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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
441.1.b.a 441.b 3.b $2$ $0.220$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{2}-q^{4}-\beta q^{11}-q^{16}-2q^{22}+\cdots\)
441.1.m.a 441.m 7.d $2$ $0.220$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{21}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{4}-\zeta_{6}q^{16}+\zeta_{6}^{2}q^{25}+\zeta_{6}q^{37}+\cdots\)
441.1.q.a 441.q 21.h $4$ $0.220$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{3})q^{11}+\cdots\)
441.1.v.a 441.v 49.f $6$ $0.220$ \(\Q(\zeta_{14})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q-\zeta_{14}^{4}q^{4}-\zeta_{14}^{2}q^{7}+(\zeta_{14}-\zeta_{14}^{3}+\cdots)q^{13}+\cdots\)
441.2.a.a 441.a 1.a $1$ $3.521$ \(\Q\) None None \(-2\) \(0\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-2q^{5}+4q^{10}+2q^{11}+\cdots\)
441.2.a.b 441.a 1.a $1$ $3.521$ \(\Q\) None None \(-2\) \(0\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+2q^{5}-4q^{10}+2q^{11}+\cdots\)
441.2.a.c 441.a 1.a $1$ $3.521$ \(\Q\) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(0\) $+$ $N(\mathrm{U}(1))$ \(q-q^{2}-q^{4}+3q^{8}-4q^{11}-q^{16}+\cdots\)
441.2.a.d 441.a 1.a $1$ $3.521$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $N(\mathrm{U}(1))$ \(q-2q^{4}-7q^{13}+4q^{16}-7q^{19}-5q^{25}+\cdots\)
441.2.a.e 441.a 1.a $1$ $3.521$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q-2q^{4}+7q^{13}+4q^{16}+7q^{19}-5q^{25}+\cdots\)
441.2.a.f 441.a 1.a $1$ $3.521$ \(\Q\) None None \(1\) \(0\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-2q^{5}-3q^{8}-2q^{10}+\cdots\)
441.2.a.g 441.a 1.a $2$ $3.521$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}+2\beta q^{5}-\beta q^{8}+6q^{10}+\cdots\)
441.2.a.h 441.a 1.a $2$ $3.521$ \(\Q(\sqrt{7}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q+\beta q^{2}+5q^{4}+3\beta q^{8}-2\beta q^{11}+11q^{16}+\cdots\)
441.2.a.i 441.a 1.a $2$ $3.521$ \(\Q(\sqrt{2}) \) None None \(2\) \(0\) \(-4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(-2+\beta )q^{5}+\cdots\)
441.2.a.j 441.a 1.a $2$ $3.521$ \(\Q(\sqrt{2}) \) None None \(2\) \(0\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(2-\beta )q^{5}+\cdots\)
441.2.c.a 441.c 21.c $4$ $3.521$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+\beta _{3}q^{5}-2\beta _{1}q^{8}-2\beta _{2}q^{10}+\cdots\)
441.2.c.b 441.c 21.c $8$ $3.521$ \(\Q(\zeta_{16})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{16}-\zeta_{16}^{2})q^{2}+(-1+2\zeta_{16}^{3}+\cdots)q^{4}+\cdots\)
441.2.e.a 441.e 7.c $2$ $3.521$ \(\Q(\sqrt{-3}) \) None None \(-1\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-2\zeta_{6}q^{5}-3q^{8}+\cdots\)
441.2.e.b 441.e 7.c $2$ $3.521$ \(\Q(\sqrt{-3}) \) None None \(-1\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+2\zeta_{6}q^{5}-3q^{8}+\cdots\)
441.2.e.c 441.e 7.c $2$ $3.521$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{3}]$ \(q+(2-2\zeta_{6})q^{4}+7q^{13}-4\zeta_{6}q^{16}+\cdots\)
441.2.e.d 441.e 7.c $2$ $3.521$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+3q^{8}+(4-4\zeta_{6})q^{11}+\cdots\)
441.2.e.e 441.e 7.c $2$ $3.521$ \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{4}+2\zeta_{6}q^{5}+\cdots\)
441.2.e.f 441.e 7.c $4$ $3.521$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(-2\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{2}+(-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
441.2.e.g 441.e 7.c $4$ $3.521$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(-2\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{2}+(-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
441.2.e.h 441.e 7.c $4$ $3.521$ \(\Q(\sqrt{-3}, \sqrt{7})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{3}]$ \(q+\beta _{1}q^{2}+5\beta _{2}q^{4}+3\beta _{3}q^{8}+(2\beta _{1}+\cdots)q^{11}+\cdots\)
441.2.e.i 441.e 7.c $4$ $3.521$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{12}^{2}q^{2}+(-1+\zeta_{12})q^{4}-2\zeta_{12}^{2}q^{5}+\cdots\)
441.2.e.j 441.e 7.c $4$ $3.521$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{12}^{2}q^{2}+(-1+\zeta_{12})q^{4}+2\zeta_{12}^{2}q^{5}+\cdots\)
441.2.f.a 441.f 9.c $2$ $3.521$ \(\Q(\sqrt{-3}) \) None None \(-1\) \(-3\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
441.2.f.b 441.f 9.c $2$ $3.521$ \(\Q(\sqrt{-3}) \) None None \(-1\) \(3\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
441.2.f.c 441.f 9.c $6$ $3.521$ \(\Q(\zeta_{18})\) None None \(-3\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{18}+\zeta_{18}^{5})q^{2}+(\zeta_{18}^{3}-\zeta_{18}^{5})q^{3}+\cdots\)
441.2.f.d 441.f 9.c $6$ $3.521$ 6.0.309123.1 None None \(1\) \(4\) \(-5\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}+(-\beta _{2}+\cdots)q^{3}+\cdots\)
441.2.f.e 441.f 9.c $10$ $3.521$ 10.0.\(\cdots\).1 None None \(2\) \(-1\) \(4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-1-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
441.2.f.f 441.f 9.c $10$ $3.521$ 10.0.\(\cdots\).1 None None \(2\) \(1\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-1-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
441.2.f.g 441.f 9.c $12$ $3.521$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{6})q^{2}+\beta _{10}q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
441.2.f.h 441.f 9.c $24$ $3.521$ None None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$
441.2.g.a 441.g 63.g $2$ $3.521$ \(\Q(\sqrt{-3}) \) None None \(-1\) \(3\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
441.2.g.b 441.g 63.g $6$ $3.521$ \(\Q(\zeta_{18})\) None None \(-3\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{18}+\zeta_{18}^{5})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{4}+\cdots)q^{3}+\cdots\)
441.2.g.c 441.g 63.g $6$ $3.521$ \(\Q(\zeta_{18})\) None None \(-3\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{18}+\zeta_{18}^{5})q^{2}+(-\zeta_{18}^{2}+\cdots)q^{3}+\cdots\)
441.2.g.d 441.g 63.g $6$ $3.521$ 6.0.309123.1 None None \(1\) \(-2\) \(10\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}+(-1+\cdots)q^{3}+\cdots\)
441.2.g.e 441.g 63.g $6$ $3.521$ 6.0.309123.1 None None \(1\) \(2\) \(-10\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}+(1-\beta _{1}+\cdots)q^{3}+\cdots\)
441.2.g.f 441.g 63.g $10$ $3.521$ 10.0.\(\cdots\).1 None None \(2\) \(-2\) \(8\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-\beta _{2}+\beta _{7})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
441.2.g.g 441.g 63.g $12$ $3.521$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{2}+\beta _{5})q^{2}+(-\beta _{8}-\beta _{10})q^{3}+\cdots\)
441.2.g.h 441.g 63.g $24$ $3.521$ None None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$
441.2.h.a 441.h 63.h $2$ $3.521$ \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(1-2\zeta_{6})q^{3}-q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
441.2.h.b 441.h 63.h $6$ $3.521$ 6.0.309123.1 None None \(-2\) \(-2\) \(-5\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{2}+\beta _{3})q^{2}+(-\beta _{1}-\beta _{2}+\beta _{5})q^{3}+\cdots\)
441.2.h.c 441.h 63.h $6$ $3.521$ 6.0.309123.1 None None \(-2\) \(2\) \(5\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{2}+\beta _{3})q^{2}+(\beta _{1}+\beta _{2}-\beta _{5})q^{3}+\cdots\)
441.2.h.d 441.h 63.h $6$ $3.521$ \(\Q(\zeta_{18})\) None None \(6\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{18}^{3}-\zeta_{18}^{4})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{5})q^{3}+\cdots\)
441.2.h.e 441.h 63.h $6$ $3.521$ \(\Q(\zeta_{18})\) None None \(6\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{18}^{3}-\zeta_{18}^{4})q^{2}+(-\zeta_{18}^{2}+\cdots)q^{3}+\cdots\)
441.2.h.f 441.h 63.h $10$ $3.521$ 10.0.\(\cdots\).1 None None \(-4\) \(1\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{5})q^{2}+\beta _{8}q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots\)
441.2.h.g 441.h 63.h $12$ $3.521$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+\beta _{10}q^{3}+(1+\beta _{2}+\beta _{4})q^{4}+\cdots\)
441.2.h.h 441.h 63.h $24$ $3.521$ None None \(-8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$
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