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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
75.2.a.a 75.a 1.a $1$ $0.599$ \(\Q\) None \(-2\) \(1\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-2q^{6}+3q^{7}+\cdots\)
75.2.a.b 75.a 1.a $1$ $0.599$ \(\Q\) None \(1\) \(1\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{6}-3q^{8}+q^{9}+\cdots\)
75.2.a.c 75.a 1.a $1$ $0.599$ \(\Q\) None \(2\) \(-1\) \(0\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}-2q^{6}-3q^{7}+\cdots\)
75.2.b.a 75.b 5.b $2$ $0.599$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}+iq^{3}-2q^{4}-2q^{6}-3iq^{7}+\cdots\)
75.2.b.b 75.b 5.b $2$ $0.599$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}+q^{4}+q^{6}+3iq^{8}+\cdots\)
75.2.e.a 75.e 15.e $4$ $0.599$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{4}-3q^{6}-\beta _{3}q^{8}+\cdots\)
75.2.e.b 75.e 15.e $4$ $0.599$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+\beta _{1}q^{3}-2\beta _{2}q^{4}+\beta _{3}q^{7}+3\beta _{2}q^{9}+\cdots\)
75.2.g.a 75.g 25.d $4$ $0.599$ \(\Q(\zeta_{10})\) None \(-1\) \(-1\) \(5\) \(0\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
75.2.g.b 75.g 25.d $8$ $0.599$ 8.0.26265625.1 None \(-1\) \(-2\) \(-5\) \(4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{3}-\beta _{7})q^{2}+(-1+\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots\)
75.2.g.c 75.g 25.d $12$ $0.599$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(3\) \(-6\) \(-12\) $\mathrm{SU}(2)[C_{5}]$ \(q-\beta _{2}q^{2}+\beta _{8}q^{3}+(-1+\beta _{1}-\beta _{5}+\cdots)q^{4}+\cdots\)
75.2.i.a 75.i 25.e $16$ $0.599$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(-1-\beta _{2}-\beta _{4}+\beta _{6}-\beta _{7}-\beta _{8}+\cdots)q^{2}+\cdots\)
75.2.l.a 75.l 75.l $64$ $0.599$ None \(0\) \(-10\) \(0\) \(-20\) $\mathrm{SU}(2)[C_{20}]$
75.3.c.a 75.c 3.b $1$ $2.044$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(-3\) \(0\) \(11\) $\mathrm{U}(1)[D_{2}]$ \(q-3q^{3}+4q^{4}+11q^{7}+9q^{9}-12q^{12}+\cdots\)
75.3.c.b 75.c 3.b $1$ $2.044$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(3\) \(0\) \(-11\) $\mathrm{U}(1)[D_{2}]$ \(q+3q^{3}+4q^{4}-11q^{7}+9q^{9}+12q^{12}+\cdots\)
75.3.c.c 75.c 3.b $2$ $2.044$ \(\Q(\sqrt{-11}) \) None \(0\) \(-5\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-2\beta )q^{2}+(-2-\beta )q^{3}-7q^{4}+\cdots\)
75.3.c.d 75.c 3.b $2$ $2.044$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+iq^{2}+3iq^{3}+3q^{4}-3q^{6}+7iq^{8}+\cdots\)
75.3.c.e 75.c 3.b $2$ $2.044$ \(\Q(\sqrt{-5}) \) None \(0\) \(4\) \(0\) \(12\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+(2-\beta )q^{3}-q^{4}+(5+2\beta )q^{6}+\cdots\)
75.3.c.f 75.c 3.b $2$ $2.044$ \(\Q(\sqrt{-11}) \) None \(0\) \(5\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-2\beta )q^{2}+(3-\beta )q^{3}-7q^{4}+(-3+\cdots)q^{6}+\cdots\)
75.3.d.a 75.d 15.d $2$ $2.044$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+3iq^{3}-4q^{4}+11iq^{7}-9q^{9}-12iq^{12}+\cdots\)
75.3.d.b 75.d 15.d $4$ $2.044$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+(\beta _{1}-\beta _{3})q^{3}+q^{4}+(5-\beta _{2}+\cdots)q^{6}+\cdots\)
75.3.d.c 75.d 15.d $4$ $2.044$ \(\Q(i, \sqrt{11})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}+\beta _{2})q^{2}+\beta _{1}q^{3}+7q^{4}+(-6+\cdots)q^{6}+\cdots\)
75.3.f.a 75.f 5.c $4$ $2.044$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}-\beta _{2}q^{4}+3q^{6}+6\beta _{1}q^{7}+\cdots\)
75.3.f.b 75.f 5.c $4$ $2.044$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+2\beta _{1}q^{2}-\beta _{3}q^{3}+8\beta _{2}q^{4}+6q^{6}+\cdots\)
75.3.f.c 75.f 5.c $4$ $2.044$ \(\Q(i, \sqrt{6})\) None \(4\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\beta _{1}+\beta _{2})q^{2}+\beta _{3}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
75.3.h.a 75.h 75.h $72$ $2.044$ None \(0\) \(-5\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
75.3.j.a 75.j 75.j $72$ $2.044$ None \(0\) \(-1\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{10}]$
75.3.k.a 75.k 25.f $80$ $2.044$ None \(4\) \(0\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{20}]$
75.4.a.a 75.a 1.a $1$ $4.425$ \(\Q\) None \(-3\) \(3\) \(0\) \(-20\) $-$ $\mathrm{SU}(2)$ \(q-3q^{2}+3q^{3}+q^{4}-9q^{6}-20q^{7}+\cdots\)
75.4.a.b 75.a 1.a $1$ $4.425$ \(\Q\) None \(-1\) \(-3\) \(0\) \(24\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-3q^{3}-7q^{4}+3q^{6}+24q^{7}+\cdots\)
75.4.a.c 75.a 1.a $2$ $4.425$ \(\Q(\sqrt{41}) \) None \(-3\) \(-6\) \(0\) \(-6\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}-3q^{3}+(3+3\beta )q^{4}+\cdots\)
75.4.a.d 75.a 1.a $2$ $4.425$ \(\Q(\sqrt{19}) \) None \(-2\) \(6\) \(0\) \(26\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+3q^{3}+(12-2\beta )q^{4}+\cdots\)
75.4.a.e 75.a 1.a $2$ $4.425$ \(\Q(\sqrt{19}) \) None \(2\) \(-6\) \(0\) \(-26\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-3q^{3}+(12+2\beta )q^{4}+(-3+\cdots)q^{6}+\cdots\)
75.4.a.f 75.a 1.a $2$ $4.425$ \(\Q(\sqrt{41}) \) None \(3\) \(6\) \(0\) \(6\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+3q^{3}+(3+3\beta )q^{4}+(3+\cdots)q^{6}+\cdots\)
75.4.b.a 75.b 5.b $2$ $4.425$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{2}+3iq^{3}-q^{4}-9q^{6}+20iq^{7}+\cdots\)
75.4.b.b 75.b 5.b $2$ $4.425$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-3iq^{3}+7q^{4}+3q^{6}-24iq^{7}+\cdots\)
75.4.b.c 75.b 5.b $4$ $4.425$ \(\Q(i, \sqrt{19})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}+\beta _{3})q^{2}-3\beta _{1}q^{3}+(-12+\cdots)q^{4}+\cdots\)
75.4.e.a 75.e 15.e $4$ $4.425$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+\beta _{1}q^{3}-8\beta _{2}q^{4}-6\beta _{3}q^{7}+3^{3}\beta _{2}q^{9}+\cdots\)
75.4.e.b 75.e 15.e $4$ $4.425$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+19\beta _{2}q^{4}+3^{3}q^{6}+\cdots\)
75.4.e.c 75.e 15.e $8$ $4.425$ 8.0.\(\cdots\).8 None \(0\) \(6\) \(0\) \(16\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{3}q^{2}+(1+\beta _{2}-\beta _{5}+\beta _{6}-\beta _{7})q^{3}+\cdots\)
75.4.e.d 75.e 15.e $16$ $4.425$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{2}-\beta _{8}q^{3}+(6\beta _{1}+\beta _{5})q^{4}+(-6+\cdots)q^{6}+\cdots\)
75.4.g.a 75.g 25.d $28$ $4.425$ None \(-4\) \(21\) \(15\) \(58\) $\mathrm{SU}(2)[C_{5}]$
75.4.g.b 75.g 25.d $28$ $4.425$ None \(0\) \(-21\) \(-15\) \(-54\) $\mathrm{SU}(2)[C_{5}]$
75.4.i.a 75.i 25.e $64$ $4.425$ None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{10}]$
75.4.l.a 75.l 75.l $224$ $4.425$ None \(0\) \(-4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{20}]$
75.5.c.a 75.c 3.b $1$ $7.753$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(-9\) \(0\) \(-23\) $\mathrm{U}(1)[D_{2}]$ \(q-9q^{3}+2^{4}q^{4}-23q^{7}+3^{4}q^{9}-12^{2}q^{12}+\cdots\)
75.5.c.b 75.c 3.b $1$ $7.753$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(9\) \(0\) \(23\) $\mathrm{U}(1)[D_{2}]$ \(q+9q^{3}+2^{4}q^{4}+23q^{7}+3^{4}q^{9}+12^{2}q^{12}+\cdots\)
75.5.c.c 75.c 3.b $2$ $7.753$ \(\Q(\sqrt{-14}) \) None \(0\) \(-10\) \(0\) \(-150\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+(-5+2\beta )q^{3}+2q^{4}+(-28+\cdots)q^{6}+\cdots\)
75.5.c.d 75.c 3.b $2$ $7.753$ \(\Q(\sqrt{-35}) \) None \(0\) \(-3\) \(0\) \(144\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-2\beta )q^{2}+(-3+3\beta )q^{3}-19q^{4}+\cdots\)
75.5.c.e 75.c 3.b $2$ $7.753$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+7iq^{2}+9iq^{3}-33q^{4}-63q^{6}+\cdots\)
75.5.c.f 75.c 3.b $2$ $7.753$ \(\Q(\sqrt{-35}) \) None \(0\) \(3\) \(0\) \(-144\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-2\beta )q^{2}+3\beta q^{3}-19q^{4}+(54+\cdots)q^{6}+\cdots\)
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