \(729\) \(9375\) \(-14608\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+3^{5}q^{3}+(1585+3\beta _{1}+\beta _{2})q^{4}+\cdots\)
15.12.b.a 15.b 5.b $12$ $11.525$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(2556\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}-\beta _{4}q^{3}+(-1359+\beta _{1})q^{4}+\cdots\)
15.12.e.a 15.e 15.e $40$ $11.525$ None \(0\) \(504\) \(0\) \(31504\) $\mathrm{SU}(2)[C_{4}]$
16.12.a.a 16.a 1.a $1$ $12.293$ \(\Q\) None \(0\) \(-252\) \(4830\) \(16744\) $-$ $\mathrm{SU}(2)$ \(q-252q^{3}+4830q^{5}+16744q^{7}+\cdots\)
16.12.a.b 16.a 1.a $1$ $12.293$ \(\Q\) None \(0\) \(36\) \(-3490\) \(55464\) $+$ $\mathrm{SU}(2)$ \(q+6^{2}q^{3}-3490q^{5}+55464q^{7}-175851q^{9}+\cdots\)
16.12.a.c 16.a 1.a $1$ $12.293$ \(\Q\) None \(0\) \(516\) \(-10530\) \(-49304\) $-$ $\mathrm{SU}(2)$ \(q+516q^{3}-10530q^{5}-49304q^{7}+\cdots\)
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