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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1875.1.c.a 1875.c 3.b $2$ $0.936$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(1\) \(q-q^{3}+q^{4}+(1-\beta )q^{7}+q^{9}-q^{12}+\cdots\)
1875.1.c.b 1875.c 3.b $2$ $0.936$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(-1\) \(q+q^{3}+q^{4}+(-1+\beta )q^{7}+q^{9}+q^{12}+\cdots\)
1875.1.d.a 1875.d 15.d $4$ $0.936$ \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}-q^{4}-\beta _{1}q^{7}-q^{9}-\beta _{3}q^{12}+\cdots\)
1875.1.h.a 1875.h 75.h $4$ $0.936$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-15}) \) None \(-3\) \(1\) \(0\) \(0\) \(q+(-1+\zeta_{10})q^{2}+\zeta_{10}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
1875.1.h.b 1875.h 75.h $4$ $0.936$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-15}) \) None \(-2\) \(-1\) \(0\) \(0\) \(q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}-\zeta_{10}q^{3}+(-\zeta_{10}+\cdots)q^{4}+\cdots\)
1875.1.h.c 1875.h 75.h $4$ $0.936$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-15}) \) None \(2\) \(1\) \(0\) \(0\) \(q+(-\zeta_{10}^{2}-\zeta_{10}^{4})q^{2}+\zeta_{10}q^{3}+(-\zeta_{10}+\cdots)q^{4}+\cdots\)
1875.1.h.d 1875.h 75.h $4$ $0.936$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-15}) \) None \(3\) \(-1\) \(0\) \(0\) \(q+(1-\zeta_{10})q^{2}-\zeta_{10}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
1875.1.h.e 1875.h 75.h $8$ $0.936$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}^{7}q^{3}+\zeta_{20}^{2}q^{4}+(\zeta_{20}+\zeta_{20}^{9}+\cdots)q^{7}+\cdots\)
1875.1.h.f 1875.h 75.h $8$ $0.936$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}^{7}q^{3}+\zeta_{20}^{2}q^{4}+(-\zeta_{20}^{3}-\zeta_{20}^{7}+\cdots)q^{7}+\cdots\)
1875.1.j.a 1875.j 75.j $4$ $0.936$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-2\) \(q+\zeta_{10}^{2}q^{3}+\zeta_{10}^{2}q^{4}+(-\zeta_{10}+\zeta_{10}^{4}+\cdots)q^{7}+\cdots\)
1875.1.j.b 1875.j 75.j $4$ $0.936$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-2\) \(q+\zeta_{10}^{2}q^{3}+\zeta_{10}^{2}q^{4}+(\zeta_{10}^{2}-\zeta_{10}^{3}+\cdots)q^{7}+\cdots\)
1875.1.j.c 1875.j 75.j $4$ $0.936$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(2\) \(q-\zeta_{10}^{2}q^{3}+\zeta_{10}^{2}q^{4}+(-\zeta_{10}^{2}+\zeta_{10}^{3}+\cdots)q^{7}+\cdots\)
1875.1.j.d 1875.j 75.j $4$ $0.936$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(2\) \(q-\zeta_{10}^{2}q^{3}+\zeta_{10}^{2}q^{4}+(\zeta_{10}-\zeta_{10}^{4}+\cdots)q^{7}+\cdots\)
1875.1.j.e 1875.j 75.j $8$ $0.936$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{20}^{5}+\zeta_{20}^{9})q^{2}-\zeta_{20}^{9}q^{3}+(-1+\cdots)q^{4}+\cdots\)
1875.1.j.f 1875.j 75.j $8$ $0.936$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{20}-\zeta_{20}^{3})q^{2}-\zeta_{20}^{9}q^{3}+(\zeta_{20}^{2}+\cdots)q^{4}+\cdots\)
1875.2.a.a 1875.a 1.a $2$ $14.972$ \(\Q(\sqrt{5}) \) None None \(-2\) \(-2\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}+(2-4\beta )q^{7}+\cdots\)
1875.2.a.b 1875.a 1.a $2$ $14.972$ \(\Q(\sqrt{5}) \) None None \(-1\) \(-2\) \(0\) \(4\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
1875.2.a.c 1875.a 1.a $2$ $14.972$ \(\Q(\sqrt{5}) \) None None \(1\) \(2\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
1875.2.a.d 1875.a 1.a $2$ $14.972$ \(\Q(\sqrt{5}) \) None None \(2\) \(2\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{6}+(-2+4\beta )q^{7}+\cdots\)
1875.2.a.e 1875.a 1.a $4$ $14.972$ 4.4.5125.1 None None \(-2\) \(-4\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
1875.2.a.f 1875.a 1.a $4$ $14.972$ \(\Q(\zeta_{15})^+\) None None \(-1\) \(4\) \(0\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q+(\beta _{2}+\beta _{3})q^{2}+q^{3}+\beta _{1}q^{4}+(\beta _{2}+\beta _{3})q^{6}+\cdots\)
1875.2.a.g 1875.a 1.a $4$ $14.972$ \(\Q(\zeta_{15})^+\) None None \(1\) \(-4\) \(0\) \(5\) $+$ $\mathrm{SU}(2)$ \(q+(-\beta _{2}-\beta _{3})q^{2}-q^{3}+\beta _{1}q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots\)
1875.2.a.h 1875.a 1.a $4$ $14.972$ 4.4.5125.1 None None \(2\) \(4\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
1875.2.a.i 1875.a 1.a $6$ $14.972$ 6.6.46840000.1 None None \(-1\) \(6\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
1875.2.a.j 1875.a 1.a $6$ $14.972$ 6.6.44400625.1 None None \(0\) \(-6\) \(0\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1-\beta _{3}+\beta _{4})q^{4}+\beta _{1}q^{6}+\cdots\)
1875.2.a.k 1875.a 1.a $6$ $14.972$ 6.6.44400625.1 None None \(0\) \(6\) \(0\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1-\beta _{3}+\beta _{4})q^{4}+\beta _{1}q^{6}+\cdots\)
1875.2.a.l 1875.a 1.a $6$ $14.972$ 6.6.46840000.1 None None \(1\) \(-6\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
1875.2.a.m 1875.a 1.a $8$ $14.972$ 8.8.5444000000.1 None None \(-4\) \(8\) \(0\) \(-8\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1875.2.a.n 1875.a 1.a $8$ $14.972$ 8.8.\(\cdots\).1 None None \(-1\) \(-8\) \(0\) \(-12\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{4}+\beta _{5})q^{4}+\beta _{1}q^{6}+\cdots\)
1875.2.a.o 1875.a 1.a $8$ $14.972$ 8.8.\(\cdots\).1 None None \(1\) \(8\) \(0\) \(12\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{4}+\beta _{5})q^{4}+\beta _{1}q^{6}+\cdots\)
1875.2.a.p 1875.a 1.a $8$ $14.972$ 8.8.5444000000.1 None None \(4\) \(-8\) \(0\) \(8\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
1875.2.b.a 1875.b 5.b $4$ $14.972$ \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}-\beta _{2}q^{6}+\cdots\)
1875.2.b.b 1875.b 5.b $4$ $14.972$ \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}-\beta _{3}q^{3}+q^{4}+q^{6}+(-4\beta _{1}+\cdots)q^{7}+\cdots\)
1875.2.b.c 1875.b 5.b $8$ $14.972$ 8.0.\(\cdots\).12 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(-2+\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots\)
1875.2.b.d 1875.b 5.b $8$ $14.972$ 8.0.324000000.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{3}-\beta _{7})q^{2}+\beta _{5}q^{3}-\beta _{4}q^{4}+\cdots\)
1875.2.b.e 1875.b 5.b $12$ $14.972$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(-2+\beta _{2})q^{4}+\beta _{11}q^{6}+\cdots\)
1875.2.b.f 1875.b 5.b $12$ $14.972$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{9}q^{3}+(-1+\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)
1875.2.b.g 1875.b 5.b $16$ $14.972$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+\beta _{2})q^{2}+\beta _{11}q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots\)
1875.2.b.h 1875.b 5.b $16$ $14.972$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}-\beta _{9})q^{2}-\beta _{9}q^{3}+(-1-\beta _{14}+\cdots)q^{4}+\cdots\)
1875.4.a.a 1875.a 1.a $10$ $110.629$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(-1\) \(-30\) \(0\) \(51\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
1875.4.a.b 1875.a 1.a $10$ $110.629$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(-1\) \(30\) \(0\) \(21\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+3q^{3}+(2+\beta _{2}-\beta _{3})q^{4}+\cdots\)
1875.4.a.c 1875.a 1.a $10$ $110.629$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(1\) \(-30\) \(0\) \(-21\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-3q^{3}+(2+\beta _{2}-\beta _{3})q^{4}+\cdots\)
1875.4.a.d 1875.a 1.a $10$ $110.629$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(1\) \(30\) \(0\) \(-51\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+3q^{3}+(4+\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
1875.4.a.e 1875.a 1.a $14$ $110.629$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(-8\) \(42\) \(0\) \(-29\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+3q^{3}+(4-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1875.4.a.f 1875.a 1.a $14$ $110.629$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(0\) \(-42\) \(0\) \(27\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+3\beta _{1}q^{6}+\cdots\)
1875.4.a.g 1875.a 1.a $14$ $110.629$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(0\) \(42\) \(0\) \(-27\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+3q^{3}+(4+\beta _{2})q^{4}+3\beta _{1}q^{6}+\cdots\)
1875.4.a.h 1875.a 1.a $14$ $110.629$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(8\) \(-42\) \(0\) \(29\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-3q^{3}+(4-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1875.4.a.i 1875.a 1.a $16$ $110.629$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-1\) \(48\) \(0\) \(-52\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+3q^{3}+(2+\beta _{2})q^{4}-3\beta _{1}q^{6}+\cdots\)
1875.4.a.j 1875.a 1.a $16$ $110.629$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(1\) \(-48\) \(0\) \(52\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-3q^{3}+(2+\beta _{2})q^{4}-3\beta _{1}q^{6}+\cdots\)
1875.4.a.k 1875.a 1.a $24$ $110.629$ None None \(-1\) \(-72\) \(0\) \(-62\) $+$ $\mathrm{SU}(2)$
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