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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1932.1.g.a 1932.g 483.c $1$ $0.964$ \(\Q\) \(\Q(\sqrt{-483}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q-q^{3}-q^{7}+q^{9}-q^{11}+q^{19}+q^{21}+\cdots\)
1932.1.g.b 1932.g 483.c $1$ $0.964$ \(\Q\) \(\Q(\sqrt{-483}) \) None \(0\) \(-1\) \(0\) \(1\) \(q-q^{3}+q^{7}+q^{9}+q^{11}-q^{19}-q^{21}+\cdots\)
1932.1.g.c 1932.g 483.c $1$ $0.964$ \(\Q\) \(\Q(\sqrt{-483}) \) None \(0\) \(1\) \(0\) \(-1\) \(q+q^{3}-q^{7}+q^{9}+q^{11}+q^{19}-q^{21}+\cdots\)
1932.1.g.d 1932.g 483.c $1$ $0.964$ \(\Q\) \(\Q(\sqrt{-483}) \) None \(0\) \(1\) \(0\) \(1\) \(q+q^{3}+q^{7}+q^{9}-q^{11}-q^{19}+q^{21}+\cdots\)
1932.1.w.a 1932.w 1932.w $2$ $0.964$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-69}) \) None \(-1\) \(-1\) \(-1\) \(1\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+\cdots\)
1932.1.w.b 1932.w 1932.w $2$ $0.964$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-69}) \) None \(-1\) \(-1\) \(1\) \(-1\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+\cdots\)
1932.1.w.c 1932.w 1932.w $2$ $0.964$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-69}) \) None \(1\) \(1\) \(-1\) \(-1\) \(q+\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+\cdots\)
1932.1.w.d 1932.w 1932.w $2$ $0.964$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-69}) \) None \(1\) \(1\) \(1\) \(1\) \(q+\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+\cdots\)
1932.1.w.e 1932.w 1932.w $4$ $0.964$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-69}) \) None \(-2\) \(2\) \(0\) \(0\) \(q+\zeta_{12}^{4}q^{2}+\zeta_{12}^{2}q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
1932.1.w.f 1932.w 1932.w $4$ $0.964$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-69}) \) None \(2\) \(-2\) \(0\) \(0\) \(q-\zeta_{12}^{4}q^{2}-\zeta_{12}^{2}q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
1932.1.bi.a 1932.bi 1932.ai $10$ $0.964$ \(\Q(\zeta_{22})\) \(\Q(\sqrt{-21}) \) None \(-1\) \(-1\) \(-2\) \(-1\) \(q-\zeta_{22}^{7}q^{2}-\zeta_{22}q^{3}-\zeta_{22}^{3}q^{4}+(-\zeta_{22}+\cdots)q^{5}+\cdots\)
1932.1.bi.b 1932.bi 1932.ai $10$ $0.964$ \(\Q(\zeta_{22})\) \(\Q(\sqrt{-21}) \) None \(-1\) \(1\) \(2\) \(1\) \(q-\zeta_{22}^{7}q^{2}+\zeta_{22}q^{3}-\zeta_{22}^{3}q^{4}+(\zeta_{22}+\cdots)q^{5}+\cdots\)
1932.1.bi.c 1932.bi 1932.ai $10$ $0.964$ \(\Q(\zeta_{22})\) \(\Q(\sqrt{-21}) \) None \(1\) \(-1\) \(2\) \(-1\) \(q+\zeta_{22}^{7}q^{2}-\zeta_{22}q^{3}-\zeta_{22}^{3}q^{4}+(\zeta_{22}+\cdots)q^{5}+\cdots\)
1932.1.bi.d 1932.bi 1932.ai $10$ $0.964$ \(\Q(\zeta_{22})\) \(\Q(\sqrt{-21}) \) None \(1\) \(1\) \(-2\) \(1\) \(q+\zeta_{22}^{7}q^{2}+\zeta_{22}q^{3}-\zeta_{22}^{3}q^{4}+(-\zeta_{22}+\cdots)q^{5}+\cdots\)
1932.2.a.a 1932.a 1.a $1$ $15.427$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{7}+q^{9}-5q^{11}-6q^{13}+\cdots\)
1932.2.a.b 1932.a 1.a $1$ $15.427$ \(\Q\) None None \(0\) \(1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{7}+q^{9}+3q^{11}+2q^{13}+\cdots\)
1932.2.a.c 1932.a 1.a $2$ $15.427$ \(\Q(\sqrt{13}) \) None None \(0\) \(-2\) \(-5\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(-2-\beta )q^{5}-q^{7}+q^{9}+(3+\cdots)q^{11}+\cdots\)
1932.2.a.d 1932.a 1.a $2$ $15.427$ \(\Q(\sqrt{5}) \) None None \(0\) \(-2\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}-q^{7}+q^{9}+(-1-2\beta )q^{11}+\cdots\)
1932.2.a.e 1932.a 1.a $2$ $15.427$ \(\Q(\sqrt{13}) \) None None \(0\) \(-2\) \(1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}+q^{7}+q^{9}+(1-2\beta )q^{11}+\cdots\)
1932.2.a.f 1932.a 1.a $2$ $15.427$ \(\Q(\sqrt{5}) \) None None \(0\) \(2\) \(-5\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-2-\beta )q^{5}+q^{7}+q^{9}-q^{11}+\cdots\)
1932.2.a.g 1932.a 1.a $2$ $15.427$ \(\Q(\sqrt{5}) \) None None \(0\) \(2\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta q^{5}-q^{7}+q^{9}-3q^{11}+(-1+\cdots)q^{13}+\cdots\)
1932.2.a.h 1932.a 1.a $2$ $15.427$ \(\Q(\sqrt{5}) \) None None \(0\) \(2\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1+3\beta )q^{5}+q^{7}+q^{9}+3q^{11}+\cdots\)
1932.2.a.i 1932.a 1.a $3$ $15.427$ 3.3.1509.1 None None \(0\) \(-3\) \(-1\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-\beta _{1}q^{5}+q^{7}+q^{9}+(1-2\beta _{1}+\cdots)q^{11}+\cdots\)
1932.2.a.j 1932.a 1.a $3$ $15.427$ 3.3.1101.1 None None \(0\) \(3\) \(1\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta _{1}q^{5}-q^{7}+q^{9}+q^{11}+(-1+\cdots)q^{13}+\cdots\)
1932.2.j.a 1932.j 21.c $4$ $15.427$ \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}+(-\beta _{1}+\beta _{3})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
1932.2.j.b 1932.j 21.c $56$ $15.427$ None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$
1932.2.k.a 1932.k 161.c $32$ $15.427$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1932.2.p.a 1932.p 69.c $48$ $15.427$ None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1932.2.q.a 1932.q 7.c $2$ $15.427$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-4\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-4\zeta_{6}q^{5}+(-2+3\zeta_{6})q^{7}+\cdots\)
1932.2.q.b 1932.q 7.c $2$ $15.427$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-2\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
1932.2.q.c 1932.q 7.c $2$ $15.427$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-2+3\zeta_{6})q^{7}+\cdots\)
1932.2.q.d 1932.q 7.c $2$ $15.427$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(1\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
1932.2.q.e 1932.q 7.c $4$ $15.427$ \(\Q(\sqrt{-3}, \sqrt{17})\) None None \(0\) \(2\) \(-1\) \(-10\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{2})q^{3}-\beta _{1}q^{5}+(-2-\beta _{2})q^{7}+\cdots\)
1932.2.q.f 1932.q 7.c $12$ $15.427$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(-6\) \(3\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{5}q^{3}+\beta _{1}q^{5}+(\beta _{8}+\beta _{11})q^{7}+(-1+\cdots)q^{9}+\cdots\)
1932.2.q.g 1932.q 7.c $16$ $15.427$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(8\) \(5\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{7}q^{3}+(1+\beta _{1}-\beta _{2}+\beta _{7})q^{5}+(-\beta _{12}+\cdots)q^{7}+\cdots\)
1932.2.q.h 1932.q 7.c $20$ $15.427$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(-10\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{7})q^{3}-\beta _{1}q^{5}+\beta _{16}q^{7}+\cdots\)
1932.2.u.a 1932.u 161.g $64$ $15.427$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
1932.3.d.a 1932.d 23.b $48$ $52.643$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1932.3.e.a 1932.e 3.b $88$ $52.643$ None None \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1932.3.f.a 1932.f 7.b $60$ $52.643$ None None \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{2}]$
1932.4.a.a 1932.a 1.a $1$ $113.992$ \(\Q\) None None \(0\) \(-3\) \(-19\) \(7\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-19q^{5}+7q^{7}+9q^{9}-8q^{11}+\cdots\)
1932.4.a.b 1932.a 1.a $1$ $113.992$ \(\Q\) None None \(0\) \(-3\) \(6\) \(7\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+6q^{5}+7q^{7}+9q^{9}+72q^{11}+\cdots\)
1932.4.a.c 1932.a 1.a $1$ $113.992$ \(\Q\) None None \(0\) \(3\) \(8\) \(7\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+8q^{5}+7q^{7}+9q^{9}+5^{2}q^{11}+\cdots\)
1932.4.a.d 1932.a 1.a $3$ $113.992$ 3.3.660841.1 None None \(0\) \(-9\) \(17\) \(21\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+(6+\beta _{2})q^{5}+7q^{7}+9q^{9}+\cdots\)
1932.4.a.e 1932.a 1.a $6$ $113.992$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(0\) \(-18\) \(-32\) \(42\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+(-5-\beta _{1})q^{5}+7q^{7}+9q^{9}+\cdots\)
1932.4.a.f 1932.a 1.a $6$ $113.992$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(0\) \(-18\) \(8\) \(42\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+(1+\beta _{1})q^{5}+7q^{7}+9q^{9}+\cdots\)
1932.4.a.g 1932.a 1.a $7$ $113.992$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(0\) \(21\) \(-23\) \(49\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+(-3-\beta _{1})q^{5}+7q^{7}+9q^{9}+\cdots\)
1932.4.a.h 1932.a 1.a $8$ $113.992$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(-24\) \(15\) \(-56\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+(2-\beta _{1})q^{5}-7q^{7}+9q^{9}+\cdots\)
1932.4.a.i 1932.a 1.a $8$ $113.992$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(24\) \(-15\) \(-56\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+(-2+\beta _{1})q^{5}-7q^{7}+9q^{9}+\cdots\)
1932.4.a.j 1932.a 1.a $9$ $113.992$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(0\) \(-27\) \(-15\) \(-63\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+(-2+\beta _{1})q^{5}-7q^{7}+9q^{9}+\cdots\)
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