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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
121.2.a.a 121.a 1.a $1$ $0.966$ \(\Q\) None \(-1\) \(2\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}-q^{4}+q^{5}-2q^{6}+2q^{7}+\cdots\)
121.2.a.b 121.a 1.a $1$ $0.966$ \(\Q\) \(\Q(\sqrt{-11}) \) \(0\) \(-1\) \(-3\) \(0\) $+$ $N(\mathrm{U}(1))$ \(q-q^{3}-2q^{4}-3q^{5}-2q^{9}+2q^{12}+\cdots\)
121.2.a.c 121.a 1.a $1$ $0.966$ \(\Q\) None \(1\) \(2\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}-q^{4}+q^{5}+2q^{6}-2q^{7}+\cdots\)
121.2.a.d 121.a 1.a $1$ $0.966$ \(\Q\) None \(2\) \(-1\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}+q^{5}-2q^{6}+2q^{7}+\cdots\)
121.2.c.a 121.c 11.c $4$ $0.966$ \(\Q(\zeta_{10})\) None \(-2\) \(1\) \(-1\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-2+2\zeta_{10}-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots\)
121.2.c.b 121.c 11.c $4$ $0.966$ \(\Q(\zeta_{10})\) None \(-1\) \(-2\) \(-1\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
121.2.c.c 121.c 11.c $4$ $0.966$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-11}) \) \(0\) \(1\) \(3\) \(0\) $\mathrm{U}(1)[D_{5}]$ \(q-\zeta_{10}^{2}q^{3}+2\zeta_{10}^{3}q^{4}+3\zeta_{10}q^{5}+\cdots\)
121.2.c.d 121.c 11.c $4$ $0.966$ \(\Q(\zeta_{10})\) None \(1\) \(-2\) \(-1\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+2\zeta_{10}^{2}q^{3}+\cdots\)
121.2.c.e 121.c 11.c $4$ $0.966$ \(\Q(\zeta_{10})\) None \(2\) \(1\) \(-1\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(2-2\zeta_{10}+2\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}+\cdots\)
121.2.e.a 121.e 121.e $100$ $0.966$ None \(-6\) \(-18\) \(-7\) \(-1\) $\mathrm{SU}(2)[C_{11}]$
121.2.g.a 121.g 121.g $400$ $0.966$ None \(-44\) \(-32\) \(-43\) \(-44\) $\mathrm{SU}(2)[C_{55}]$
121.3.b.a 121.b 11.b $2$ $3.297$ \(\Q(\sqrt{-2}) \) None \(0\) \(-2\) \(-14\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-q^{3}+2q^{4}-7q^{5}-\beta q^{6}+\cdots\)
121.3.b.b 121.b 11.b $4$ $3.297$ \(\Q(\zeta_{10})\) None \(0\) \(10\) \(16\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{10}-\zeta_{10}^{3})q^{2}+(2-\zeta_{10}^{2})q^{3}+\cdots\)
121.3.b.c 121.b 11.b $8$ $3.297$ 8.0.\(\cdots\).1 None \(0\) \(-4\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{3}+\beta _{5})q^{3}+(-3+\cdots)q^{4}+\cdots\)
121.3.d.a 121.d 11.d $4$ $3.297$ \(\Q(\zeta_{10})\) None \(-5\) \(-5\) \(-4\) \(20\) $\mathrm{SU}(2)[C_{10}]$ \(q+(-2-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+(-3+\cdots)q^{3}+\cdots\)
121.3.d.b 121.d 11.d $4$ $3.297$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-11}) \) \(0\) \(5\) \(1\) \(0\) $\mathrm{U}(1)[D_{10}]$ \(q+(5-5\zeta_{10}+5\zeta_{10}^{2}-5\zeta_{10}^{3})q^{3}+\cdots\)
121.3.d.c 121.d 11.d $4$ $3.297$ \(\Q(\zeta_{10})\) None \(5\) \(-5\) \(-4\) \(-20\) $\mathrm{SU}(2)[C_{10}]$ \(q+(2+2\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-3+2\zeta_{10}+\cdots)q^{3}+\cdots\)
121.3.d.d 121.d 11.d $4$ $3.297$ \(\Q(\zeta_{10})\) None \(5\) \(0\) \(-4\) \(-10\) $\mathrm{SU}(2)[C_{10}]$ \(q+(2\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+(-2+\cdots)q^{3}+\cdots\)
121.3.d.e 121.d 11.d $8$ $3.297$ 8.0.64000000.1 None \(0\) \(2\) \(14\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+\beta _{1}q^{2}+(1-\beta _{2}+\beta _{4}-\beta _{6})q^{3}-2\beta _{2}q^{4}+\cdots\)
121.3.d.f 121.d 11.d $32$ $3.297$ None \(0\) \(4\) \(4\) \(0\) $\mathrm{SU}(2)[C_{10}]$
121.3.f.a 121.f 121.f $210$ $3.297$ None \(-11\) \(-16\) \(-7\) \(-11\) $\mathrm{SU}(2)[C_{22}]$
121.3.h.a 121.h 121.h $840$ $3.297$ None \(-39\) \(-34\) \(-43\) \(-54\) $\mathrm{SU}(2)[C_{110}]$
121.4.a.a 121.a 1.a $1$ $7.139$ \(\Q\) \(\Q(\sqrt{-11}) \) \(0\) \(8\) \(18\) \(0\) $+$ $N(\mathrm{U}(1))$ \(q+8q^{3}-8q^{4}+18q^{5}+37q^{9}-2^{6}q^{12}+\cdots\)
121.4.a.b 121.a 1.a $2$ $7.139$ \(\Q(\sqrt{3}) \) None \(-2\) \(-8\) \(-10\) \(-8\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(-4+\beta )q^{3}+(5-2\beta )q^{4}+\cdots\)
121.4.a.c 121.a 1.a $2$ $7.139$ \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(2\) \(-20\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(-1+4\beta )q^{3}+(-4+\cdots)q^{4}+\cdots\)
121.4.a.d 121.a 1.a $2$ $7.139$ \(\Q(\sqrt{26}) \) None \(0\) \(-10\) \(10\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-5q^{3}+18q^{4}+5q^{5}-5\beta q^{6}+\cdots\)
121.4.a.e 121.a 1.a $2$ $7.139$ \(\Q(\sqrt{3}) \) None \(2\) \(-8\) \(-10\) \(8\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(-4-\beta )q^{3}+(5+2\beta )q^{4}+\cdots\)
121.4.a.f 121.a 1.a $4$ $7.139$ \(\Q(\sqrt{5}, \sqrt{37})\) None \(-4\) \(6\) \(-11\) \(-25\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1}+\beta _{2})q^{2}+(1-\beta _{2})q^{3}+\cdots\)
121.4.a.g 121.a 1.a $4$ $7.139$ \(\Q(\sqrt{5}, \sqrt{37})\) None \(4\) \(6\) \(-11\) \(25\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1}+\beta _{2})q^{2}+(2+\beta _{2})q^{3}+(3+\cdots)q^{4}+\cdots\)
121.4.a.h 121.a 1.a $6$ $7.139$ 6.6.\(\cdots\).1 None \(0\) \(8\) \(14\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(3+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
121.4.c.a 121.c 11.c $4$ $7.139$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-11}) \) \(0\) \(-8\) \(-18\) \(0\) $\mathrm{U}(1)[D_{5}]$ \(q+8\zeta_{10}^{2}q^{3}+8\zeta_{10}^{3}q^{4}-18\zeta_{10}q^{5}+\cdots\)
121.4.c.b 121.c 11.c $8$ $7.139$ 8.0.\(\cdots\).1 None \(-3\) \(-3\) \(18\) \(-10\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{4}+\beta _{5}+\beta _{6})q^{2}+(\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
121.4.c.c 121.c 11.c $8$ $7.139$ 8.0.324000000.3 None \(-2\) \(2\) \(-2\) \(-20\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{2}+\beta _{7})q^{2}+(-4\beta _{1}-\beta _{6})q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
121.4.c.d 121.c 11.c $8$ $7.139$ 8.0.324000000.3 None \(-2\) \(8\) \(10\) \(-8\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{2}-\beta _{7})q^{2}+(\beta _{1}-4\beta _{6})q^{3}+(2\beta _{1}+\cdots)q^{4}+\cdots\)
121.4.c.e 121.c 11.c $8$ $7.139$ 8.0.\(\cdots\).7 None \(0\) \(10\) \(-10\) \(0\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{7}q^{2}-5\beta _{6}q^{3}+18\beta _{4}q^{4}+(-5+\cdots)q^{5}+\cdots\)
121.4.c.f 121.c 11.c $8$ $7.139$ 8.0.324000000.3 None \(2\) \(2\) \(-2\) \(20\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{2}+\beta _{7})q^{2}+(4\beta _{1}-\beta _{6})q^{3}+(2\beta _{1}+\cdots)q^{4}+\cdots\)
121.4.c.g 121.c 11.c $8$ $7.139$ 8.0.324000000.3 None \(2\) \(8\) \(10\) \(8\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{2}+\beta _{7})q^{2}+(\beta _{1}-4\beta _{6})q^{3}+(2\beta _{1}+\cdots)q^{4}+\cdots\)
121.4.c.h 121.c 11.c $8$ $7.139$ 8.0.\(\cdots\).1 None \(3\) \(-3\) \(18\) \(10\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1+2\beta _{4}+\beta _{6}-\beta _{7})q^{2}+(-\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
121.4.c.i 121.c 11.c $8$ $7.139$ 8.0.\(\cdots\).1 None \(7\) \(-3\) \(-7\) \(35\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\beta _{1}-\beta _{2}+\beta _{4})q^{2}+(-2-2\beta _{2}+\cdots)q^{3}+\cdots\)
121.4.c.j 121.c 11.c $24$ $7.139$ None \(0\) \(-8\) \(-14\) \(0\) $\mathrm{SU}(2)[C_{5}]$
121.4.e.a 121.e 121.e $320$ $7.139$ None \(-13\) \(-18\) \(-17\) \(-31\) $\mathrm{SU}(2)[C_{11}]$
121.4.g.a 121.g 121.g $1280$ $7.139$ None \(-37\) \(-32\) \(-33\) \(-9\) $\mathrm{SU}(2)[C_{55}]$
121.5.b.a 121.b 11.b $8$ $12.508$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(10\) \(-42\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(-12+\beta _{2}+\cdots)q^{4}+\cdots\)
121.5.b.b 121.b 11.b $12$ $12.508$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(-26\) \(-28\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(-2+\beta _{3})q^{3}+(-6+\beta _{7}+\cdots)q^{4}+\cdots\)
121.5.b.c 121.b 11.b $12$ $12.508$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(20\) \(60\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(2-\beta _{4})q^{3}+(-6+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
121.5.d.a 121.d 11.d $4$ $12.508$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-11}) \) \(0\) \(-7\) \(49\) \(0\) $\mathrm{U}(1)[D_{10}]$ \(q+(-7+7\zeta_{10}-7\zeta_{10}^{2}+7\zeta_{10}^{3})q^{3}+\cdots\)
121.5.d.b 121.d 11.d $8$ $12.508$ 8.0.5184000000.5 None \(0\) \(6\) \(-62\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(\beta _{4}+\beta _{5}+\beta _{6}+\beta _{7})q^{2}+3\beta _{1}q^{3}+\cdots\)
121.5.d.c 121.d 11.d $12$ $12.508$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-15\) \(19\) \(32\) \(200\) $\mathrm{SU}(2)[C_{10}]$ \(q+(-1+\beta _{1}+\beta _{3}-\beta _{6}-\beta _{7}+\beta _{8}+\cdots)q^{2}+\cdots\)
121.5.d.d 121.d 11.d $12$ $12.508$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(5\) \(-6\) \(-18\) \(80\) $\mathrm{SU}(2)[C_{10}]$ \(q+(1+\beta _{2}+2\beta _{3}+\beta _{4}-\beta _{7})q^{2}+(1+\cdots)q^{3}+\cdots\)
121.5.d.e 121.d 11.d $12$ $12.508$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(15\) \(19\) \(32\) \(-200\) $\mathrm{SU}(2)[C_{10}]$ \(q+(1-\beta _{1}-\beta _{3}+\beta _{6}+\beta _{7}-\beta _{8})q^{2}+\cdots\)
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